Explicit Dynamics With LS-DYNA

EXPLICIT DYNAMICS WITH LS-DYNA

Maurício Michelon Bernard Patury 08.08.09

September 2013

Explicit Dynamics with LS-DYNA

Introduction Overview:

                   

Introduction; Comparison of explicit and implicit time integration; Time step control; Program execution syntax; Description of keyword input; Element library; Hