HeliusMCT-UsersGuide-Abaqus

User’s Guide Helius:MCT™ Version 4.0 for ABAQUS February 1, 2011

Abstract This document describes the use of Helius:MCT for Abaqus/Standard in performing enhanced finite element analysis of composite structures. For questions, comments or further information, contact Firehole Composites at [email protected].

Legal Notices Copyright 2011, Firehole Technologies, Inc. Helius:MCT is a trademark of Firehole Technologies, Inc. Any use of the Helius:MCT trademark requires the prior written consent of Firehole Technologies, Inc. Abaqus/Standard is a trademark of Dassault Systemes S.A. and Dassault Systemes SIMULIA Corp.

Table of Contents 1

INTRODUCTION TO HELIUS:MCT ................................................................................................... 5 1.1 1.2 1.3

2

GENERAL REQUIREMENTS FOR ABAQUS INPUT FILES .......................................................... 10 2.1 2.2 2.3 2.4

3

IDENTIFICATION AND DEFINITION OF HELIUS:MCT MATERIALS ....................................................... 10 DEFINITION OF EXTRANEOUS STIFFNESS PARAMETERS FOR CERTAIN TYPES OF ELEMENTS ............ 11 NONLINEAR SOLUTION CONTROL PARAMETERS FOR HELIUS:MCT ................................................ 11 REQUESTING OUTPUT OF SOLUTION VARIABLES THAT ARE UNIQUE TO HELIUS:MCT ...................... 12

USING ABAQUS/CAE TO CREATE ABAQUS INPUT FILES FOR USE WITH HELIUS:MCT ...... 13 3.1 3.2 3.3 3.4 3.5 3.6 3.7

4

A NOTE ON THE HELIUS:MCT- LINEAR VERSION ............................................................................ 5 HELIUS:MCT INTERACTION WITH ABAQUS/STANDARD .................................................................... 6 HELIUS:MCT SUPPORT DOCUMENTATION ..................................................................................... 8

CREATING COMPOSITE MATERIALS WITH THE HELIUS:MCT PLY GUI ............................................. 13 CREATING COHESIVE MATERIALS WITH THE HELIUS:MCT COHESIVE GUI...................................... 22 SPECIFYING EXTRANEOUS STIFFNESS PARAMETERS REQUIRED BY CERTAIN ELEMENT TYPES ........ 25 STEP MODIFICATIONS ................................................................................................................. 26 REQUESTING MCT STATE VARIABLE OUTPUT FOR COMPOSITE MATERIALS ................................... 28 REQUESTING MCT STATE VARIABLE OUTPUT FOR COHESIVE MATERIALS ..................................... 30 DELETING A HELIUS:MCT MATERIAL ........................................................................................... 30

USING A TEXT EDITOR TO CONVERT PRE-EXISTING ABAQUS INPUT FILES FOR USE WITH HELIUS:MCT .................................................................................................................................. 31 4.1 4.2 4.3 4.4 4.5 4.6 4.7

DEFINING A HELIUS:MCT COMPOSITE MATERIAL ......................................................................... 31 DEFINING A HELIUS:MCT COHESIVE MATERIAL ............................................................................ 38 MODIFYING THE SECTION DEFINITIONS ........................................................................................ 39 MODELING ISSUES FOR IMPOSING TEMPERATURE CHANGES ......................................................... 41 NONLINEAR SOLUTION CONTROL PARAMETERS FOR HELIUS:MCT ................................................ 41 REQUESTING OUTPUT OF THE MCT STATE VARIABLES ................................................................. 42 MODELING DAMAGE TOLERANCE IN COMPOSITE MATERIALS ......................................................... 43

5

RUNNING HELIUS:MCT ON LINUX................................................................................................ 45

6

EXAMINING HELIUS:MCT RESULTS WITH ABAQUS/VIEWER ................................................... 46 6.1 6.2

USING CONTOUR PLOTS TO VIEW THE MCT STATE VARIABLES ....................................................... 46 DETECTION OF GLOBAL STRUCTURAL FAILURE .............................................................................. 51

APPENDIX A APPENDIX A.1 APPENDIX A.2 APPENDIX A.3 APPENDIX A.4 APPENDIX A.5 APPENDIX A.6 APPENDIX A.7 APPENDIX A.10 APPENDIX A.11 APPENDIX A.12 APPENDIX A.13 APPENDIX B

USER MATERIAL CONSTANTS FOR COMPOSITE MATERIALS .......................... 55 USER MATERIAL CONSTANT #1: SYSTEMS OF UNITS ................................................... 56 USER MATERIAL CONSTANT #2: PRINCIPAL MATERIAL COORDINATE SYSTEM ............... 58 USER MATERIAL CONSTANT #3: PROGRESSIVE FAILURE ANALYSIS .............................. 61 USER MATERIAL CONSTANT #4: PRE-FAILURE NONLINEARITY ..................................... 63 USER MATERIAL CONSTANT #5: POST-FAILURE NONLINEARITY AND ENERGY-BASED DEGRADATION........................................................................................................... 64 USER MATERIAL CONSTANT #6: HYDROSTATIC STRENGTHENING................................. 70 USER MATERIAL CONSTANT #7: THERMAL RESIDUAL STRESSES ................................. 71 USER MATERIAL CONSTANT #10: NOT CURRENTLY USED ........................................... 73 USER MATERIAL CONSTANT #11: AVERAGE ELEMENT THICKNESS ............................... 73 USER MATERIAL CONSTANT #12: MATRIX POST-FAILURE STIFFNESS / MATRIX DEGRADATION ENERGY ............................................................................................... 1 USER MATERIAL CONSTANT #13: FIBER POST-FAILURE STIFFNESS / FIBER DEGRADATION ENERGY ..................................................................................................................... 3 USER MATERIAL CONSTANTS FOR COHESIVE MATERIALS ............................... 5

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APPENDIX B.1 APPENDIX B.2 APPENDIX B.3 APPENDIX B.4 APPENDIX C APPENDIX C.1 APPENDIX C.2 APPENDIX C.3 APPENDIX C.4

USER MATERIAL CONSTANT #1: DAMAGE CRITERIA ...................................................... 5 USER MATERIAL CONSTANTS #2-4: MATERIAL STIFFNESS............................................. 6 USER MATERIAL CONSTANTS #5-7: DAMAGE INITIATION ................................................ 6 USER MATERIAL CONSTANTS #8-11: DAMAGE EVOLUTION ............................................ 7 EXTRANEOUS STIFFNESS PARAMETERS ............................................................ 10 DESCRIPTION OF THE EXTRANEOUS STIFFNESS PARAMETERS ...................................... 11 FORMATTING OF THE EXTRANEOUS STIFFNESS PARAMETERS....................................... 13 CALCULATION OF EXTRANEOUS STIFFNESS PARAMETERS ............................................ 16 USING ABAQUS/CAE TO INSERT THE EXTRANEOUS STIFFNESS PARAMETERS................ 24

APPENDIX D

MCT STATE VARIABLES FOR COMPOSITE MATERIALS .................................... 27

APPENDIX E

MCT STATE VARIABLES FOR COHESIVE MATERIALS ....................................... 36

APPENDIX F

TROUBLESHOOTING ............................................................................................... 37

APPENDIX F.1 APPENDIX F.2

MANUAL RESOLUTION OF KEYWORD CONFLICTS PRODUCED BY ABAQUS/CAE .............. 37 SYSTEM ERROR CODES ............................................................................................. 39

Table of Figures FIGURE 1: SCHEMATIC DIAGRAM OF THE INDIVIDUAL COMPONENTS OF THE HELIUS:MCT SOFTWARE AND THEIR INTERACTION WITH THE ABAQUS/STANDARD SOFTWARE COMPONENTS ...................... 7 FIGURE 2: THE HELIUS:MCT PLY GRAPHICAL USER INTERFACE (GUI) .............................................. 14 FIGURE 3: KEYWORDS EDITOR SHOWING THE KEYWORD STATEMENTS THAT COLLECTIVELY DEFINE A HELIUS:MCT MATERIAL................................................................................................................... 22 FIGURE 4: HELIUS:MCT COHESIVE GUI IN ABAQUS/CAE..................................................................... 23 FIGURE 5: LOCATION OF INCREMENTATION PARAMETERS IN THE EDIT STEP DIALOG BOX.................. 27 FIGURE 6: GENERAL SOLUTION CONTROLS EDITOR DIALOG BOX ........................................................ 28 FIGURE 7: LOCATIONS OF SDV AND SECTION POINT OUTPUT PARAMETERS IN THE EDIT FIELD OUTPUT REQUEST DIALOG BOX ...................................................................................................... 29 FIGURE 8: KEYWORDS CONFLICT DIALOG BOX ...................................................................................... 30 FIGURE 9: LOCATION OF SECTION POINTS WITHIN AN ELEMENT CONTAINING 4 MATERIAL PLIES ........ 43 FIGURE 10: CONTOUR PLOT OPTIONS DIALOG BOX ............................................................................... 47 FIGURE 11: COMPARISON OF A BANDED CONTOUR PLOT AND A QUILT CONTOUR PLOT USING THREE DISCRETE COLOR CONTOURS TO REPRESENT DISTRIBUTION OF SDV1=1,2,3 ............................ 48 FIGURE 12: SECTION POINTS DIALOG BOX ............................................................................................ 49 FIGURE 13: ENVELOPE, QUILTED CONTOUR PLOTS OF SDV1 AT SEVERAL DIFFERENT POINTS IN TIME DURING A PROGRESSIVE FAILURE ANALYSIS .................................................................................. 50 FIGURE 14: 8-PLY COMPOSITE PLATE UNDER IMPOSED AXIAL DISPLACEMENT .................................... 52 FIGURE 15: THE GLOBAL STRUCTURAL FORCE IS OBTAINED BY SUMMING THE VERTICAL REACTIONS FORCES AT ALL NODES ALONG THE TOP EDGE OF THE COMPOSITE PLATE ................................... 52 FIGURE 16: GLOBAL STRUCTURAL FORCE VS. GLOBAL STRUCTURAL DEFORMATION .......................... 53 FIGURE A17. THE FIBER DIRECTION FOR EACH ELEMENT IS INDICATED BY THE RED LINES................. 59 FIGURE A18: HELIUS:MCT SOLUTION FOR FAILURE PROPAGATION IN THE 0° PLIES OF A COMPOSITE LAMINATE LOADED IN TENSION ........................................................................................................ 62 FIGURE A19: COMPARISON OF PREDICTED VS. MEASURED LONGITUDINAL SHEAR RESPONSE FOR A TYPICAL FIBER-REINFORCED COMPOSITE LAMINA. ......................................................................... 63

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FIGURE A20: HELIUS:MCT STRESS-STRAIN SOLUTIONS FOR THE CENTRAL 90° PLY WITHIN A (0/90/0) LAMINATE UNDER AXIAL TENSION, SHOWING THE EFFECT OF INCLUDING THE POST-FAILURE NONLINEARITY FEATURE .................................................................................................................. 65 FIGURE A21: STRESS/STRAIN RESPONSE FOR A LINEAR DEGRADATION USING ENERGY-BASED DEGRADATION. ................................................................................................................................. 66 FIGURE A22 ENERGY-BASED LINEAR DEGRADATION INTERVAL PARTITIONING. ................................... 68 FIGURE A23 LINEAR DEGRADATION FOR LARGE ENERGY PROBLEM USING SECANT MODULUS INTERVAL DIVISIONS. ....................................................................................................................... 69 FIGURE B24. TYPICAL COHESIVE MATERIAL TRACTION-DISPLACEMENT CURVE. ................................... 8 FIGURE B25. COHESIVE MATERIAL RESPONSE........................................................................................ 9 FIGURE C26: HELIUS:MCT GUI WITH IM7_8552 SELECTED AS A MATERIAL ...................................... 18 FIGURE C27: ABAQUS COMMAND WINDOW FROM WHICH TO RUN THE DATACHECK ANALYSIS ........... 19 FIGURE C28: SEQUENCE OF COMMANDS TO RUN A DATACHECK ANALYSIS ......................................... 20 FIGURE C29: LOCATIONS OF SECTION POISSON’S RATIO, THICKNESS MODULUS, AND TRANSVERSE SHEAR STIFFNESS SETTINGS IN THE EDIT COMPOSITE LAYUP DIALOG BOX ................................ 24 FIGURE C30: LOCATIONS OF HOURGLASS STIFFNESS SETTINGS IN THE ELEMENT TYPE DIALOG BOX 25 FIGURE C31: LOCATION OF HOURGLASS STIFFNESS PARAMETERS IN THE KEYWORDS EDITOR ......... 26 FIGURE F32. THE PROCESS OF ACCESSING THE KEYWORD EDITOR IN ABAQUS/CAE ...................... 38 FIGURE F33: KEYWORDS EDITOR, SHOWING A KEYWORD CONFLICT CAUSED BY AN EXTRANEOUS *DEPVAR STATEMENT ................................................................................................................... 39

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1 Introduction to Helius:MCT Helius:MCT is composed of a set of software modules and a composite material library that integrate seamlessly with the Abaqus/Standard finite element analysis system, providing the user with state-of-the-art material modeling capability for unidirectional and woven fiber-reinforced composite materials. Helius:MCT utilizes a form of multiscale material modeling that is based on Multicontinuum Theory (MCT) which has been under continuous joint development by the University of Wyoming and Firehole Composites over the past 15 years. The MCT modeling methodology provides an unsurpassed combination of accuracy, efficiency and convergence robustness in predicting damage evolution and material failure in composite materials. In sharp contrast to traditional continuum mechanics, where physical quantities of interest (e.g., stress and strain) are averaged over the entire heterogeneous microstructure of the composite material, MCT retains the identities of the distinct material constituents within the microstructure. Consequently, physical quantities of interest (e.g., stress and strain) are averaged over each individual constituent material. These constituent average quantities provide much deeper insight into the thermo-mechanical behavior of the composite material than the traditional composite average quantities. To briefly summarize, MCT focuses on two concepts: 1) the development of relationships between the various constituent average quantities of interest, and 2) the development of relationships that link the composite average quantities to the constituent average quantities. For a complete discussion of MCT and the advantages that it provides in the analysis of composite materials, refer to the Helius:MCT Theory Manual. Additionally, Helius:MCT can provide delamination predictions using Abaqus cohesive elements (COH2D4 and COH3D8) defined with a Helius:MCT Cohesive user material. The delamination model uses some of the same material models provided by Abaqus/Standard, however, Helius:MCT provides robust convergence. Helius:MCT allows analyses to use both ply level and cohesive level progressive failure models without a significant increase in analysis time.

1.1

A Note on the Helius:MCT- Linear Version

Firehole Composites also offers a limited-functionality version of Helius:MCT referred to as Helius:MCT-Linear. Helius:MCT-Linear provides users access to advanced multi-scale analysis, constituent level stress and strain values and multi-scale failure indices when running linear elastic finite element simulations. Helius:MCT-Linear does not provide access to many of the advanced, nonlinear functionalities that are available in the full version of Helius:MCT such as progressive failure modeling, material nonlinearity, cohesive functionality and other advanced features. In an effort to delineate in this document the features that are not available in the Linear version of Helius:MCT, the following graphic will be displayed when describing a feature that requires a license to the full-featured version of Helius:MCT. Functionality not available in Helius:MCT Linear

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1.2

Helius:MCT Interaction with Abaqus/Standard

In an Abaqus structural-level finite element analysis of a composite structure, Helius:MCT quickly and accurately decomposes the composite average stress/strain field into constituent average stress/strain fields. The constituent average stress states are then used by Helius:MCT to predict damage evolution and material failure individually for each constituent material that is present in the microstructure. Subsequently, Helius:MCT homogenizes the current damaged microstructure in order to provide an accurate assessment of the current composite average stiffness for use in the structural-level finite element analysis. Helius:MCT is designed to provide this enhanced composite modeling capability without significantly increasing the time required to run the structural-level finite element analysis. For example, using Helius:MCT to enhance a structural-level finite element analysis usually increases the time required to perform a single structural-level equilibrium iteration by only two to three percent (a very small price to pay for the increased solution accuracy provided by Helius:MCT). However, Helius:MCT is specifically developed to increase the convergence robustness of structural-level progressive failure simulations; consequently, analyses that are enhanced by Helius:MCT are more likely to successfully resolve the entire load history while using fewer total equilibrium iterations. Figure 1 shows a schematic diagram of the individual components of the Helius:MCT software and their interaction with the Abaqus/Standard software components. In Figure 1, bold rectangles indicate the components of the Abaqus/Standard finite element modeling package, while ovals indicate the individual components of the Helius:MCT software. In Figure 1, the Helius:MCT Graphical User Interface (GUI) is accessed from within Abaqus/CAE and assists the user in defining the Abaqus input file parameters that are required during a finite element analysis that employs Helius:MCT. The Helius:MCT User-Defined Material Subroutine (see Figure 1) calculates constitutive relations and computes stresses for the Abaqus/Standard finite element code. The Helius:MCT User-Defined Material Subroutine contains all of the MCT constitutive relations for the individual constituents (fiber and matrix) and the homogenized composite material. In addition, the Helius:MCT User-Defined Material Subroutine contains the constituent-based failure criteria and the nonlinear constituent damage algorithms which degrade the stiffness of the constituents and the homogenized composite material to reflect the current damage state of the composite. The Abaqus/Standard finite element code calls the Helius:MCT User-Defined Material Subroutine at each Gaussian integration point in the model where constitutive relations or stresses are requested. In Figure 1, the Helius:MCT Composite Material Library is used to store all of the material coefficients that are needed to completely define the MCT multiscale material model for various composite materials. Before a particular composite material can be used in a Helius:MCT-enhanced finite element model, the composite material must undergo MCT material characterization, and a unique material file must be added to the Helius:MCT Composite Material Library. As shown in Figure 1, the Helius:MCT User-Defined Material Subroutine opens and reads the Helius:MCT Composite Material Library to extract the necessary material coefficients for any composite materials that are used in the finite element model. Note that material libraries are not necessary for Helius:MCT cohesive materials. Since the number of inputs required to define a cohesive material are much less than a composite, the entire material is defined within the Abaqus input file.

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Helius:MCT Abaqus/CAE

Graphical User Interface (GUI)

Abaqus input file

Helius:MCT Abaqus/Standard

User-Defined Material Subroutine

Abaqus output file

Helius:MCT Abaqus/Viewer

Composite Material Library

Figure 1: Schematic diagram of the individual components of the Helius:MCT software and their interaction with the Abaqus/Standard software components

In addition to the software modules depicted in Figure 1, Helius:MCT contains two additional auxiliary programs: Helius Material Manager and xSTIFF. Helius:Material Manager is a stand-alone program that allows the user to characterize new composite materials and add them to the Helius:MCT Composite Material Library. xSTIFF is a stand-alone program that greatly simplifies the creation of Helius:MCT-compatible Abaqus input files by automatically calculating and inserting any extraneous stiffness parameters that are required by elements that use reduced integration . Note that xSTIFF is not required for analyses that use strictly Helius:MCT cohesive materials.

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1.3

Helius:MCT Support Documentation

This User’s Guide assumes the reader is familiar with the basic use and concepts of the Abaqus/Standard finite element modeling system, including the following three processes: 1) Creating input files for Abaqus/Standard, 2) Running Abaqus/Standard finite element analyses, and 3) Viewing the results from an Abaqus/Standard finite element analysis. Given this assumption, the purpose of this document is to describe those aspects of creating an Abaqus input file that are unique to finite element analyses that utilize Helius:MCT for enhanced multiscale modeling of fiber-reinforced composite structures. In addition, this document discusses appropriate methods for viewing the enhanced results that are available in the output file when Helius:MCT is used in the finite element analysis. The remainder of this document is organized as follows: Section 2

Section 3

Section 4

Section 5 Section 6

This section identifies the Abaqus keyword statements that should be present in an Abaqus input file to achieve compatibility with Helius:MCT and take full advantage of its superior convergence characteristics for nonlinear problems. This section describes the use of Abaqus/CAE to create Abaqus input files that are compatible with Helius:MCT. More specifically, Section 3 describes the use of the Helius:MCT Graphical User Interfaces (GUIs) that are accessed from within Abaqus/CAE. For users who choose to employ a text editor to manually create their Abaqus input files, Section 4 describes the process of manually converting existing Abaqus input files to achieve compatibility with Helius:MCT. For users who want to run Helius:MCT on Linux this section describes the necessary steps to do so. Finally, this section describes each of the enhanced solution variables that are computed by Helius:MCT during a finite element simulation, and describes the use of Abaqus/Viewer to view the enhanced MCT results.

The collective documentation for Helius:MCT is divided into several documents. These documents are listed below along with a brief description of each one. Helius:MCT Installation Guide The installation guide explains the installation of the Helius:MCT software on your computer. Helius:MCT User’s Guide The user’s guide is a general reference for using Helius:MCT to provide enhanced composite modeling capabilities for Abaqus/Standard finite element analyses of composite structures.

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Helius Material Manager User’s Guide The Material Manager User’s Guide provides step-by-step guidelines for using the Helius Material Manager, a convenient graphical user interface (GUI) for creating a material file required to execute a Helius:MCT analysis. xSTIFF User’s Guide xSTIFF is a command line program that reads an Abaqus input file and automatically computes and inserts all of the extraneous stiffness parameters that are required by any reduced integration elements that utilize Helius:MCT composite materials. This auxiliary program significantly improves the speed and accuracy of the model building process. Helius:MCT Theory Manual The Theory Manual provides an in-depth explanation of MCT theory and discusses the various features that are implemented in the Helius:MCT User-Defined Material Subroutine. In addition, the Theory Manual describes the important process of characterizing a composite material for use with the MCT decomposition. Helius:MCT Tutorials 1, 2, 3 and 4 These documents are step-by-step tutorials that demonstrate the use of Helius:MCT. The primary emphasis is the creation of Abaqus input files that are compatible with Tutorials 1 & 2 Helius:MCT and the viewing of special solution variables that are computed by Include progressive Helius:MCT. failure functionality • Tutorial 1 demonstrates the ply-based functionality of Helius:MCT and the use of not available in Helius:MCT Linear Abaqus/CAE in building an Abaqus input file . • Tutorial 2 demonstrates the process of manually converting an existing Abaqus input file to achieve compatibility with Helius:MCT. • Tutorial 3 demonstrates the use of Abaqus/CAE and Helius:MCT Linear in building an Abaqus input file. • Tutorial 4 demonstrates the cohesive-based functionality of Helius:MCT and the use of Abaqus/CAE in building an Abaqus input file. Helius:MCT Example Problems 1, 2, and 3 The example problem documents provide examples of how to use the functionality provided by Helius:MCT to execute a finite element analysis of a composite structure. Example Problem 1 • Example Problem 1 details how the mesh density and element type affect a includes progressive failure analysis that typical composite structure analysis and compares the Helius:MCT progressive is not available in failure analysis capabilities with the built in Abaqus composite analysis Helius:MCT Linear functionality. • Example Problem 2 details how to use the pre-failure nonlinearity functionality of Helius:MCT to get the most accurate analysis of a composite structure. Example Problem 2 • Example Problem 3 demonstrates the use of temperature dependent material include pre-failure nonlinearity not properties and residual thermal stresses. available in Helius:MCT Linear

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2 General Requirements for Abaqus Input Files This section identifies the keyword statements that should be present in an Abaqus input file to ensure complete compatibility with Helius:MCT and to take full advantage of its superior convergence characteristics for nonlinear, progressive failure problems. More specifically, this section explains the need for these keyword statements in terms of the unique characteristics of Helius:MCT. This section does not discuss the formatting requirements of any keyword statement, nor does it discuss any of the specific options or data of any keyword statement; these issues are covered in Sections 3 and 4.

2.1

Identification and Definition of Helius:MCT Materials

If Helius:MCT is used to provide the constitutive relations for a particular composite or cohesive material, then Abaqus/Standard considers the material to be a 'user-defined material type.' Consequently, Abaqus/Standard requires the following three keyword statements for each “user-defined material type” that is used in the finite element model: 1. *MATERIAL, 2. *USER MATERIAL, and 3. *DEPVAR. A detailed description of each of these keywords and their functionality in Abaqus/Standard can be found in the Abaqus Keywords Reference Manual; however, their use in defining materials for Helius:MCT is briefly described below. The *MATERIAL keyword statement is used to identify the name of the composite or cohesive material. When defining a composite material the name must precisely match the name of a composite material that is stored in the Helius:MCT composite material database. For more information on how to create a material file that can be added to the Helius:MCT composite material database, please refer to the Helius Material Manager User’s Guide. The *USER MATERIAL keyword statement identifies the material as a “user-defined material type.” In addition, the data and options of the *USER MATERIAL keyword statement are used by Helius:MCT to identify the specific type of multiscale constitutive relations that should be used for the material. The *DEPVAR statement is used to request storage space within Abaqus/Standard for the MCT state variables that must be tracked at each integration point in the model. The specific data and options of the *MATERIAL, *USER MATERIAL, and *DEPVAR keyword statements (along with their formatting requirements) are discussed in Sections 3 and 4. For now, it suffices that the reader is aware that the *MATERIAL, *USER MATERIAL, and *DEPVAR keyword statements will be used collectively to identify each of the composite materials that will be processed by Helius:MCT and to identify the specific form of the multiscale constitutive relations that will be used for each of the composite materials.

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2.2

Definition of Extraneous Stiffness Parameters for Certain Types of Elements

Certain types of Abaqus elements (e.g., shell elements and reduced integration elements) require extraneous stiffness parameters in order to stabilize their response to deformation modes whose stiffness is not provided by material constitutive relations. Depending on the specific type of element, these extraneous stiffness parameters may include one or more of the following: transverse shear stiffnesses, hourglass control stiffnesses, thickness modulus, and thickness Poisson ratio. Provided that the finite element model uses only standard Abaqus material types, Abaqus/Standard will automatically compute all of the required extraneous stiffness parameters at runtime. However, when the finite element model contains user-defined material types, Abaqus/Standard cannot automatically compute all of the extraneous stiffness parameters that are required. In that case, the Abaqus input file must explicitly define any required extraneous stiffness parameters. These extraneous stiffness parameters are defined as options or data in the various section keyword statements (e.g., *SOLID SECTION, *SHELL SECTION, etc.). Please refer to Appendix C.1 of this User's Guide for a description of the extraneous stiffness parameters that are required for various element types. In earlier versions Helius:MCT, the calculation of these extraneous stiffness parameters and their insertion in the Abaqus input file required a rather cumbersome manual procedure that is described in detail in Appendices C.2-C.4 of this User's Guide. However, Helius:MCT now includes a new auxiliary program (xSTIFF) that automatically calculates and inserts the required extraneous stiffness parameters into the Abaqus input file. The use of xSTIFF is highly recommended as it greatly accelerates the model building process, while at the same time minimizing the chance for errors to be introduced into the input file. For more information on using xSTIFF to automatically calculate and insert the required extraneous stiffness parameters into the Abaqus input file, please refer to the xSTIFF User’s Guide. Note that extraneous stiffness parameters are not required for cohesive sections, so running xSTIFF is not required for analyses that strictly use Helius:MCT cohesive materials.

2.3

Nonlinear Solution Control Parameters for Helius:MCT

It is a widely accepted notion that good convergence (or any convergence at all) is difficult to achieve in a progressive failure simulation of a composite structure. In fact, many progressive failure simulations terminate early, not due to global structural failure, but rather due to the inability of the finite element code to obtain a converged solution at a particular load increment. Helius:MCT significantly improves the overall convergence rate and Nonlinear solution robustness of finite element simulations of progressive failure of composite control parameters are not required for structures. Experienced users of Abaqus/Standard are no doubt familiar with simulations using the code’s tendency to reduce (or cut-back) the time increment size when the Helius:MCT Linear code senses that convergence is difficult to achieve. However, when Helius:MCT is used in conjunction with Abaqus/Standard to perform a progressive failure analysis, the increased robustness of the solution greatly diminishes the need for time incrementation reductions (or cut-backs), thus the analysis can be completed much faster than without the use of Helius:MCT. In order to take full advantage of the superior convergence characteristics of Helius:MCT, the user must change some of the default settings that govern the nonlinear solution process used by Abaqus/Standard. These changes can be enacted using the *CONTROLS keyword statement. In Abaqus/Standard, the default settings for the nonlinear solution process are based on the fundamental assumption of the Newton-Raphson algorithm that the nonlinear response of the composite structure is sufficiently smooth at both the local and global levels. However, in a progressive failure Helius:MCT User’s Guide – Abaqus

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simulation of a composite structure, the nonlinear response of the composite structure is not smooth, especially at the local level, and it is this situation that is primarily responsible for the difficulty in obtaining convergence. Helius:MCT is specifically designed to efficiently handle this localized ”jagged” material response; however, the default settings of Abaqus/Standard must be changed in order to allow Helius:MCT to improve the convergence characteristics of the finite element simulation. These default settings can be changed via the data line of the *CONTROLS keyword statement. In this case, the data line of the *CONTROLS keyword statement is used to significantly increase the number of equilibrium iterations that Abaqus/Standard will perform before the code evaluates the need for a reduction (or cutback) in time step size. The specific data and options that are used with the *CONTROLS keyword statement is discussed in Sections 3.4 and 4.5. For now, it suffices that the reader is aware that the *CONTROLS keyword statement is used to provide Helius:MCT with the freedom to drastically improve the speed and robustness of convergence in progressive failure simulations.

2.4

Requesting Output of Solution Variables that are Unique to Helius:MCT

Helius:MCT calculates a number of specialized state variables that define the constituent average stress and strain fields, in addition to the damage state of the composite material. These state variables are stored by Abaqus/Standard at each individual integration point within the finite element model. To allow these state variables to be examined in Abaqus/Viewer, the Abaqus input file must explicitly identify the state variables that will be written in the Abaqus output file. This request is made via the data lines of the *ELEMENT OUTPUT keyword statement. Specific usage and formatting of the *ELEMENT OUTPUT keyword statement are discussed in Sections 3 and 4. For now, it should be understood that the *DEPVAR and the *ELEMENT OUTPUT keywords allow the user to request which solution dependent state variables should be available for post-processing. Appendices D and E of this User's Guide contains a detailed description of each of the MCT state variables for composite and cohesive materials.

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3 Using Abaqus/CAE To Create Abaqus Input Files For Use With Helius:MCT Section 3 describes the use of Abaqus/CAE to create an Abaqus input file that is completely compatible with Helius:MCT. It is assumed that the reader is familiar with the process of using Abaqus/CAE to create an Abaqus input file. Consequently, this section focuses primarily on those aspects of model creation that are unique to models utilizing Helius:MCT. In particular, this section explains the use of the two Helius:MCT Graphical User Interfaces (GUI’s) that can be accessed from within Abaqus/CAE. The Helius:MCT Ply GUI provides a simple, intuitive means for the user to create composite material definitions that are compatible with Helius:MCT. The Helius:MCT Cohesive GUI allows the user to create cohesive material definitions for delamination predictions in Helius:MCT.

3.1

Creating Composite Materials with the Helius:MCT Ply GUI

Each composite material that is processed by Helius:MCT is considered by Abaqus/Standard to be a user-defined material type. The Helius:MCT Ply GUI provides a simple means of creating these composite material definitions in the Abaqus input file. Helius:MCT Ply allows the user to select a composite material from the Helius:MCT composite material database and then select a number of different options for the multiscale constitutive relations that will be used to define the thermomechanical response of the composite material. To open the Helius:MCT Ply GUI from within Abaqus/CAE, go to the main toolbar and select Plug-ins  Helius:MCT - Ply. The GUI will appear as shown in Figure 2.

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5 6 7 8 9 10 11

12 13 14 15 16

Figure 2: The Helius:MCT Ply Graphical User Interface (GUI)

As shown in Figure 2, there are sixteen possible steps involved in using the Helius:MCT Ply GUI to define a composite material type for Helius:MCT. Each of the fifteen steps is discussed below.

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1. Composite Material Selection – The user selects a composite material from the Helius:MCT material library. If the material library does not contain a composite material that the user would like to use in an analysis, a material data file must first be created and added to the material library (refer to Helius Material Manager User’s Guide). Once a composite material is selected, the homogenized (or composite average) engineering constants for that material will be displayed in the box labeled “Engineering Constants for Your Selected Composite”. These constants are displayed in Helius:MCT’s default system of units (N/m/K). To display these constants in a different coordinate system, the user may select a different system of units (see step 2). 2. System of Units – The user selects the system of units that should be used by Helius:MCT to compute constitutive relations and stresses. By default, Helius:MCT expresses constitutive relations and computes stress in the (N/m/K) system of units. If the finite element model is created using a different system of units, then Helius:MCT must convert its constitutive calculations to the system of units required by the finite element model. For such purposes, Helius:MCT contains conversion factors for four commonly used systems of units: N/m/K, N/mm/K, lb/in/R, and lb/ft/R. If the finite element model uses one of these four systems of units, the user must select the appropriate system from the drop-down list. In the event that the finite element model’s system of units does not appear in the drop-down list, the user should select the default system of N/m/K and then refer to Appendix A.1 for details on how to manually modify the Abaqus input file to utilize a custom system of units. The reader can also refer to Appendix A.1 for more detailed information on systems of units in general. 3. Principal Material Coordinate System – Helius:MCT expresses constitutive relations and computes stresses in the principal material coordinate system of the composite material. Here the user selects one of two or three possible orientations for the composite’s principal material coordinate system. For Unidirectional Microstructures: Helius:MCT’s default principal material coordinate system is oriented with the ‘1’ direction aligned with the fiber direction, while the ‘2’ and ‘3’ directions lie in the material’s plane of transverse isotropy. This default orientation of the principal material coordinate system corresponds to the selection of "1" from the fiber direction drop down menu. However, in situations where it adds convenience or simplicity to the model creation process, the user may change the orientation of the principal material coordinate system so that the ‘2’ direction is aligned with the fiber direction, while the ‘1’ and ‘3’ directions lie in the composite material’s plane of transverse isotropy. This particular orientation of the principal material coordinate system corresponds to the selection of "2" from the fiber direction drop down menu. If the user selects the value ‘2’ from the dropdown list, the Helius:MCT GUI updates the contents of the display box labeled “Engineering Constants for Your Selected Composite”. For Woven Microstructures: Helius:MCT’s default principal material coordinate system is oriented with the ‘1’ direction aligned with the fill tow direction, while the ‘2’ direction corresponds to the warp tow direction, and the ‘3’ direction corresponds with the out-of-plane direction. This default orientation of the principal material coordinate system corresponds to the selection of "1" from the fiber direction drop down menu. However, in situations where it adds convenience or simplicity to the model creation process, the user may change the orientation of the principal material coordinate system so that the ‘2’ direction is aligned with the fill tow direction, while the ‘1’ direction corresponds to the warp tow direction. This particular orientation of the principal material coordinate system corresponds to the selection of "2" from the fiber direction drop down menu. Additionally, the user may change the Helius:MCT User’s Guide – Abaqus

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orientation of the principal material coordinate system so that the ‘3’ direction is aligned with the fill tow direction while the ‘2’ direction corresponds to the warp tow direction. This particular orientation of the principal material coordinate system corresponds to the selection of "3" from the fiber direction drop down menu. For more information on the orientation of principal material coordinate systems, please refer to Appendix A.2.

4. Temperature Dependence – (unidirectional composites only) If a list of temperatures is displayed, then the material data file for the selected material contains material properties at multiple temperatures. After selecting a temperature, the properties that are stored for that temperature are displayed in the “Engineering Constants for Your Selected Composite”. During a finite element analysis, Helius:MCT linearly interpolates the composite and constituent properties for any given temperature that lies within the bounds of the lowest and highest temperature points stored in the material file. For temperatures below the lowest stored temperature datum, Helius:MCT will use the material properties stored at the lowest temperature datum (Helius will not extrapolate properties beyond the bounding stored temperature data points). The same is true for temperatures above the highest stored temperature datum. For further information on the use of temperature dependent material properties in Helius:MCT, please refer to section 9 of the Helius:MCT Theory Manual. For further information on adding a new temperature dependent material to the Helius:MCT material library, please refer to the Helius:MCT Material Manager User’s Guide. Steps 5, 6, 7, 8, 9, 10, 12 and 13 listed below do not apply to Helius:MCT Linear

5. Progressive Failure - The user chooses whether or not to perform a Progressive Failure Analysis. If the user checks this box, then Helius:MCT will routinely evaluate both the matrix failure criterion and the fiber failure criterion to determine if either constituent has failed. Each constituent failure criterion is based on the corresponding constituent average stress state. In the event that one or both of the constituents fail, the stiffness of the failed constituent(s) and the stiffness of the composite are appropriately reduced instantaneously. It should be emphasized that an instantaneous reduction of the stiffness of a failed constituent effectively results in a discontinuous, piecewise linear stress/strain response for the constituent and the composite. However, when this type of discrete material response is applied independently at each of the integration points in a large finite element model, the net result is a gradual (or progressive) degradation of the overall stiffness of the composite structure (hence the name Progressive Failure Analysis). The progressive failure analysis feature is the foundation component of Helius:MCT’s nonlinear multiscale constitutive relations. Other aspects of material nonlinearity can be invoked (as shown in steps 6, 7 and 8); however, these additional forms of nonlinearity cannot be activated unless the progressive failure analysis feature is also activated. Consequently, if the user chooses not to check the progressive failure analysis box, then Helius:MCT will use linear elastic constitutive relations. For further information on progressive failure analyses and constituent failure criteria, refer to Appendix A.3 of this User's Guide and Section 4 of the Helius:MCT Theory Manual.

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6. Calculate Failed Plain Weave Properties - (plain weave composites only) Selecting this option will force Helius:MCT to calculate the failed plain weave properties using the matrix and fiber degradation levels specified in steps 11 and 12. If this option is not selected, the failed material properties that were calculated when the material data file was created using Helius:Material Manager are used. For example, if the matrix degradation value was 0.7 and the fiber degradation value was 0.015 when the material was created (using Helius Material Manager) and this option is unselected, the failed material properties corresponding to a matrix degradation of 0.7 and a fiber degradation of 0.015 are used. If, on the other hand, this option is selected and, for example, the user specifies a matrix degradation of 0.8 and a fiber degradation of 0.001 in steps 11 and 12, then the failed material properties corresponding to a matrix degradation of 0.8 and a fiber degradation of 0.001 are used. Note: The matrix degradation for woven lamina is recommended to be not less than 0.7. 7. Hydrostatic Strengthening of the Composite – (unidirectional composite only) The user chooses whether or not to account for the experimentally observed strengthening of the composite in the presence of a hydrostatic compressive stress. If the user checks this box, then Helius:MCT will monitor the hydrostatic compressive stress level in the matrix constituent. If the hydrostatic compressive stress level in the matrix constituent exceeds a threshold value, then the strength of both the matrix constituent and the fiber constituent are scaled upwards commensurate with the level of hydrostatic compressive stress level in the matrix constituent. For further information on Hydrostatic Strengthening of the Composite, refer to Appendix A.6 of this User's Guide and Section 7 of the Helius:MCT Theory Manual. 8. Energy-Based Degradation – (unidirectional composites only) The user chooses whether or not to use an Energy-Based approach to degrade composite stiffness as a function of increasing strain. If the user checks this box, then Helius:MCT will employ a piecewise linear degradation of composite stiffness after a failure event, while conserving the total energy supplied by the user. The type of failure event (i.e. fiber or matrix failure) determines which composite stiffnesses are reduced linearly with increasing strain. In this case, the constituent failure criteria are assumed to simply identify the onset of a failure event. As the deformation of the lamina continues to increase, the stiffness of the composite is subject to a series of discrete reductions until the stiffness of the composite finally reaches its minimal level indicating complete failure of the constituent. It is of importance to note a consistent set of material properties is enforced between the microscopic and macroscopic scales to allow for the composite material properties to degrade along with the matrix after the matrix constituent fails. For instance, a matrix failure event will c c c c c result in a linear degradation of composite E22, E33, G12, G13 and G23, while also degrading m

m

m

m

m

m

matrix E11, E22, E33, G12, G13 and G23. However, a fiber failure event will result in a linear c

c

c

degradation of composite E11, G12 and G13, but the constituents are no longer degraded as the stresses and strains in the constituents are no longer useful. It should be emphasized that this feature and Post-Failure Nonlinearity are mutually exclusive for all analyses. For further information on Energy-Based degradation and its impact on analyses, refer to Appendix A.5 of this User's Guide and the Helius:MCT Theory Manual. 9. Pre-Failure Nonlinearity – (unidirectional composites only) The user chooses whether or not to account for the nonlinear longitudinal shear stress/strain response that is commonly observed in fiber-reinforced composite materials. If the user checks this box, then Helius:MCT will employ a four-segment, piecewise linear representation of the longitudinal shear stress/strain response Helius:MCT User’s Guide – Abaqus

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c

c

c

c

(i.e., σ12 vs. ε12, and σ13 vs. ε13), while the responses of the other four stress and strain components remain unaffected by this feature. The entire series of three discrete reductions in the longitudinal shear moduli of the composite is conducted in such a way that the piecewise linear longitudinal shear response closely matches experimentally measured longitudinal shear data for the composite. It should be emphasized that this feature is only available for those unidirectional composite materials where a longitudinal shear stress/strain curve was supplied during the MCT material characterization process. If this feature is requested for a composite material that was characterized without a longitudinal shear stress/strain curve, then Helius:MCT will issue an error message at runtime and execution will halt. For further information on the Pre-Failure Nonlinearity feature, refer to Appendix A.4 of this User's Guide, Section 5 of the Helius:MCT Theory Manual, and Example Problem 2. For further information on characterizing new composite materials with Pre-Failure Nonlinearity capability, please refer to the Helius:MCT Material Manager User’s Guide. 10. Post-Failure Nonlinearity – (unidirectional composites only) The user chooses whether or not to account for the support that is provided to a failed lamina by the surrounding un-failed lamina. When individual matrix cracks appear in a lamina, the surrounding undamaged lamina are able (via interlaminar shear stresses) to divert the load path around the individual matrix cracks and back into the failed lamina. The net result of this process is that matrix failure in a lamina is not a discrete catastrophic event, rather it is a gradual process marked by a gradual increase in the density of matrix cracks. In this case, the matrix failure criterion is assumed to simply identify the onset of matrix crack development. As the deformation of the lamina continues to increase, the stiffness of the matrix constituent is subject to a series of discrete reductions until the stiffness of the matrix constituent finally reaches its minimal level indicating complete matrix failure (i.e., matrix crack saturation). It is of importance to note a consistent set of material properties is enforced between the microscopic and macroscopic scales to allow for the composite material properties to degrade along with the matrix. It should be emphasized that this feature is only available for those unidirectional composite materials where the transverse normal failure strain was supplied during the MCT material characterization process. If this feature is requested for a composite material that was characterized without a transverse normal failure strain, then Helius:MCT will issue an error message at runtime and execution will halt. This feature is also mutually exclusive with the Energy-Based Degradation option discussed above. For further information on the Post-Failure Nonlinearity feature, refer to Appendix A.5 of this User's Guide and Section 6 of the Helius:MCT Theory Manual. For further information on characterizing new composite materials with PostFailure Nonlinearity capability, please refer to the Helius:MCT Material Manager User’s Guide. 11. Residual Stresses – (applicable to unidirectional composites only) This option is used to specify whether or not to explicitly account for thermal residual stresses in the response of the composite material. If this option is checked, then Helius:MCT computes the ply-level and constituent-level thermal residual stresses that are caused by the post-cure cool down from the stress-free temperature displayed under “Engineering Constants for Your Selected Composite” to ambient temperature (defaults to 72.5°F = 22.5°C = 295.65°K). In this case, these ply-level and constituent-level thermal residual stresses will be present prior to the application of any external mechanical and/or thermal loads that are imposed during the simulation. If the user chooses to explicitly account for thermal residual stresses in the analysis, then the user should verify that the

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stress-free temperature (synonymous with cure temperature) displayed under “Engineering Constants for Your Selected Composite” is indeed a reasonable value; otherwise, the predicted thermal residual stresses could be quite erroneous. If this option is not checked for a particular composite material, then thermal residual stresses are not included in the response of that particular composite material during the simulation. In this case, the stress free temperature of the composite material defaults to Tsf =0° (regardless of the system of units employed), and the temperature change that is used in the constitutive relations [σ = C(ε−α∆T)] is simply computed as ∆T = T − Tsf = T. Several points should be emphasized here. First, the stress free temperature Tsf defaults to 0° even if the composite material data file (Mdata file) explicitly defines a non-zero stress free temperature. Second, regardless of the system of units that are employed by the finite element model, the current temperature T completely defines the temperature change ∆T that is used in the constitutive relations. Third, for composite materials that are characterized at multiple temperatures, the current temperature T will be used to interpolate the various material properties that contribute to the constitutive relations; consequently, it is recommended that a singletemperature characterization (i.e., a single-temperature Mdata file) should be used for the composite material in question. In summary, if the user does not request this option, then the current temperature T influences Eqs. 10.1 of the Theory Manual in two different ways: 1) the temperature change used in the constitutive relations simply becomes ∆T=T, and 2) T is used to interpolate the temperature-dependent material properties that contribute to the constitutive relations. Refer to Section 10 of the Helius:MCT Theory Manual for further information on the thermal residual stresses formulation used by Helius:MCT. It should be emphasized that the default temperature in Abaqus/Standard is 0°. This default temperature is completely compatible with the default stress free temperature of 0° that is assumed when the seventh user material constant is specified as 0. In this case, the model can still be subjected to temperature changes by simply imposing a temperature other than 0°; however, these thermal stresses develop over the course of the analysis, as opposed to being present at the start of the analysis. 12. Matrix Post-Failure Stiffness / Matrix Degradation Energy – For analyses not using EnergyBased Degradation, this value is a fraction that is used to define the damaged elastic moduli of the matrix constituent after matrix constituent failure occurs. Specifically, the value is the ratio of the failed matrix constituent moduli to the unfailed matrix constituent moduli. A value of 0.1 would mean that after a matrix failure occurs at an integration point, all six of the matrix constituent m m m m m m moduli (E11, E22, E33, G12, G13, G23) are reduced to 10% of the original undamaged matrix constituent moduli. The matrix post-failure stiffness value must be greater than 0, and less than or equal to 1. By default, the matrix post-failure stiffness value is set to 0.1. If the post-failure nonlinearity feature is turned on, this value will be ignored. For analyses using Energy-Based Degradation, this value is the total energy dissipated before and after a matrix failure assuming a linear degradation of composite stiffness after a c c c c c failure event. Specifically, composite E22, E33, G12, G13, G23 are degraded after a matrix failure event according to this energy, the composite stress state at fiber failure and the volume of the element. For more information on the computation of the energy values, refer to Appendix A.5 of this document and the Helius:MCT Theory Manual.

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13. Fiber Post-Failure Stiffness / Fiber Degradation Energy – For analyses not using EnergyBased Degradation, this value is a fraction that is used to define the damaged elastic moduli of the fiber constituent after fiber constituent failure occurs. Specifically, the value is the ratio of the failed fiber constituent moduli to the unfailed fiber constituent moduli. A value of 0.01 would mean that after a fiber failure occurs at an integration point, all six of the fiber constituent moduli f f f f f f (E11, E22, E33, G12, G13, G23) are reduced to 1% of the original undamaged fiber constituent moduli. The fiber post-failure stiffness value must be greater than 0, and less than or equal to 1. The default value of the fiber post-failure stiffness is automatically set to 1E-06. For analyses using Energy-Based Degradation, this value is the total energy dissipated for a fiber failure assuming a linear degradation of composite stiffness before and after a fiber failure c c c event. Specifically, composite E11, G12, and G13 are degraded linearly after a fiber failure event according to this energy, the composite stress state at fiber failure, and the volume of the element. For more information on the computation of the energy values, refer to Appendix A.5 of this document and the Helius:MCT Theory Manual. 14. Average Element Thickness – (unidirectional composite only) If Energy-Based Degradation is selected for unidirectional materials, this value represents the average thickness of the threedimensional elements assigned to the material, where the thickness is measured through the thickness of the laminate. For two-dimensional elements (i.e. shells, plane stress), this value should be set to 1.0. 15. Output Constituent Average Stress and Strain States – The user chooses whether or not to output the fiber average stress and strain fields and the matrix average stress and strain field to the output database file (.odb file). If the user checks this box for a unidirectional composite, then the number of MCT state variables output to the .odb file increases from 6 to 34 (10 to 34 if EnergyBased Degradation is requested). If the user checks this box for a woven composite, then the number of MCT state variables output to the .odb file increases from 6 to 90. Printing these extra state variables increases the total run time slightly and significantly increases the size of the .odb file. Thus, this option should only be selected if the constituent average stress and strain states are of interest to the user. 16. Name State Dependent Variables – The user chooses whether or not to allow the Helius:MCT GUI to re-name the first 6 MCT state variables (or 10 if Energy-Based Degradation is requested). If the user checks this box, then the first 6 MCT state variables will be re-named from their Abaqus default names (SDV1, SDV2, …, SDV6) to descriptive names. See Appendix D for a complete description of each of the MCT state variables. Warning: Invoking this feature might cause Abaqus/CAE to produce input files that contain conflicting keywords. See Appendix F for a description of this problem and the suggested method of resolving this issue. After completing steps 1 through 16, the user should click the OK button on the Helius:MCT GUI to create a user-defined composite material that is compatible with Helius:MCT. Once the OK button is clicked, a new material will be created and the appropriate Abaqus keyword statements are created for the new user-defined composite material. The newly created Abaqus keyword statements (*MATERIAL, *DEPVAR, and *USER MATERIAL) can be viewed in the Keywords Editor. To access the Keywords Editor from the main toolbar, select Model  Edit Keywords  “Name of Model”. Figure 3 shows an example of the Keyword Editor containing the *MATERIAL, *DEPVAR, and *USER MATERIAL

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keyword statements. The following list describes each of the Abaqus keyword statements that are shown in Figure 3. •

*Material, name=IM7_8552 creates a material and assigns it the name IM7_8552. Note that the name IM7_8552 was selected via Step 1 from the pull-down list of materials in the Helius:MCT composite material database.

•

*DepVar creates storage space for 6 MCT state variables that Abaqus/Standard will track at each integration point in the finite element model. If the user had requested output of the constituent average stress and strain states via Step 12, the number of MCT states variables would increase to 34. Note that each of the 6 MCT state variables is being re-named; for example, SDV1 is renamed MAT_STATE, and SDV2 is re-named FI_MATRIX. This re-naming is only present in the *DEPVAR statement if the user checks the Name State Dependent Variables box via Step 15. Otherwise, the Abaqus default names will be used (SDV1, SDV2, …, SDV6).

•

*User Material, constants=13 identifies the material as a user-defined material that employs 13 different constants to specify information needed in the definition of the material. The values of these 13 constants are listed in the data line as 1., 1., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0.1, 0.01. These constants (referred to as user material constants) are used by the Helius:MCT User-Defined Material Subroutine to convey the specific choices made by the user in completing Steps 2 through 13 of the Helius:MCT GUI. The thirteen constants, in order, pertain to the system of units, the orientation of the principal material coordinate system, progressive failure analysis, prefailure nonlinearity, post-failure nonlinearity or energy-based degradation, hydrostatic strengthening, stress free temperature, (constants 8-11 are currently unused), matrix post-failure stiffness or matrix degradation energy, and fiber post-failure stiffness or fiber degradation energy. For user material constants 3, 4, 6, and 7, a value of 1 means the option is ‘on’, and a value of 0 means the option is ‘off’. For user material constant 5, a value of 0 indicates both post-failure nonlinearity and energy-based degradation are turned off, a value of 1 indicates post-failure nonlinearity is turned on, and a value of 2 indicates energy-based degradation is turned on. In this example, the default system of units (N/m/K) is selected; the principal material coordinate system is oriented with the ‘1’ direction aligned with the fiber direction; progressive failure analysis is turned ‘on’, pre-failure nonlinearity is turned ‘off’; post-failure nonlinearity and energy-based degradation are turned ‘off’, hydrostatic strengthening is turned ‘off’, the stress free temperature is set to zero, matrix post-failure stiffness is set to 10%, and fiber post-failure stiffness is set to 1%. Note: Appendix A provides a complete description of each of the user material constants.

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Figure 3: Keywords Editor showing the keyword statements that collectively define a Helius:MCT material

3.2

Creating Cohesive Materials with the Helius:MCT Cohesive GUI

Each cohesive material that is processed by Helius:MCT is considered by Abaqus/Standard to be a user-defined material type. The Helius:MCT Cohesive GUI provides a simple means of creating these cohesive material definitions in the Abaqus input file. Helius:MCT Cohesive allows the user to fully define the cohesive material including damage initiation and damage evolution parameters. To open the Helius:MCT Cohesive GUI from within Abaqus/CAE, go to the main toolbar and select Plug-ins  Helius:MCT - Cohesive. The GUI will appear as shown in Figure 4.

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1 2 3 4 5 6 7 8 9 10-12 13 14 15 Figure 4: Helius:MCT Cohesive GUI in Abaqus/CAE

As shown in Figure 4, there are fifteen possible steps involved in using the Helius:MCT Cohesive GUI to define a cohesive material type for Helius:MCT. Each of the fifteen steps is discussed below. See Appendix B for a technical discussion of these parameters. 1. Material Name - Enter the name of your material. This name will be displayed under the Materials tree in Abaqus/CAE once the material is added. 2. Normal Stiffness - A number greater than zero which defines the normal stiffness, Knn, of the cohesive material. Knn relates the normal traction in the cohesive material to the strain as tn = Knnεn where tn is the normal traction and εn is the strain in the normal direction (local 3-direction).

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3. First Shear Stiffness - A number greater than zero which defines the first shear stiffness, Kss, of the cohesive material. Kss relates the traction in the local 1-direction in the cohesive material to the strain as ts = Kssεs where ts is the first shear traction and εs is the strain in the local 1-direction 4. Second Shear Stiffness - A number greater than zero which defines the second shear stiffness, Ktt, of the cohesive material. Ktt relates the traction in the local 2-direction in the cohesive material to the strain as tt = Kttεt where tt is the second shear traction and εt is the strain in the local 2-direction. 5. Maximum Normal Traction - A number greater than zero which represents the maximum amount of traction the cohesive material can sustain in the normal direction (local 3-direction) before damage initiates, Sn. 6. Maximum First Shear Traction - A number greater than zero which represents the maximum amount of traction the cohesive material can sustain in the local 1-direction before damage initiates, Ss. 7. Maximum Second Shear Traction - A number greater than zero which represents the maximum amount of traction the cohesive material can sustain in the local 2-direction before damage initiates, St. 8. Damage Initiation Criterion - Allows the user to select a maximum traction or quadratic based damage initiation criterion. The maximum traction criterion defines damage initiation as the point when any of the tractions meet or exceed their corresponding maximum traction value. The quadratic based criterion uses a quadratic interaction of the traction to maximum traction ratios to predict damage initiation. 9. Softening Type - Allows the user to select how damage will evolve after damage initiation. Once damage initiates in a cohesive material the stiffness of the material decreases as material deformation increases. Eventually, the stiffness of the cohesive material will reduce to zero and the material will no longer sustain any load. For a softening type of "Displacement" see step 10 below, for "Energy" see step 11, and for "Energy (Mixed Mode, Power Law)" see steps 12-15. 10. Displacement At Failure - A number greater than zero which defines the difference between the effective displacement at complete failure and the effective displacement at damage f o initiation, δm - δm . 11. Fracture Energy - A number greater than zero which defines the total energy dissipated due to failure, GC. In mathematical terms, this value is the area under the traction - separation curve. 12. Normal Mode Fracture Energy - A number greater than zero which defines the total energy C dissipated due to failure under a pure normal mode, Gn . Helius:MCT User’s Guide – Abaqus

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13. First Shear Mode Fracture Energy - A number greater than zero which defines the total energy C dissipated due to failure under a pure first shear mode, Gs . 14. Second Shear Mode Fracture Energy - A number greater than zero which defines the total C energy dissipated due to failure under a second shear normal mode, Gt . 15. Alpha - The exponent used in the mixed mode power law damage evolution equation, α.

3.3

Specifying Extraneous Stiffness Parameters Required by Certain Element Types

Certain types of Abaqus elements (e.g., beam elements, shell elements, and reduced integration elements) require extraneous stiffness parameters in order to stabilize their response against deformation modes that are not governed directly by material constitutive relations. These extraneous stiffness parameters are defined as either options or data in the Section keyword statement that is referenced by the element in question. Depending upon the specific type of element being used, one or more of the following types of extraneous stiffness parameters may need to be specified as part of the Section definition that is referenced by the element. • • • • •

Section Poisson Ratio Section Thickness Modulus ts ts ts Section Transverse Shear Stiffnesses: K11, K22, and K12 Membrane Hourglass Stiffness Control Parameter Bending Hourglass Stiffness Control Parameter

Appendix B.1 provides a detailed discussion of each type of extraneous stiffness parameter, in addition to listing the specific extraneous stiffness parameters that are required by each type of element. In earlier versions of Helius:MCT, the calculation of these extraneous stiffness parameters and their insertion in the Abaqus input file required a rather cumbersome manual procedure that is described in detail in Appendices C.2-C.4 of this User's Guide. However, Helius:MCT now includes an auxiliary program (xSTIFF) that automatically calculates and inserts the required extraneous stiffness parameters into the Abaqus input file. The use of xSTIFF is highly recommended as it greatly accelerates the model building process, while at the same time minimizing the chance for errors to be introduced into the input file. With the availability of xSTIFF, the user can now postpone the task of defining the extraneous stiffness parameters until the model building process is completed and an Abaqus input file is saved. xSTIFF can then be run to automatically add any required extraneous stiffness parameters to the saved Abaqus input file. For more information on using xSTIFF to automatically calculate and insert the required extraneous stiffness parameters into the Abaqus input file, please refer to the xSTIFF User’s Guide. Note that if the analyses uses exclusively Helius:MCT cohesive materials (in addition to Abaqus material types), xSTIFF is not required. It is only required for analyses that use Helius:MCT ply materials.

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Note: If the user chooses to manually define the extraneous stiffness parameters, Appendices C.1-C.4 completely describe the processes of identifying the required extraneous stiffness parameters, calculating their values, and inserting the correctly formatted values into the Abaqus input file. Step modifications referenced below are only applicable to the full version of Helius:MCT as they pertain to progressive failure simulations.

3.4

Step Modifications

Helius:MCT significantly improves the overall convergence rate and robustness of finite element simulations of progressive failure of composite structures. However, in order to take full advantage of the superior convergence characteristics of Helius:MCT, the user must change some of the default settings that govern the nonlinear solution process used by Abaqus/Standard. This section discusses the use of Abaqus/CAE to make the recommended changes to the parameters that govern the nonlinear solution process used by Abaqus/Standard. It is recommended that the user specify the time incrementation parameters that are desired in the progressive failure analysis. Since the use of Helius:MCT provides more robust convergence, it is anticipated that the progressive failure analysis will require far fewer time incrementation reductions (or cut-backs) than would be possible without Helius:MCT. This characteristic may influence the user’s choice of time incrementation parameters. The time incrementation parameters can be specified from the Incrementation Tab in the Edit Step dialog box as shown in Figure 5. There are four settings that can be changed: the maximum allowable number of time increments, the value of the initial time increment, the minimum allowable value of a time increment, and the maximum allowable value of a time increment. For analyses that use Helius:MCT cohesive materials, the Extrapolation parameter should be set to None. This can be set from the “Other” tab shown in Figure 5.

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Figure 5: Location of incrementation parameters in the Edit Step dialog box

The user also should change some of the default settings that control the nonlinear solution process employed by Abaqus/Standard. These solution control parameters can be changed in the General Solution Controls Editor dialog box. The General Solution Controls Editor dialog box can be accessed from the Step module by clicking Other  General Solution Controls  Edit  “name of step” from the main toolbar. The General Solution Controls Editor dialog box is shown in Figure 6 with the Time Integration Tab selected. In Figure 6, there are two parameters shown with their default values (Io=4 and IR=8). Both of these parameters should be set to the same large value, say 1000 (e.g., Io=1000 and IR=1000). After specifying the values of Io and IR, click the first of the three tabs that are labeled ‘more’. From the list of parameters that appears, the values of IP, IC, IL and IS should each be set to 1000, and the value of IT should be set to 10. The greatly increased values of Io, IR, IP, IC, IL and IS will ensure that Abaqus/Standard can take full advantage of the improved convergence characteristics provided by Helius:MCT. For a complete discussion of the effect that Helius:MCT exerts on the convergence behavior of the finite element solution, see Section 11 of the Helius:MCT Theory Manual.

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Figure 6: General Solution Controls Editor dialog box

3.5

Requesting MCT State Variable Output for Composite Materials

The solution-dependent MCT state variables are used to track constitutive quantities of interest at each integration point in the finite element model. If the user checked the box labeled “Output Constitutive Stress/Strain” in the Helius:MCT Ply GUI, then 34 MCT state variables are tracked for unidirectional composite materials or 90 MCT state variables are tracked for woven composite materials; otherwise, 6 MCT state variables are tracked for analyses not using energy-based degradation, and 10 MCT state variables are tracked for analyses requesting the use of energy-based degradation. The default naming convention for the solution-dependent MCT state variables is SDVi, where i=1, 2, 3, …, 6 or 10 or 34 or 90. The most useful of the MCT state variables is SDV1 which is used to track the discrete failure state of the composite material at each integration point in the finite element model. The exact interpretation of the discrete values of SDV1 will depend upon the specific set of Helius:MCT material nonlinearity features that are used in the analysis. Appendix D provides a complete description of each of the MCT state variables, including tables that define the interpretation of the discrete values of SDV1 for various combinations of material type and material nonlinearity features invoked. By default, the MCT state variables are not automatically written to the output database file (*.odb file) and must be explicitly requested. Output of the MCT state variables can be requested by the user in Helius:MCT User’s Guide – Abaqus

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the Edit Field Output Request dialog box, which can be accessed from the Step module by clicking Output  Field Output Requests  Edit  “Name of output request” in the main toolbar. To request MCT state variable output, select the box labeled "SDV, Solution Dependent State Variables" from the scroll-bar list of output variables shown in Figure 7. By default, the field variables (including the MCT state variables) are only output at the bottom and top section points of each layered element. In order to view the field variables within each material ply, additional section points can be specified by entering their values in the text box that is highlighted in Figure 7. As an example, consider a flat composite plate with 4 plies and 3 section points per ply, for a total of 12 section points as shown in Figure 9. If the default section point values are used, only results for points 1 and 12 will available for viewing; the user will not have access to the results for the interior material plies. However, if output is requested for each section point, then the complete solution results for each ply can be viewed.

Figure 7: Locations of SDV and section point output parameters in the Edit Field Output Request dialog box

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3.6

Requesting MCT State Variable Output for Cohesive Materials

State variables for Helius:MCT cohesive materials are requested in a similar manner to requesting state variables for composite materials (Section 3.5). However, it is slightly less complex since cohesive elements do not contain section points and therefore do not require output to be requested at individual section points. The number of state variables for cohesive materials is always 9. See Appendix E for a list and description of the state variables for Helius:MCT cohesive materials.

3.7

Deleting a Helius:MCT Material

Deleting a material is usually accomplished by simply deleting the material from the model tree or the Material Manager. Because a Helius:MCT material is a user-defined material type, Abaqus/CAE will not automatically delete the *USER MATERIAL or *DEPVAR statements that are part of the material definition. In light of this situation, the procedure for deleting a Helius:MCT material from a finite element model is listed below. 1. Delete the material from the model tree or the Material Manager. The Material Manager can be accessed by clicking Material  Manager in the main toolbar. To delete the material from the model tree, right click on the material and select Delete. 2. To remove the keywords that are associated with the deleted material, open the Helius:MCT GUI by clicking Plug-ins  Helius:MCT from the main toolbar. Helius:MCT will automatically detect that the material has been deleted and a dialog box will appear as shown in Figure 8. Clicking Continue in this dialog box will result in the removal of the *USER MATERIAL and *DEPVAR statements associated with the deleted Helius:MCT material. The Helius:MCT GUI then reloads and appears on the screen. 3. Within the Helius:MCT GUI, the user can now click the Cancel button to dismiss the Helius:MCT GUI.

Figure 8: Keywords conflict dialog box

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4 Using a Text Editor to Convert Pre-Existing Abaqus Input Files for Use with Helius:MCT For those users who choose to employ a text editor to manually create and modify their Abaqus input files, this section describes the process of modifying an existing Abaqus input file to achieve complete compatibility with Helius:MCT.

4.1

Defining a Helius:MCT Composite Material

In an Abaqus input file, there are three different keyword statements that collectively define a Helius:MCT user-defined composite material. These three keyword statements are *MATERIAL, *DEPVAR, and *USER MATERIAL. Consider the following lines from an Abaqus input file that completely specify a Helius:MCT user-defined composite material. *MATERIAL, name=IM7_8552 *DEPVAR 6 1, MAT_STATE 2, FI_MATRIX 3, FI_FIBER 4, ETA_SM 5, ETA_NM 6, SIM_O *USER MATERIAL, constants=13 1,1,1,0,0,0,0,0 0,0,0,0.1,0.01 The *MATERIAL keyword denotes the start of the material definition, and the option ‘name=IM7_8552’ is used to specify the name of the composite material. The name ‘IM7_ 8552’ must exactly match the name of a material found in the Helius:MCT composite material database and a name specified in the section definition of the input file. The *DEPVAR keyword is used to identify the number of solution-dependent MCT state variables that must be tracked at each integration point in the finite element model. The number of solutiondependent MCT state variables is specified on the first data line that follows the *DEPVAR statement. In this example, there are 6 solution-dependent MCT state variables. The remaining data lines that follow the *DEPVAR keyword statement are optional and are simply used to assign new names to each of the 6 MCT state variables. For example, MCT state variable 1 is re-named MAT_STATE, and state variable 2 is re-named FI_MATRIX. If these optional name assignments are not present, then the 6 MCT state variables would simply retain their Abaqus defaults names of SDV1, SDV2, SDV3, …, SDV6. Allowable values for the number of MCT state variables requested in the *DEPVAR statement are the minimal set of 6 if energy-based degradation is not requested, 10 if energy-based degradation is requested (only for unidirectional composites), or the full set of 34 for unidirectional composites, or the full set of 90 for woven composites. It is highly recommended that for both unidirectional and woven composites, the minimal set of 6 MCT state variables should be requested in the *DEPVAR statement unless the user desires post-processing access to the constituent average stresses and strains. See Appendix D for a complete description of the different MCT state variables that are available for unidirectional and woven composite materials.

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The *USER MATERIAL keyword indicates that the material is a user-defined material type. The option ‘constants=13’ indicates that there are a total of 13 user material constants specified for the material. Collectively, the user material constants are used by the Helius:MCT User-Material Subroutine to determine the precise form of multiscale constitutive relations that will be used for the material. For any given Helius:MCT material, the number of user material constants must be between 3 and 16. The first three user material constants are The third material constant, while required for all Helius:MCT materials. The last three user material constants th th th required is not (i.e., the 14 , 15 , and 16 constants) are only required if the finite element utilized in model is defined using a custom system of units. User material constants 8-11 Helius:MCT Linear are not utilized and should be left blank or set to 0. Appendix A provides a and its value will detailed description of each of the nine utilized user material constants, default to zero. including the range of allowable values for each constant and the impact that each constant has on the multiscale constitutive relations used to represent the material. Each of the nine user material constants typically defined in an analysis incorporating Helius:MCT are listed below along with a brief description. For a more detailed description of any particular user material constant, refer to the appropriate section of Appendix A. •

System of Units – The first user material constant specifies the system of units that should be used by Helius:MCT in computing the constitutive relations and stresses. In the example provided above, the first user material constant has a value of 1, indicating that Helius:MCT should compute the constitutive relations and stresses in its default system of units (N/m/K). There are three other systems of units (2 → N/mm/K, 3 → lb/in/R, and 4 → lb/ft/R) that can be requested via specific values of the first user material constant, in addition to a custom (or userdefined) system of units. For more information on defining custom systems of units or more information on systems of units in general, please refer to Appendix A.1 which provides a detailed discussion of the first user material constant.

•

Principal Material Coordinate System – Helius:MCT expresses constitutive relations and computes stress in the principal material coordinate system of the composite material. The second user material constant specifies the specific orientation of the principal material coordinate system that will be used by Helius:MCT. •

Unidirectional Microstructures: Helius:MCT’s default principal material coordinate system is oriented with the ‘1’ direction aligned with the fiber direction, while the ‘2’ and ‘3’ directions lie in the material’s plane of transverse isotropy. This default orientation of the principal material coordinate system is selected by setting the second user material constant to a value of 1. However, in situations where it adds convenience or simplicity to the model creation process, the user may change the orientation of the principal material coordinate system so that the ‘2’ direction is aligned with the fiber direction, while the ‘1’ and ‘3’ directions lie in the composite material’s plane of transverse isotropy. This alternative orientation of the principal material coordinate system is selected by setting the second user material constant to a value of 2. In general, the numerical value of the second user material constant identifies the specific principal material axis that is aligned with the fiber direction. For more information, refer to Appendix A.2 which provides a detailed discussion of the second user material constant.

•

Woven Microstructures: Helius:MCT’s default principal material coordinate system is oriented with the ‘1’ direction aligned with the fill tow direction, while the ‘2’ direction

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corresponds to the warp tow direction and the ‘3’ direction corresponds with the out-ofplane direction. This default orientation of the principal material coordinate system is selected by setting the second user material constant to a value of 1. However, in situations where it adds convenience or simplicity to the model creation process, the user may change the orientation of the principal material coordinate system so that the ‘2’ direction is aligned with the fill tow direction, while the ‘1’ direction corresponds to the warp tow direction. This alternative orientation of the principal material coordinate system is selected by setting the second user material constant to a value of 2. Additionally, the user may change the orientation of the principal material coordinate system so that the ‘3’ direction is aligned with the fill tow direction while the ‘2’ direction corresponds to the warp tow direction. This particular orientation of the principal material coordinate system is selected by setting the second user material constant to a value of 3. In general, the numerical value of the second user material constant identifies the specific principal material axis that is aligned with the fill tow direction. For more information, refer to Appendix A.2 which provides a detailed discussion of the second user material constant. •

•

Progressive Failure Analysis – The third user material constant activates or deactivates Helius:MCT’s progressive failure analysis feature. If the progressive failure feature is activated, then Helius:MCT will routinely evaluate both the matrix and fiber failure criterion to determine if either constituent material has failed. Each constituent failure criterion is based on the corresponding constituent average stress state. In the event that one or both of the constituents fail, the stiffnesses of the failed constituent(s) and the stiffnesses of the composite are appropriately reduced to the respective post-failure stiffnesses. It should be emphasized that the progressive failure analysis feature is the foundation component of Helius:MCT’s nonlinear multiscale constitutive relations. Other aspects of material nonlinearity can be invoked via the 4th, 5th and 6th user material constants; however, these additional forms of nonlinearity cannot be activated unless the progressive failure analysis feature is also activated. For more information on the progressive failure analysis feature, refer to Appendix A.3 of this document and Section 4 of the Helius:MCT Theory Manual. •

Unidirectional Microstructures: A value of 1 activates the progressive failure analysis feature, while a value of 0 deactivates the progressive failure analysis feature.

•

Woven Microstructures: A value of 0 deactivates the progressive failure feature, a value of 1 activates the progressive failure feature and uses the matrix and fiber degradation levels from the material data file to calculate the failed material properties, and a value of 2 activates the progressive failure feature and uses the matrix and fiber degradations levels specified by the twelfth and thirteenth user material constants to calculate the failed material properties. Selecting a value of 2 for plain weaves will add approximately 45-60 seconds to the pre-processing time per woven material. A value of 1 will not add run-time during pre-processing because the failed material properties (at the matrix and fiber degradation levels specified during material creation in Helius Material Manager) are already stored in the material file.

Pre-Failure Nonlinearity (optional, for unidirectional composites only) – The fourth user material constant activates or deactivates Helius:MCT’s Pre-Failure Nonlinearity feature. A value of 1 activates the pre-failure nonlinearity feature, while the default value of 0 deactivates the pre-failure nonlinearity feature. If the pre-failure nonlinearity feature is activated, then

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Helius:MCT will explicitly account for the nonlinear longitudinal shear stress/strain response that is typically observed in unidirectional fiber-reinforced composite materials. The Pre-Failure Nonlinearity feature imposes a series of discrete reductions in the longitudinal shear stiffness of the matrix constituent material, causing the composite material’s nonlinear longitudinal shear response to closely match experimentally measured data. It should be emphasized that the PreFailure Nonlinearity feature only affects the longitudinal shear moduli of the composite c c c c (i.e., σ12 vs. ε12, and σ13 vs. ε13), while the responses of the other four composite stress and strain components remain unaffected by this feature. Also, the Pre-Failure Nonlinearity feature will not alter the shear stress level at which the composite fails; however, it will result in an overall increase in longitudinal shear deformation of the composite prior to failure. For further information on the Pre-Failure Nonlinearity feature, refer to Appendix A.4 of this document and Section 5 of the Helius:MCT Theory Manual. Note: The Pre-Failure Nonlinearity feature is only available for unidirectional composite materials. The fourth user material constant is ignored by woven composites. •

Post-Failure Nonlinearity and Energy-Based Degradation (optional, for unidirectional composites only) – The fifth user material constant activates or deactivates Helius:MCT’s PostFailure Nonlinearity feature or Helius:MCT’s Energy-Based Degradation feature. A value of 1 activates the Post-Failure Nonlinearity feature, a value of 2 activates the Energy-Based Degradation feature, and the default value of 0 deactivates both the Post-Failure Nonlinearity and Energy-Based Degradation features. •

Post-Failure Nonlinearity: If the Post-Failure Nonlinearity feature is activated, then Helius:MCT will gradually reduce the stiffness of the matrix constituent moduli to their minimum values. When the Post-Failure Nonlinearity feature is activated, the matrix failure criterion simply identifies the initiation of the matrix failure process (or the initiation of matrix cracking). After the matrix failure criterion is triggered, the matrix constituent stiffness is gradually reduced via a series of discrete stiffness reductions that are applied as the matrix average strain state continues to increase beyond the level present at failure initiation. For further information on Post-Failure Nonlinearity, refer to Appendix A.5 of this document and Section 6 of the Helius:MCT Theory Manual.

•

Energy-Based Degradation: If the Energy-Based Degradation feature is activated, then Helius:MCT will gradually reduce the stiffness of the composite moduli to their minimum values in a linear fashion after a failure event has been detected while conserving the energy given in the twelfth and thirteenth user material constants. If three-dimensional elements are used with Energy-Based Degradation, the eleventh user material constant represents the average thickness of the three-dimensional elements. When the Energy-Based Degradation feature is activated, the constituent failure criteria simply identify the initiation of the constituent failure process. After a failure criterion is triggered, the composite stiffness is gradually reduced via a series of discrete stiffness reductions that are applied as the composite strain state continues to increase beyond the level present at failure initiation. The specific stiffness that is affected depends entirely on the constituent failures that have been triggered. For further information on EnergyBased Degradation, refer to Appendix A.5 of this document and the Helius:MCT Theory Manual.

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Note: Both the Post-Failure Nonlinearity and Energy-Based Degradation features are only available for unidirectional composite materials. The fifth user material constant is ignored by woven composites. Note: The Post-Failure Nonlinearity and Energy-Based Degradation features are mutually exclusive. Note: The Post-Failure Nonlinearity feature is only available for those unidirectional ult composite materials where the transverse tensile failure strain ( ε22 ) was supplied during the MCT material characterization process. If this feature is requested for a composite material that was characterized without a transverse tensile failure strain, then Helius:MCT will issue an error message at runtime and execution will halt. For more information on the MCT material characterization process, please refer to the Helius Material Manager User’s Guide. Note: If the Post-Failure Nonlinearity feature is turned on, then the matrix post-failure stiffness value (the twelfth user material constant) is ignored. Note: If the Energy-Based degradation feature is turned on, then the twelfth and thirteenth user material constants represent the energies dissipated for a matrix and fiber failure, respectively. Note: If the Energy-Based degradation feature is turned on, the minimum number of solution-dependent MCT state variables must be increased from 6 to 10. •

Hydrostatic Strengthening (optional, for unidirectional composites only) – The sixth user material constant activates or deactivates Helius:MCT’s hydrostatic strengthening feature. A value of 1 activates the hydrostatic strengthening feature, while the default value of 0 deactivates the hydrostatic strengthening feature. If the hydrostatic strengthening feature is activated, then Helius:MCT explicitly accounts for the experimentally observed strengthening of the composite in the presence of a hydrostatic compressive stress. If the hydrostatic compressive stress in the matrix constituent exceeds a threshold value, then the strength of both the matrix constituent and the fiber constituent are scaled upwards commensurate with the level of hydrostatic compressive stress level in the matrix constituent. For further information on the hydrostatic strengthening feature, refer to Appendix A.6 of this document and Section 7 of the Helius:MCT Theory Manual. Note: The Hydrostatic Strengthening feature is only available for unidirectional composite materials. The sixth user material constant is ignored by woven composites.

•

Thermal Residual Stress (optional, for unidirectional composites only) – The seventh user material constant (0 or 1) is used to specify whether or not to explicitly account for thermal residual stresses in the response of the unidirectional composite material. If the seventh user material constant is specified as 1, then Helius:MCT computes the ply-level and constituent-level thermal residual stresses that are caused by the post-cure cool down from the stress-free temperature (i.e. cure temperature) to ambient temperature. In this case, the stress free temperature is read from the material data file (Mdata file) and ambient temperature corresponds to 72.5°F, 22.5°C or 295.65°K. If the seventh user material constant is specified as 1, ply-level and constituent-level thermal residual stresses will be present in the composite material prior to

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the application of any external mechanical and/or thermal loads that are imposed during the actual simulation. If the user chooses to explicitly account for thermal residual stresses in the analysis, then the user should verify the material data file (Mdata file) actually contains a defined stress free temperature; otherwise, the stress free temperature will default to 0° and the predicted thermal residual stresses will be quite erroneous. If the seventh user material constant is specified as the default value of 0, then thermal residual stresses are not included in the response of that particular composite material during the simulation. In this case, the stress free temperature of the composite material defaults to Tsf =0° (regardless of the system of units employed), and the temperature change that is used in the constitutive relations [σ = C(ε−α∆T)] is simply computed as ∆T = T − Tsf = T. Several points should be emphasized here. First, the stress free temperature Tsf defaults to 0° even if the composite material data file (Mdata file) explicitly defines a non-zero stress free temperature. Second, regardless of the system of units that are employed by the finite element model, the current temperature T completely defines the temperature change ∆T that is used in the constitutive relations. Third, for composite materials that are characterized at multiple temperatures, the current temperature T will be used to interpolate the various material properties that contribute to the constitutive relations; consequently, it is recommended that a singletemperature characterization (i.e., a single-temperature Mdata file) should be used for the composite material in question. In summary, if the user does not request this option, then the current temperature T influences the constitutive relations in two different ways: 1) the temperature change used in the constitutive relations simply becomes ∆T=T, and 2) T is used to interpolate the temperature-dependent material properties that contribute to the constitutive relations. It should be emphasized that the default temperature in Abaqus/Standard is 0°. This default temperature is completely compatible with the default stress free temperature of 0° that is assumed when the seventh user material constant is specified as 0. In this case, the model can still be subjected to temperature changes by simply imposing a temperature other than 0°; however, these thermal stresses develop over the course of the analysis, as opposed to being present at the start of the analysis. •

User Material Constants 8-10 are not used and should be set to 0 or left blank.

•

Average Element Thickness – For analyses using Energy-Based Degradation, this value represents the average element thickness of the three-dimensional (i.e. solid) elements associated with the material. The average element thickness is used with solid elements to compute a representative element length that represents the area of the element in the plane of a lamina. For two-dimensional elements (i.e. shell elements and plane stress elements), this value is ignored, and should be entered as 1.0. Note: The Average Element Thickness is only available for analyses using Energy-Based Degradation. For analyses not using Energy-Based Degradation this value is ignored. Note: The Average Element Thickness is only available for unidirectional composite materials. The eleventh user material constant is ignored by woven composites.

•

Matrix Post-Failure Stiffness / Matrix Degradation Energy – For analyses not using EnergyBased Degradation, the twelfth user material constant is a fraction that is used to define the

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damaged elastic moduli of the matrix constituent after matrix constituent failure occurs. Specifically, the value is the ratio of the failed matrix constituent moduli to the unfailed matrix constituent moduli. A value of 0.1 would mean that after a matrix failure occurs at an integration m m m m m m point, all six of the matrix constituent moduli (E11, E22, E33, G12, G13, G23) are reduced to 10% of the original undamaged matrix constituent moduli. The matrix post-failure stiffness value must be greater than 0, and less than or equal to 1. By default, the matrix post-failure stiffness value is set to 0.1. If the post-failure nonlinearity feature is turned on, this value will be ignored. For more information on the matrix post-failure stiffness, please refer to Appendix A.12 of this documentation. For analyses using Energy-Based Degradation, this value is the total energy dissipated before and after a matrix failure assuming a linear degradation of composite stiffness after a c c c c c failure event. Specifically, composite E22, E33, G12, G13 and G23 are degraded after a matrix failure event according to this energy, the composite stress state at fiber failure, and the volume of the element. For more information on the computation of the energy values, refer to Appendix A.5 of this document and the Helius:MCT Theory Manual. Note: For unidirectional materials, if the Post-Failure Nonlinearity feature is turned on, then the twelfth user material constant will be ignored since the matrix post-failure stiffness is determined by the Post-Failure Nonlinearity feature. Note: For woven composites, if the matrix post-failure stiffness is specified, the third user material constant (Progressive Failure analysis) must be set to a value of 2. If the third constant is set to a value of 1, the twelfth user constant will be ignored. •

Fiber Post-Failure Stiffness / Fiber Degradation Energy –For analyses not using EnergyBased Degradation, the thirteenth user material constant is a fraction that is used to define the damaged elastic moduli of the fiber constituent after fiber constituent failure occurs. Specifically, the value is the ratio of the failed fiber constituent moduli to the unfailed fiber constituent moduli. A value of 0.01 would mean that after a fiber failure occurs at an integration point, all six of the f f f f f f fiber constituent moduli (E11, E22, E33, G12, G13, G23) are reduced to 1% of the original undamaged fiber constituent moduli. The fiber post-failure stiffness value must be greater than 0, and less than or equal to 1. The default value of the fiber post-failure stiffness is automatically set to 0.01. For more information on the fiber post-failure stiffness, please refer to Appendix A.12 of this documentation. For analyses using Energy-Based Degradation, this value is the total energy dissipated for a fiber failure assuming a linear degradation of composite stiffness before and after a fiber failure c c c event. Specifically, composite E11, G12, and G13 are degraded linearly after a fiber failure event according to this energy, the composite stress state at fiber failure, and the volume of the element. For more information on the computation of the energy values, refer to Appendix A.5 of this document and the Helius:MCT Theory Manual. Note: For woven composites, if the fiber post-failure stiffness is specified, the third user material constant (Progressive Failure analysis) must be set to a value of 2. If the third constant is set to a value of 1, the thirteenth user constant will be ignored

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•

User Material Constants 14, 15, 16 – .The 14th, 15th, and 16th user material constants are only required if the finite element model is defined using a custom system of units. If using a custom set of units, please refer to Appendix A.1 for formatting details.

Progressive failure analysis, pre-failure nonlinearity, post-failure nonlinearity, hydrostatic strengthening, post-failure stiffnesses and degradation energies do not apply to Helius:MCT Linear

4.2

Defining a Helius:MCT Cohesive Material

A Helius:MCT cohesive material is defined similar to a composite material (Section 4.1) using the three keyword statements *MATERIAL, *DEPVAR, and *USER MATERIAL. Consider the following lines from an Abaqus input file that completely specify a Helius:MCT user-defined cohesive material. *MATERIAL, name=cohesive *DEPVAR 9 *USER MATERIAL, constants=11 23, 1.0E+10, 1.0E+10, 1.0E+10, 1.0E+6, 1.0E+6, 1.0E+6, 100 200, 200, 1.25 For any given Helius:MCT cohesive material, the number of user material constants must be between 8 and 11. Appendix B provides a detailed description of each of the user material constants, including the range of allowable values for each constant and the impact that each constant has on the constitutive relations used to represent the material. Each of the user material constants typically defined in an analysis incorporating a Helius:MCT cohesive material are listed below along with a brief description. For a more detailed description of any particular user material constant, refer to the appropriate section of Appendix B. •

Damage Criteria - The first user material constant selects the damage initiation and damage evolution criteria. It is a two digit integer where the tens place holds the damage initiation criterion selection and the ones place holds the damage evolution type selection. The damage initiation flag can be 1 for maximum traction or 2 for a quadratic based criterion. The damage evolution flag can be 1 for displacement based softening, 2 for energy based, or 3 for energy based using a mixed mode power law. For example, if the first user material constant is 12 the maximum traction damage initiation criterion will be used with the energy based softening law.

•

Stiffnesses - User material constants 2-4 specify the material stiffness in the normal, first shear, and second shear directions respectively.

•

Strengths - User material constants 5-7 specify the maximum tractions the material can sustain before damage initiates in the normal, first shear, and second shear directions respectively.

•

Displacement Based Damage Evolution - The following user material constants must be defined if the displacement based damage evolution is chosen.

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o •

Energy Based Damage Evolution - The following user material constants must be defined if the energy based damage evolution is chosen. o

•

4.3

Effective Displacement at Failure - User material constant 8 is a positive number which defines difference in effective displacement at complete failure and at damage initiation.

Total Fracture Energy - User material constant 8 is a positive number which defines the total energy dissipated due to a failure. In mathematical terms, this is the area under the traction - separation curve.

Energy Based Damage Evolution (Mixed Mode Power Law) - The following user material constants must be defined if the energy based damage evolution with a mixed mode power law is chosen. o

Normal Mode Fracture Energy - User material constant 8 is a positive number which defines the total energy dissipated due to a pure normal mode failure.

o

First Shear Mode Fracture Energy - User material constant 9 is a positive number which defines the total energy dissipated due to a pure first shear mode failure.

o

Second Shear Mode Fracture Energy - User material constant 10 is a positive number which defines the total energy dissipated due to a pure second shear mode failure.

o

Power Law Exponent (Alpha) - User material constant 11 is a positive exponent used in the mixed mode power law function used to determine the rate of softening in the damaged cohesive material.

Modifying the Section Definitions

After creating new material definitions for each of the Helius:MCT composite materials that appear in the Abaqus input file (described previously in Section 4.1), the next step is to incorporate the new materials into the various Section definitions that appear in the Abaqus input file. This process simply involves changing the name of each material ply in the composite section layup to the name of a valid Helius:MCT material that was defined as described in Section 4.1. For example, consider the following shell section definition excerpted from an Abaqus input file. *SHELL SECTION, elset=PlateLayup-1, composite, orientation=Ori1, stack direction=3, layup=PlateLayup 1., 3, MATERIAL_1, 0, Ply-1 1., 3, MATERIAL_1, 45, Ply-2 1., 3, MATERIAL_1, -45, Ply-3 1., 3, MATERIAL_1, 90, Ply-4 1., 3, MATERIAL_1, 90, Ply-5 1., 3, MATERIAL_1, -45, Ply-6 1., 3, MATERIAL_1, 45, Ply-7 1., 3, MATERIAL_1, 0, Ply-8 The composite section layup contains eight material plies, where each ply is composed of a material named "MATERIAL_1". This material name should be replaced by the name of the appropriate

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Helius:MCT material, for example, "IM7_8552" as defined in Section 4.1. The updated shell section definition is shown below. *SHELL SECTION, elset=PlateLayup-1, composite, orientation=Ori1, stack direction=3, layup=PlateLayup, 1., 3, IM7_8552, 0, Ply-1 1., 3, IM7_8552, 45, Ply-2 1., 3, IM7_8552, -45, Ply-3 1., 3, IM7_8552, 90, Ply-4 1., 3, IM7_8552, 90, Ply-5 1., 3, IM7_8552, -45, Ply-6 1., 3, IM7_8552, 45, Ply-7 1., 3, IM7_8552, 0, Ply-8 Certain types of Abaqus elements (e.g., beam elements, shell elements, and reduced integration elements) require extraneous stiffness parameters in order to stabilize their response against deformation modes that are not governed directly by material constitutive relations. These extraneous stiffness parameters are defined as either options or data in the Section keyword statement that is referenced by the element in question. Depending upon the specific type of element being used, one or more of the following types of extraneous stiffness parameters may need to be specified as part of the Section definition that is referenced by the element. • • • • •

Section Poisson Ratio Section Thickness Modulus ts ts ts Section Transverse Shear Stiffnesses: K11, K22, and K12 Membrane Hourglass Stiffness Control Parameter Bending Hourglass Stiffness Control Parameter

Appendix C.1 provides a detailed discussion of each type of extraneous stiffness parameter, in addition to listing the specific extraneous stiffness parameters that are required by each type of element. In earlier versions of Helius:MCT, the calculation of these extraneous stiffness parameters and their insertion in the Abaqus input file required a rather cumbersome manual procedure that is described in detail in Appendices C.2-C.4 of this User's Guide. However, Helius:MCT now includes an auxiliary program (xSTIFF) that automatically calculates and inserts the required extraneous stiffness parameters into the Abaqus input file. The use of xSTIFF is highly recommended as it greatly accelerates the model building process, while at the same time minimizing the chance for errors being introduced into the input file. With the availability of xSTIFF, the user can now postpone the task of defining the extraneous stiffness parameters until the model building process is completed and an Abaqus input file is saved. xSTIFF can then be run to automatically add any required extraneous stiffness parameters to the saved Abaqus input file. For more information on using xSTIFF to automatically calculate and insert the required extraneous stiffness parameters into the Abaqus input file, please refer to the xSTIFF User’s Guide. Note: If the user chooses to manually define the extraneous stiffness parameters, Appendices C.1-C.4 completely describe the processes of identifying the required extraneous stiffness parameters, calculating their values, and inserting the correctly formatted values into the Abaqus input file.

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For cohesive sections, the response parameter must be set to RESPONSE = TRACTION SEPARATION.

4.4

Modeling Issues for Imposing Temperature Changes

The composite materials that are stored in the Helius:MCT Composite Material Database are defaulted to have a stress-free temperature (cure temperature) of 0° in the system of units that is specified by the value of the 1st user material constant unless it is specified by the seventh user constant that the stress-free temperature stored in the material file should be used. Any initial temperature specified via the *INITIAL CONDITIONS, TYPE=TEMPERATURE statement (including the default value of 0°) will be used to calculate the residual stresses present in each of the constituents and the composite due to the unmatched coefficients of thermal expansion between the fiber and matrix. For details on how the temperature changes imposed in a model affect how Helius:MCT calculates residual stresses, please refer to Section 10 in the Helius Theory Manual.

4.5

Nonlinear Solution Control Parameters for Helius:MCT

It is a widely accepted notion that good convergence (or any convergence at all) is difficult to achieve in a progressive failure simulation of a composite structure. In fact, many progressive failure simulations terminate early, not due to global structural failure, but simply due to the inability of the finite element code to obtain a converged solution at a particular load step. In light of this problem, one of the major advantages of Helius:MCT is that it has been optimized to significantly improve the overall convergence rate and robustness of finite element simulations of progressive failure of composite structures. However, in order to take full advantage of the superior convergence characteristics of Helius:MCT, the user must change some of the default settings that govern the nonlinear solution process used by Abaqus/Standard. These changes can be enacted using the *CONTROLS keyword statement. In Abaqus/Standard, the default settings for the nonlinear solution process are based on the fundamental assumption of the Newton-Raphson algorithm that the nonlinear response of the composite structure is sufficiently smooth at both the global and local levels. However, in a progressive failure simulation of a composite structure, the nonlinear response of the composite structure is not smooth, especially at the local level where material failure results in an instantaneous reduction of material moduli. This non-smooth material response is one of the primary factors responsible for the difficulty in obtaining convergence in progressive failure simulations. Helius:MCT’s method of managing material nonlinearity is specifically designed to handle this localized non-smooth material response. However, the default settings of Abaqus’ convergence control parameters must be changed in order to allow Helius:MCT to improve the convergence characteristics of the finite element simulation. These default settings can be changed via the first data line of the *CONTROLS keyword statement. The *CONTROLS keyword statement should be placed in the input file immediately after the *STATIC keyword statement. The first data line in the *CONTROLS keyword statement contains 11 quantities. The default values of these 11 quantities are shown below in the *CONTROLS keyword statement below. *CONTROLS, PARAMETERS=TIME INCREMENTATION 4,8,9,16,10,4,12,5,5,3,50 Qualitatively speaking, the changes that should be made to these default values are intended to significantly increase the number of equilibrium iterations that Abaqus/Standard will perform before the code evaluates the need for a reduction (or cut-back) in the time increment size. If Helius:MCT is used in

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the finite element solution, then the Abaqus input file should use the following *CONTROLS keyword statement. *CONTROLS, PARAMETERS=TIME INCREMENTATION 1000,1000,1000,1000,1000, , , , ,10,1000 Note that the value of the quantities 1, 2, 3, 4, 5 and 11 have been set to 1000, while the value of the 10th quantity has been set to 10. For all other quantities on the data line, the default values are acceptable. These changes force Abaqus to wait until 1000 equilibrium iterations have been completed before evaluating the need to reduce the time increment size. The familiar *STATIC keyword statement is present in the Abaqus input file for all quasi-static analyses. The single data line used by the *STATIC statement contains four quantities that collectively specify the desired time incrementation scheme. The first quantity specifies the size of the initial time increment. The second quantity specifies the total amount of time to be analyzed in the current step. The third quantity specifies the minimum allowable size of the time increments used in the current step. The fourth quantity specifies the maximum allowable size of the time increments used in the current step. Since the use of Helius:MCT significantly improves the ability of Abaqus to obtain a converged solution for any particular time increment, it is likely that the entire analysis can be performed without any time increment reductions; therefore, the user may wish to experiment with the parameters that he or she routinely employs in the data line of the *STATIC keyword statement. Nonlinear Solution Control Parameters are not used in Helius:MCT Linear.

4.6

Requesting Output of the MCT State Variables

Solution-dependent MCT state variables are used to track the history of certain quantities that are computed in the Helius:MCT User-Defined Material Subroutine. Appendix D describes all 34 of the MCT state variables that pertain to unidirectional composites and all 90 of the MCT state variables that pertain to woven composites. These MCT state variables are not written to the output database file unless explicitly requested in the Abaqus input file. To request MCT state variable output, the user must add the identifying key ‘SDV’ to the list of output variables that are requested in the *ELEMENT OUTPUT keyword statement. For example, the following *ELEMENT OUTPUT keyword statement requests that stresses (S), strains (E), and MCT state variables (SDV) should be written in the output database file (note that the stresses (S) and strains (E) are not necessary for a Helius:MCT analysis but are included here for demonstrative purposes): *ELEMENT OUTPUT S,E,SDV It should be emphasized that the number of MCT state variables that are written to the output file depends on the number of state varaibles that are requested by the *DEPVAR statement Another issue that should be considered when requesting output is the number and location of the section points where the output variables are calculated. In an element that contains multiple material layers, the default section points correspond to the top and bottom surface of the element, thus the output variables are not available for any of the internal material layers. If the user wishes to view the output variables for each of the material layers within an element, the user must explicitly list the section points

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where the output variables should be computed. As an example, consider a 4 ply composite plate with 3 section points per ply, for a total of 12 section points as shown in Figure 9. By default, the output variables will only be computed for section points 1 and 12 corresponding to the top and bottom surfaces of the element. In order to view results for each material layer of the element, it is most expedient to request that the output variables should be computed at the mid-surface of each material layer (i.e., section points 2, 5, 8, 11). In order to request specific section points for the calculation of output variables, the user must add a data line immediately after the *ELEMENT OUTPUT keyword statement. This data line lists the specific section points where the output variables will be computed. For example, the following *ELEMENT OUTPUT keyword statement requests calculation of stress (S), strain (E) and the MCT state variables (SDV) at section points 2, 5, 8 and 11. *ELEMENT OUTPUT 2,5,8,11 S,E,SDV X

12 X 11 X X

6 5 X4

9 X8 X7

X

10

X X

3 X2 X1

Ply 4 Ply 3 Ply 2 Ply 1

Figure 9: Location of section points within an element containing 4 material plies

Be aware that Abaqus allows only 16 quantities to be entered on the section point data line of the *ELEMENT OUTPUT keyword statement. For elements that contain large numbers of material layers, more than one *ELEMENT OUTPUT keyword statement is required to request all of the desired section points. For example, consider an element with 24 material layers. The following pair of *ELEMENT OUTPUT keyword statements is used to request output at the mid-surface of each of the 24 material layers. *ELEMENT OUTPUT 2,5,8,11,14,17,20,23,26,29,32,35,38,41,44,47 S,E,SDV *ELEMENT OUTPUT 50,53,56,59,62,65,68,71 S,E,SDV

4.7

Modeling Damage Tolerance in Composite Materials

Damage tolerance is the ability of a structure to retain required structural strength or stiffness after it has sustained damaged. When a composite part is damaged, there are numerous failure modes that can exist. These failure modes are constituent-level defects (i.e. fiber and matrix level defects), so it is appropriate to model damage at this level. Helius:MCT is well-suited for modeling damage tolerance because it allows the user to specify constituent-level damage in elements at the start of the analysis. For

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example, if a plate was impacted by a mass and there is diffuse matrix damage in impacted region, the user can create an element set that represents the damaged region and assign matrix failure to that region prior to the start of the analysis. At the start of the analysis, this region will have an SDV1 value of 2 (matrix failure) and as the simulation progresses, the region can undergo fiber failure which will result in an SDV1 value of 3. In other words, the initial value of SDV1 that is assigned to the element set is not fixed and can change if either the matrix or fiber failure criterion is satisfied. The initial value of SDV1 must be an integer value equal to 1, 2, or 3. For unidirectional materials, 1 corresponds to no failure, 2 corresponds to matrix failure, and 3 corresponds to fiber and matrix failure. For plain weaves, 1 corresponds to no failure, 2 corresponds to matrix failure in all tows and the matrix pocket, and 3 corresponds to fiber failure in all tows plus matrix failure in all tows and the matrix pocket. The Abaqus keyword, *INITIAL CONDITIONS, TYPE=SOLUTION is used to activate damage tolerance and is not supported by Abaqus/CAE. The following keyword statement demonstrates the use of damage tolerance with Helius:MCT. *INITIAL CONDITIONS, TYPE=SOLUTION DAMAGED_ELEMENTS, 3 In the above statement, DAMAGED_ELEMENTS is the name of the element set that represents the failed region and 3 indicates that this region will have fiber and matrix damage at the start of the analysis.

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5 Running Helius:MCT on Linux Before running Helius:MCT in a Linux environment it is assumed the following steps are done: •

The Abaqus input file has been created

•

The utility provided by Firehole Composites to automatically write extraneous stiffness parameters to an Abaqus input file, xSTIFF, is not supported on Linux. Therefore, if the target input file uses any elements or sections that require extraneous stiffness parameters, xSTIFF must be executed on a supported Windows machine prior to copying the input file to the target Linux machine.

•

The necessary Helius:MCT material files have been created and stored in the Firehole materials directory. Note the following. o

The application used to create Helius:MCT material files, Helius Material Manager, is not supported on Linux. Therefore, material files must be created on a supported Windows machine and copied to the target Linux machine.

o

Helius:MCT resolves material files via the following convention: MATERIAL_FILE_DIR/Material_Name/mdata.xml where Material_Name is the name of the name of the material in the Abaqus input file. Unlike Windows, Linux directories are case sensitive and Abaqus always modifies material names to use all upper-case characters. Therefore the Material_Name folder must always be in upper-case text.

•

Abaqus has been pointed to the Helius:MCT libstandardU.so file. This is done via the usub_lib_dir variable in the abaqus_v6.env file. The variable must be set as one of the following (replace with the path of the base Firehole installation directory, i.e., /usr/local/firehole): o o

usub_lib_dir = '/hmct/4.0' - For non cluster jobs usub_lib_dir = '/hmct/4.0/mimd' - For jobs run on a cluster of machines utilizing the Message Passing Interface (MPI).

This variable can be set in the global abaqus_v6.env file or if multiple users run jobs on this machine it is recommended to copy this file into the appropriate user's home directory. From there it can be modified. This file can also reside in the current working directory. Abaqus searches for this file in the following order: o Current working directory o The user's home directory o The Abaqus site directory See sections 3.1.1, and 3.2.2 of the Abaqus Analysis User's Manual for more information on the abaqus_v6.env file and the usub_lib_dir variable. Once the above steps have been performed, the input file can be executed just as any other standard Abaqus analysis.

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6 Examining Helius:MCT Results with Abaqus/Viewer This section discusses the use of Abaqus/Viewer to examine the finite element results that are generated by Helius:MCT. It is assumed that the reader is familiar with using Abaqus/Viewer to view finite element results and perform any necessary post-processing of finite element results. Therefore, this section focuses on issues that are unique to the processes of examining and interpreting the progressive failure results generated by Helius:MCT. This section is divided into two parts, the first of which focuses on the generation of contour plots for the MCT state variables. The second part deals with the issue of correlating damage distribution with overall changes in structural stiffness, including the detection of global structural failure.

6.1

Using contour plots to view the MCT state variables

The MCT state variables are element output variables stored at each integration point within each element. Consequently, the same familiar methods used to view the stress and strain fields at each time increment can be used to view the MCT state variables. However, in order to view any of the MCT state variables in Abaqus/Viewer, the Abaqus input file must first request that they be written to the Abaqus output database file (see Sections 3.5 and 4.5). For a complete description of each of the MCT state variables, refer to Appendix D. Contour plots are usually the most appropriate means of examining the distribution of the MCT state variables. To generate a contour plot within Abaqus/Viewer, click the contour icon or select Plot  Contours  On Deformed Shape from the main toolbar. The default variable Abaqus/Viewer plots is the von Mises stress. To view the MCT state variables that are computed by Helius:MCT, open the Field Output dialog box by selecting Result  Field Output from the main toolbar. The MCT state variables (SDV1, SDV2, SDV3, …, etc.) are listed within the Field Output dialog box along with the more familiar variables such as stress (S) and strain (E). The number of SDVs that are available in the Field Output dialog box depends entirely on the number of SDVs that were requested by the Abaqus input file via the *DEPVAR keyword statement. Note that the SDV variables may have been renamed (SDV1 → MAT_STATE, SDV2 → FI_MATRIX, etc.) by the same *DEPVAR keyword statement. The fundamental MCT state variable is SDV1 which indicates the discrete damage state of the composite material. SDV1 is a real variable that can assume a finite number of discrete values between 1.0 ≤ SDV1 < 4.0. The specific set of discrete values that can be assumed by SDV1 depends upon the type of composite material (unidirectional or woven) and the specific set of material nonlinearity features that are used by Helius:MCT during the finite element solution (see Appendix D). As a specific example, if Helius:MCT is used on a unidirectional microstructure with its progressive failure feature activated and its pre-failure and post-failure nonlinearity features de-activated, then SDV1 can only assume the values 1.0, 2.0, or 3.0 as shown in the table below. However, regardless of the features requested, all the discrete values of SDV1 between 1 and 2 generally indicate some level of matrix failure, and all values between 2 and 3 generally indicate some form of fiber failure. An MCT file (*.mct) is generated when a Helius:MCT enhanced analysis is submitted and contains the specific set of values that can be assumed by SDV1 for each material in the model. It should be noted that contour plots of fully-integrated elements can show values of SDV1 that are less than 1 and greater than 4. This is entirely due to the scheme Abaqus uses to compute contour values. For element-based values, such as SDV1, the computations vary depending on several criteria. In general, the extrapolation of integration point values to the nodal locations is the reason SDV1 can be less than 1 and greater than 4 for fully-integrated elements. To view the exact values for SDV1 at each Helius:MCT User’s Guide – Abaqus

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integration point within a specific element, use the Probe Values tool in the Abaqus Query toolset. For more information on how contour values are computed, refer to Section 42.1.1 of the Abaqus/CAE v6.10 User’s Manual. Unidirectional Microstructure Progressive Failure Analysis (activated) Pre-Failure Nonlinearity (de-activated) Post-Failure Nonlinearity (de-activated) Allowable Discrete Values for SDV1 1.0 2.0 3.0

Discrete Composite Damage State No Failure or Degradation Matrix Failure only Matrix & Fiber Failure

Because SDV1 is a discrete real variable taking values 1.0 ≤ SDV1 < 4.0, it is important for the user to change the settings of Abaqus/Viewer so that a unique color contour is associated with each discrete value of integer value of SDV1. In the case where SDV1 can assume values of 1.0, 2.0, or 3.0, the user should set the number of color contours to 3. The number of contour intervals used in a contour plot can be specified from the Contour Plot Options dialog box, which is accessed by clicking Options  Contour from the main toolbar. The Contour Plot Options dialog box is shown in Figure 10. Under the heading ‘Contour Intervals’, the user should choose ‘Discrete’ and then use the slider bar to select the number of discrete color contours to match the number of integer values that SDV1 can assume.

Figure 10: Contour Plot Options dialog box

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Figure 11 shows two different 3-color contour plots of the integer variable SDV1 for an axially loaded composite plate with a central hole. In Figure 11, the use of three discrete colors makes it easy to identify the regions where each of the three discrete composite damage states occur. The blue elements (SDV1=1) are completely undamaged; the green elements (SDV1=2) have failed matrix constituents and undamaged fibers; the red elements (SDV1=3) have failed matrix constituents and failed fiber constituents. Note that the quilt contour plot shows the average value of SDV1 for each individual element, while the banded contour plot simply uses the values of SDV1 at the individual integration points to establish the color contours independent of the element boundaries.

Figure 11: Comparison of a banded contour plot and a quilt contour plot using three discrete color contours to represent distribution of SDV1=1,2,3

The remaining MCT state variables (SDV2, SDV3, SDV4, …,SDV90) are continuous real variables. Therefore, in generating contour plots of these variables, it is not critical to manage the number of color contours. Furthermore, the standard practices used in viewing stress and strain distributions are also appropriate for viewing SDV2, SDV3, SDV4, …, etc..

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Selection of Section Points When viewing finite element solution results for laminated composite structures, the user must be acutely aware of the numbering of the section points through the thickness of multilayer elements. A contour plot will only use the values of the variable stored at a particular section point. Therefore, to view a contour plot for a specific material layer, the user must choose a section point that lies within that material layer. To choose a specific section point, access the Section Points dialog box by selecting Results  Section Points from the main toolbar. The Section Points dialog box is shown in Figure 12. The default section point that is plotted by Abaqus/Viewer is the bottom section point (i.e., the section point at the bottom of the element). To view results for a particular material ply, the Plies option can be checked and the appropriate ply can be selected. To view results for all section points in the same plot, an envelope plot can be used by selecting the Envelope option. Envelope plots show the maximum absolute, maximum, or minimum value of the selected variable across all of the plies in a layup. For more information on selecting section points, refer to Section 40.4.8 of the Abaqus/CAE v6.10 User’s Manual.

Figure 12: Section Points dialog box

As an example of the above recommendations, consider Figure 13 which shows envelope quilted contour plots of SDV1=1,2,3 at several points in time during a progressive failure analysis of a composite plate with a central hole. The plate has eight material plies and is loaded in tension. Since these contour plots are envelope plots, the color at any location represents the highest value of SDV1 that is achieved at any of the section points distributed through the thickness of the 8-ply laminate. In these plots, blue elements have no failure at any of the section points that are distributed through the laminate thickness. The green elements have at least one section point where matrix failure has occurred, while the red elements have at least one section point where both matrix failure and fiber failure occurred.

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Figure 13: Envelope, quilted contour plots of SDV1 at several different points in time during a progressive failure analysis

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Several important observations can be made regarding the sequence of envelope quilted contour plots shown in Figure 13: • • • • • •

6.2

At time = 0.3, every element is blue, which means that no points in the composite plate have experienced any type of failure. At time = 0.4 there are some green elements at the edges of the hole. Within these green elements, at least one material ply has experienced a matrix constituent failure. However, the plot does not specify which of the material plies have experienced a matrix constituent failure. Comparing the plots at times 0.4 and 0.5 indicates the progression of matrix constituent failure as the load increases. At time = 0.7, the matrix failure has spread further, and there are three elements with fiber failure, as indicated by the red elements. Again, the red elements indicate that at least one of the 8 material plies has experienced a fiber constituent failure. At time = 0.9045, there is significant matrix failure, and the fiber failure has spread out towards the plate edges. At time = 1.0, there is additional matrix and fiber failure.

Detection of global structural failure

In Section 6.1, we used color contour plots to examine the distribution of the discrete composite failure state (SDV1) within a composite structure. In viewing these contour plots, it is easily appreciated that each of the damaged regions represents material whose stiffness has been significantly degraded. Furthermore, by examining the changes that occur in these contour plots over time, we can clearly see the cascade of localized material failure that occurs during a progressive failure analysis. However, viewing the distribution of material failure does not provide any indication of the overall impact of the material failure on the global stiffness of the structure. Moreover, it is impossible to detect global structural failure by simply examining the distribution of material failure over the structure. In order to detect global structural failure or to associate a particular distribution of damage with a decrease in overall structural stiffness, we must first examine the relationship between global structural force and global structural deformation. This type of relationship is best examined using a simple 2-D plot of force vs. deformation; however, the key issue is to select an appropriate measure of global structural force and an appropriate measure of global structural deformation. As an example, let us consider an 8-ply composite plate shown in Figure 14. Note that this is the same composite plate problem examined earlier in Section 6.1. As seen earlier in Figure 13, the distribution of damage within the composite plate is shown at several different points in time over the course of the analysis. However, simply viewing the contours plots shown in Figure 13 does not provide us with an understanding of how each of the damage distributions affects the global structural stiffness of the composite plate. To understand the degradation of global structural stiffness as localized failures spread throughout the composite plate, let us examine a simple 2-D plot of global structural force vs. global structural deformation. Since this composite plate is subjected to a uniform axial displacement that is imposed along the top edge of the plate, the imposed axial displacement will serve as an appropriate measure of the overall structural deformation in the plate. Similarly, the total axial reaction force along the top edge of the plate will serve as an appropriate measure of global structural force in the plate. This total reaction force is obtained by summing the nodal reaction forces for all of the nodes on the top edge of the plate (see Figure 15). Figure 16 shows a plot of global structural force vs. global structural deformation for the composite plate.

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Figure 14: 8-ply composite plate under imposed axial displacement

Figure 15: The global structural force is obtained by summing the vertical reactions forces at all nodes along the top edge of the composite plate

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Figure 16: Global structural force vs. global structural deformation

Beginning at an imposed displacement of 0.13, the overall secant stiffness of the structure starts to deteriorate rapidly. Beyond this point, as the imposed axial displacement is further increased, the structure is unable to resist the additional imposed displacement with additional structural force. Examination of Figure 16 reveals that the global force/displacement response of the composite structure appears to remain linear until the imposed displacement reaches a value of approximately 0.095. Interestingly, if we examine Part C of Figure 13, we see that by the time the imposed axial displacement has reached the value of 0.08, the composite plate has accumulated a significant amount of matrix constituent failure along the vertical edges of the circular hole. However, this amount of matrix constituent failure is insufficient to make a visually detectable impact on the global stiffness of the composite plate. As the imposed displacement is increased from 0.095 to approximately 0.13, the global stiffness of the composite plate undergoes a visually detectable reduction in Figure 16; however, the structure is still able to respond to increasing displacement with increasing structural force. In examining Part D of Figure 13, we see that at an imposed displacement of 0.112, the composite plate has experienced a small amount of fiber constituent failure along the vertical edges of the circular hole. Note that this localized fiber constituent failure has not yet prevented the composite plate from responding to increased displacement with increased structural force. As the imposed displacement reaches approximately 0.133, the global stiffness of the composite plate exhibits a drastic reduction indicting a significant cascading of localized fiber constituent failures (i.e., a major failure event has occurred). As the imposed displacement is increased beyond 0.133, the composite plate no longer responds to increasing Helius:MCT User’s Guide – Abaqus

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displacement with increasing structural force. Instead, the overall structural force in the composite plate remains relatively constant, indicating that the spread of localized failures is too rapid to build any additional structural force. However, as seen by the two dotted lines in Figure 16, the overall secant stiffness of the composite plate continues to decrease despite the fact that the overall structural force remains relatively constant. There are many possible ways to define global structural failure. The exact point that signals global structural failure depends upon the intended use of the composite plate. The point that should be emphasized here is that the detection of global structural failure requires an examination of the global structural force vs. global structural deformation. In summary, contour plots of the MCT state variables (especially SDV1) provide the analyst with a clear picture of the extent of localized failures at any particular point in time. In order to correlate any of the damage distributions with decreased overall stiffness of the composite structural, one must examine plots of global structural force vs. global structural deformation. In this way, the analyst can associate observed changes in the global stiffness of the structure with specific damage distributions.

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Appendix A

User Material Constants for Composite Materials

A set of user material constants are provided in the data line that immediately follows the *USER MATERIAL keyword statement. The Helius:MCT User-Defined Material Subroutine uses these constants to determine the precise form of multiscale constitutive relations that should be used for the composite material. For any type of Helius:MCT composite material, the number of user material constants must be between 3 and 16. The first three user material constants are required for all Helius:MCT materials. The last three user material constants (i.e., the 14th, 15th, and 16th constants) are only required if the finite element model is defined using a custom system of units (see Appendix A.1). Table A1 provides a short description of the constitutive modeling issue that is controlled by each of the possible user material constants along with the allowable range of values for each constant. Material constants 3-6 and 11-13 are not used in Helius:MCT Linear.

Table A1. Helius:MCT User Material Constants For Composite Materials

User Material Constant 1

Constitutive Issue Controlled by the User Material Constant System of Units

2

Principal Material Coordinate System

3

Progressive Failure Analysis

4

Pre-Failure Nonlinearity

5

Post-Failure Nonlinearity / EnergyBased Degradation

6

Hydrostatic Strengthening

7

Stress Free Temperature

8 9 10 11

Not currently used Not currently used Not currently used Average Element Thickness Matrix Post Failure Stiffness / Matrix Degradation Energy Fiber Post Failure Stiffness / Fiber Degradation Energy Force Conversion for Custom Units Length Conversion for Custom Units Temperature Difference Conversion for Custom Units

12 13 14 15 16

Allowable Values 1,2,3,4,5 Unidirectional → 1, 2 Woven → 1, 2, 3 Uni → 0 (off), 1 (on) Woven → 0 (off), 1 or 2 (on) 0 (off), 1 (on) 0 (off) 1 (Post-Failure Nonlinearity) 2 (Energy-Based Degradation) 0 (off), 1 (on) 0 (0°), 1 (temperature read from material file) 0 or blank 0 or blank 0 or blank Must be greater than zero 0 < value ≤ 1 / Must be greater than zero 0 < value ≤ 1 / Must be greater than zero Must be greater than zero Must be greater than zero Must be greater than zero

In the remainder of Appendix A, each of the material constants is discussed in detail, including the impact of the constant on the multiscale constitutive relations used to represent the composite material.

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Appendix A.1

User Material Constant #1: Systems of Units

All numerical quantities in a finite element input file must be expressed in a consistent set of units. For example, if the geometry of the model is specified in centimeters and the force is specified in Newtons, then the material moduli must be expressed in units of N/cm2. All material properties in the Helius:MCT composite material database are stored using the (N/m/K) system of units (i.e., force is expressed in Newtons, length is expressed in meters, and temperature is expressed in degrees Kelvin). Therefore, if a model is built using a different system of units, then the user must identify the appropriate system of units so that Helius:MCT can provide stiffness and stress to the Abaqus/Standard finite element code in the correct units. Helius:MCT has preprogrammed conversion factors that can be used to express constitutive information in several commonly used systems of units. In addition, Helius:MCT has the capability to provide constitutive information in a user-defined (or custom) system of units. The system of units that will be used by the Helius:MCT User-Defined Material Subroutine is defined by the first user material constant listed on the data line that immediately follows the *USER MATERIAL statement. Table A2 shows the allowable range of integer values for the first user material constant and lists the system of units specified by each value. Table A2. System of Units specified by User Material Constant #1

User Material Constant #1 1 2 3 4 5

System of Units N, m, K N, mm, K lb, in, R lb, ft, R Custom

If the first user material constant is assigned a value of 1, 2, 3, or 4, then Helius:MCT will automatically perform the appropriate unit conversions and provide the constitutive relations in the system of units shown in Table A2. However, if the model is defined using a system of units that is not represented in Table A2, then the user must set the value of the first user material constant to 5, indicating that a 'custom' system of units will be used. In this case, the user must specify the three conversion factors that are needed by Helius:MCT to convert from the default units of Newtons, meters, and Kelvin to the custom system of units. These three conversion factors for force, length, and temperature will be listed as the 14th, 15th, and 16th user material constants respectively in the data line of the *USER MATERIAL statement. Note that the 14th, 15th, and 16th user material constants are required only if the value of the 1st user material constant is 5. As an example of a custom system of units, let’s say that a finite element model is created using units of kilonewtons, centimeters, and degrees Fahrenheit. Since this particular system of units is not included in Table A2, it will be considered a custom system of units. Consequently the first user material constant for any Helius:MCT materials should be assigned a value of 5. Now we must compute the conversion factors for force, length, and temperature that will be listed as the 14th, 15th, and 16th user material constants respectively. The force conversion factor that is required to convert from the default units of Newtons, to the desired units of kilonewtons is computed as,

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Fconv =

1kN kN . = 0.001 1000 N N

The length conversion factor that is required to convert from the default units of meters, to the desired units of centimeters is computed as,

Lconv =

100cm cm . = 100 1m m

The conversion factor for temperature changes (∆T) that is required to convert temperature change from the default units of K to the desired units of °F is computed as, ∆ Tconv =

°F 9 / 5° F . = 1.8 1K K

The 14th, 15th, and 16th user material constants should be assigned values of 0.001, 100, and 1.8 respectively. In this case, the data line immediately following the *USER MATERIAL statement would have sixteen user material constants as shown below. The first user material constant (value=5) indicates that a ‘custom’ system of units will be used. The 14th, 15th, and 16th user material constants specify the factors needed to convert from the default units of Newtons, meters, and Kelvin to the desired units of kilonewtons, centimeters, and degrees Fahrenheit respectively. An example of the *USER MATERIAL keyword statement is shown below. *USER MATERIAL, CONSTANTS=16 5, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0.1, 0.01, 0.001, 100, 1.8 Note that the *USER MATERIAL statement includes the parameter ‘CONSTANTS=16’ to indicate that there are sixteen user material constants on the data line. Two additional points should be emphasized regarding the choice of values for the 1st user material constant. First, all stress results printed in the Abaqus output files will be expressed in the units specified by the user via the first user material constant. For example, if the first user material constant has a value of 3 (specifying the pound, inch, degree Rankine system of units), Abaqus will output all stresses in units of lb/in2. Second, custom units are not supported by the Helius:MCT GUI and must be specified manually by the user by either changing the material definition in the Abaqus/CAE keyword editor or by directly editing the input (*.inp) file with a text editor such as Notepad.

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Appendix A.2

User Material Constant #2: Principal Material Coordinate System

Helius:MCT expresses constitutive relations and computes stress in the principal material coordinate system of the composite material. For unidirectional microstructures, Helius:MCT’s default principal material coordinate system is oriented with the ‘1’ direction aligned with the fiber direction, while the ‘2’ and ‘3’ directions lie in the composite material’s plane of transverse isotropy. However, in situations where it adds convenience or simplicity to the model creation process, the user may change the orientation of Helius:MCT’s principal material coordinate system so that the ‘2’ direction is aligned with the fiber direction, while the ‘1’ and ‘3’ directions lie in the composite material’s plane of transverse isotropy. For woven microstructures, Helius:MCT’s default principal material coordinate system is oriented with the ‘1’ direction aligned with the fill tow direction, while the ‘2’ direction corresponds to the warp tow direction and the ‘3’ direction corresponds with the out-of-plane direction. However, in situations where it adds convenience or simplicity to the model creation process, the user may change the orientation of the principal material coordinate system so that the ‘2’ direction is aligned with the fill tow direction, while the ‘1’ direction corresponds to the warp tow direction. Additionally, the user may change the orientation of the principal material coordinate system so that the ‘3’ direction is aligned with the fill tow direction while the ‘2’ direction corresponds to the warp tow direction. The second user material constant is used to specify the orientation of the principal material coordinate system that will be used by Helius:MCT. The numerical value (1 or 2 for unidirectional materials and 1, 2 or 3 for woven materials) of the second user material constant specifies which of the principal material coordinate axes will be aligned with the fiber direction (for unidirectional composites) or the fill tow direction (for woven composites). The availability of alternative orientations for the principal material coordinate system provides the user with more flexibility in specifying the orientation of the material plies within a section definition. The user should be aware that Abaqus/Standard outputs the composite average state of stress and strain in the coordinate system that is specified by the second user material constant; however, the constituent average states of stress and strain (stored in SDV7, SDV8, ..., SDV90) are always output in Helius:MCT's default principal material coordinate system. As an example, if the second user material constant is specified as 2, all composite average stress and strain states will be output in the local system defined by the user, with the local 2 direction corresponding to either the longitudinal axis of the fibers for unidirectional materials, or the fill axis for woven materials. However, all constituent average stress and strain states will be reported in the default principal coordinate system of the unidirectional or woven composite material. • •

For unidirectional microstructures, Helius:MCT’s default principal material coordinate system is oriented with the ‘1’ direction aligned with the fiber direction, while the ‘2’ and ‘3’ directions lie in the composite material’s plane of transverse isotropy. For woven microstructures, Helius:MCT’s default principal material coordinate system is oriented with the ‘1’ direction aligned with the fill tow direction, while the ‘2’ direction corresponds to the warp tow direction and the ‘3’ direction corresponds with the out-of-plane direction.

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Consider the following *USER MATERIAL statement that appears in an Abaqus input file representing a unidirectional microstructure. *USER MATERIAL, CONSTANTS=13 1, 2, 1, 0, 0, 0, 0, 0 0, 0, 0, 0.1, 0.01 Note that the second user material constant is assigned a value of 2. Therefore, this particular material will use a principal material coordinate system where the ‘2’ axis is aligned with the reinforcing fibers, and the ‘1’ and ‘3’ axes lie in the composite material’s plane of transverse isotropy. The following example problem illustrates the consequences of assigning the second user material constant a value of 2. Example: Consider a cylindrical tube that is composed of two unidirectional composite material plies (see Figure A17). Both composite plies are made of the same composite material, but the two plies differ in the orientation of the reinforcing fibers. The reinforcing fibers of the inner ply are aligned with the axial direction of the cylinder, and the reinforcing fibers of the outer ply are aligned with the hoop direction of the cylinder. The red lines in Figure A17 show the orientation of the reinforcing fibers in the inner and outer composite plies.

Figure A17. The fiber direction for each element is indicated by the red lines

To illustrate the consequences of specifying a value of 2 for the second user material constant, consider the following statements that are excerpted from an Abaqus input file. The second user material constant is assigned a value of 2 indicating that the ‘2’ axis of the principal material coordinate system is aligned with the reinforcing fibers. Note that ** indicates a comment in an Abaqus input file. ** Define a Helius:MCT composite material. ** Note that the ‘2’ axis of the principal material ** coordinate system is aligned with the fiber direction. *MATERIAL, name=IM7_8552 *DEPVAR 6

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*USER MATERIAL, CONSTANTS=13 1, 2, 1, 0, 0, 0, 0, 0 0, 0, 0, 0.1, 0.01 ** ** Define a local cylindrical coordinate system for the ** inner composite ply. Note that the local cylindrical ** coordinate system is rotated so that the local ‘2’ axis ** points in the global axial direction. *Orientation, name=axial_fibers, system=CYLINDRICAL 0., 0., 0., 0., 0., 1. 1, 90. ** ** Define a solid section for the inner composite ply. *Solid Section, elset=innerPly, orientation=axial_fibers, material=IM7_8552 ** ** Define a local cylindrical coordinate system for the ** outer composite ply. Note that there is no need to ** rotate the local cylindrical coordinate system since ** the local ‘2’ axis points in the global hoop direction. *Orientation, name=hoop_fibers, system=CYLINDRICAL 0., 0., 0., 0., 0., 1. 1, 0. ** ** Define a solid section for the outer composite ply. *Solid Section, elset=outerPly, orientation=hoop_fibers, material=IM7_8552 Notice that the orientation of the local cylindrical coordinate systems (given in the *ORIENTATION statements) must be consistent with the convention chosen for the principal material coordinate system. For example, the local cylindrical coordinate system for the inner ply is rotated so that the local ‘2’ axis points always points in the global axial direction. In contrast, the local cylindrical coordinate system for the outer ply does not need to be rotated since its local ‘2’ axis always points in the global hoop direction.

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Appendix A.3

User Material Constant #3: Progressive Failure Analysis Progressive Failure Analysis is not available in Helius:MCT Linear.

The third user material constant is used to activate or deactivate Helius:MCT’s progressive failure analysis feature. If the progressive failure feature is activated, then Helius:MCT will routinely evaluate both the matrix failure criterion and the fiber failure criterion to determine if either constituent material has failed. Each constituent failure criterion is based on the corresponding constituent average stress state. For the purposes of this specific discussion, it is assumed that pre-failure and post-failure nonlinearity are de-activated. In the event that one or both of the constituents fail, the stiffness of the failed matrix and fiber are appropriately reduced to the values specified by the 12th and 13th material constants, respectively. Helius:MCT then calculates the current composite average stiffness based on the current state (failed, or not failed) of each constituent material. The value of the third user material constant has different implications depending on the microstructure of the material. Unidirectional Microstructures: A value of 1 activates the progressive failure analysis feature, while a value of 0 deactivates the progressive failure analysis feature. Woven Microstructures: A value of 0 deactivates the progressive failure feature, a value of 1 activates the progressive failure feature and uses the matrix and fiber degradation levels from the material data file to calculate the failed material properties, and a value of 2 activates the progressive failure feature and uses the matrix and fiber degradations levels specified by the twelfth and thirteenth user material constants to calculate the failed material properties. Selecting a value of 2 for plain weaves will add approximately 45-60 seconds to the pre-processing time per woven material. A value of 1 will not add run-time during pre-processing because the failed material properties (at the matrix and fiber degradation levels specified during material creation in Helius Material Manager) are already stored in the material file. The progressive failure analysis feature is the foundation component of Helius:MCT’s nonlinear multiscale constitutive relations. Other aspects of material nonlinearity can be invoked (via the 4th, 5th, and 6th user material constants); however, these additional forms of nonlinearity cannot be activated unless the progressive failure analysis feature is also activated. The discrete values that can be assumed by SDV1 differ depending on the microstructure of the underlying composite and additional forms of material nonlinearity invoked. A comprehensive listing of the allowable discrete values for SDV1 is provided in Appendix D. Additionally, a description of each discrete composite damage state is written in the summary file (*.mct) created by Helius:MCT during the preprocessing phase of the analysis. Figure A18 shows a [0°/ ±45°]s unidirectional composite plate that was analyzed using Helius:MCT’s progressive failure feature. Figure A18 shows a contour plot of the MCT state variable SDV1, representing the composite damage state in the 0° plies. The blue areas represent composite material with unfailed constituents (SDV1=1), the green areas represent composite material with a failed matrix constituent (SDV1=2), and the red areas represent composite material with matrix and fiber constituents that have failed (SDV1=3).

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Failure Key No failure Matrix failure Matrix & Fiber Failure

Figure A18: Helius:MCT solution for failure propagation in the 0° plies of a composite laminate loaded in tension

Note: The number of possible discrete damage states for the composite material depends on the type of composite material (unidirectional or woven) and the specific set of material nonlinearity features that are used by Helius:MCT. For any given case, a description of each discrete composite damage state and its associated SDV1 value is written in the summary file (*.mct) created by Helius:MCT during the preprocessing phase of the analysis. Additionally, the user is referred to Appendix C which describes all of the discrete damage states that can be assumed by any composite material under any circumstances. For further information on the Helius:MCT’s progressive failure analysis feature, refer to Section 4 of the Helius:MCT Theory Manual.

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Appendix A.4

User Material Constant #4: Pre-Failure Nonlinearity

(Unidirectional composites only, not available for woven composites) Pre-Failure Nonlinearity is not available in Helius:MCT Linear.

The fourth user material constant activates or deactivates Helius:MCT’s pre-failure nonlinearity feature. A value of 1 activates the pre-failure nonlinearity feature, while the default value of 0 deactivates the pre-failure nonlinearity feature. The pre-failure nonlinearity feature is intended to account for the nonlinear longitudinal shear (softening) response that is commonly observed in fiber-reinforced composite materials prior to ultimate failure. This additional form of nonlinearity involves imposing a series of three discrete reductions in the m m longitudinal shear stiffness of the matrix constituent material (G12 and G13) which directly results in a corresponding series of three discrete reductions in the longitudinal shear stiffness of the composite c c material (G12 and G13). Imposition of these three discrete reductions in the longitudinal shear moduli are completed prior to matrix constituent failure, thus providing a longitudinal shear softening effect prior to matrix failure. Figure A19 shows a typical measured longitudinal stress/strain curve for a unidirectional carbon/epoxy lamina. Helius:MCT’s pre-failure nonlinearity feature approximates this type of nonlinear longitudinal shear response with a four-segment, piecewise linear representation of the longitudinal shear response. For further information on the pre-failure nonlinearity feature, refer to Section 5 of the Helius:MCT Theory Manual. Appendix D details the discrete values that the solution state variable SDV1 can assume during a progressive failure analysis where the pre-fail nonlinearity feature is activated. 80

Longitudinal Shear Strength

Experimental Data Helius:MCT Pre Fail NL Off

measured data

Composite Average Longitudinal Shear Shear Stress (MPa)Stress (MPa)

70

Helius:MCT Pre Fail NL On

progressive failure without pre-failure nonlinearity 60

progressive failure with pre-failure nonlinearity Threshold

50

matrix constituent failure

40

30

20







Interval 1

Interval 2

Interval 3

10

0 0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

Shear Strain (%)

Composite Average Longitudinal Shear Strain (%)

Figure A19: Comparison of predicted vs. measured longitudinal shear response for a typical fiber-reinforced composite lamina. Helius:MCT User’s Guide – Abaqus

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Appendix A.5

User Material Constant #5: Post-Failure Nonlinearity and Energy-Based Degradation

(Unidirectional composites only, not available for woven composites) Post-Failure Nonlinearity and Energy-Based Degradation are not available in Helius:MCT Linear.

The fifth user material constant activates or deactivates Helius:MCT’s post-failure nonlinearity or energy-based degradation features. A value of 1 activates the post-failure nonlinearity feature, a value of 2 activates the energy-based degradation functionality, while the default value of 0 deactivates the postfailure nonlinearity feature and the energy-based degradation feature.

Post-Failure Nonlinearity Helius:MCT’s post-failure nonlinearity feature is intended to account for the residual load carrying capability of a failed composite lamina that is embedded in a composite laminate. If the post-failure nonlinearity feature is activated, then Helius:MCT will gradually reduce the stiffness of the matrix constituent material after the matrix failure criterion is triggered, instead of instantaneously reducing the matrix stiffness to its minimum value. In this case, the matrix failure criterion simply identifies the initiation of the matrix failure process (or the initiation of matrix cracking). After the matrix failure criterion is triggered, the matrix constituent stiffness is gradually reduced via a series four discrete stiffness reductions that are applied as the strain state continues to increase beyond the level present at matrix failure initiation. When using this feature, the MCT state variable SDV1 can be used to identify the condition of matrix crack saturation which is useful in determining leakage of a pressurized fluid through a composite laminate. For further information on the post-failure nonlinearity feature, refer to Section 6 of the Helius:MCT Theory Manual.

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Figure A20: Helius:MCT stress-strain solutions for the central 90° ply within a (0/90/0) laminate under axial tension, showing the effect of including the post-failure nonlinearity feature

Energy-Based Degradation Helius:MCT’s energy-based degradation feature is intended to account for the residual load carrying capability of a failed composite lamina that is embedded in a composite laminate. If the energybased degradation feature is activated, then Helius:MCT will gradually reduce the stiffness of the composite after a failure criteria is triggered, instead of instantaneously reducing the composite stiffness. In this case, the failure criterion simply identifies the initiation of failure. After the failure criterion is triggered, the composite constituent stiffness is gradually reduced via a series of discrete stiffness reductions that are applied as the strain state continues to increase beyond the level present at failure initiation. When using this feature, the MCT state variable SDV1 can be used to identify the progression of composite damage as the strain continues to increase. For a detailed description of the energy-based nonlinearity feature, refer to the Helius:MCT Theory Manual. The specific stiffness reductions that occur depend entirely on the failure state of the composite.

Matrix Failures c c c c c In the case of a matrix failure, composite E22, E33, G12, G13, G23 degrade linearly using the relation c

m

c

Pd = (1.0 - d ) P0 c

(A5) c

m

where Pd is the degraded composite property, P0 is the virgin composite property, and d is the degradation constant due to matrix failure given by

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f

m

d =

0

εeff(εeff - εeff) f

0

εeff(εeff - εeff)

.

(A6)

In the above equation, εeff is a composite effective strain measure given by εeff =

2

2

2

2

2

ε22 + ε33 + ε12 + ε13 + ε23 ,

0

(A7)

f

εeff is the value of the composite effective strain at matrix failure, and εeff is the final effective strain value given by m

2G εeff = 0 , σeffLe f

(A8)

m

where G is the total energy dissipated in the composite before and after a matrix failure (user material 0 constants 12), σeff is the effective stress of the composite at matrix failure computed in the same manner as Equation A5, and Le is the representative element length defined by Abaqus. In the case of threedimensional elements (i.e. bricks and continuum shell) the element length is the cubed root of the volume. In the case of two-dimensional elements (i.e. shell and plane stress elements) the element length is the square root of the area. The definition of the final effective strain given in Equation A8 assumes a linear degradation of the effective stress vs. effective strain relationship of the composite, as shown in Figure A21.

Figure A21: Stress/strain response for a linear degradation using energy-based degradation.

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To keep the MCT decomposition intact, and accurately capture the stresses in the constituents after a matrix failure, the properties of the matrix constituent are also degraded to enforce a consistent relationship from the micro to macro scale. Fiber Failures c c c A fiber failure event will result in a linear degradation of composite E11, G12, and G13 in a similar manner to the degradation of the composite properties due to a matrix failure with the effective strain being defined as εeff =

2

ε11 ,

(A9)

and the effective stress defined in a similar manner. However, the longitudinal shear degradation is given by c

f

m

c

Pd = (1.0 - d ) (1.0 - d ) P0,

(A10)

which forces the shear stiffness to be a strictly decreasing function of effective strain. The major difference between matrix failures and fiber failures is the need for constituent information. If the fiber fails, the matrix is assumed to fail as well, and the need for constituent information is not required for further failure calculations, so the constituent properties are not updated after fiber failures. Therefore, providing the dissipation energies for matrix and fiber failure events allows the energy-based degradation scheme to compute the degraded composite and constituent properties after a failure event as a function of increasing composite strain. The energy-based degradation will alleviate some mesh dependence on a final solution and provide a robust progressive failure analysis. c

c

c

Note: If the matrix constituent has failed prior to fiber failure E22, E33, G23 are degraded according to the c

c

c

Matrix Degradation Energy, otherwise E22, E33, G23 are degraded according to the Fiber Degradation Energy.

A Note on Discrete Interval Partitioning The Energy-Based damage feature of Helius:MCT uses multiple discrete intervals when linearly degrading the composite, as shown in Figure A22. Each interval uses a secant modulus to define the response of the composite in that specific interval. For problems where the total energy represents something similar to an isosceles triangle, the intervals will accurately capture the response of the composite.

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Figure A22 Energy-based linear degradation interval partitioning.

For analyses where the total energy represents a very heavily skewed triangle, as shown in Figure A23, the interval partitioning will not accurately capture the linear softening of the composite at the early strain levels. This is entirely due to the number of intervals used to achieve the most rapid and robust convergence of the problem. Specifically, the stress secant intervals at strain levels near failure retain a high stiffness and can cause a misrepresentation of the stress state of the composite. If the user has analyses which must define a linear degradation curve in which the final effective strain is over 100 times the initial effective strain, please contact Firehole Composites for support.

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Figure A23 Linear degradation for large energy problem using secant modulus interval divisions.

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Appendix A.6

User Material Constant #6: Hydrostatic Strengthening

(Unidirectional composites only, not available for woven composites) Hydrostatic Strengthening is not available in Helius:MCT Linear.

The sixth user material constant activates or deactivates Helius:MCT’s hydrostatic strengthening feature. A value of 1 activates the hydrostatic strengthening feature, while the default value of 0 deactivates the hydrostatic strengthening feature. If the hydrostatic strengthening feature is activated, then Helius:MCT explicitly accounts for the experimentally observed strengthening of the composite in the presence of a hydrostatic compressive stress in the matrix constituent. If the hydrostatic compressive stress in the matrix constituent exceeds a threshold value, then the strength of both the matrix constituent and the fiber constituent are scaled upwards commensurate with the level of hydrostatic compressive stress level in the matrix constituent. The threshold value of the matrix average hydrostatic compressive stress is an experimentally m* m* determined quantity denoted in index notation by σkk , where σkk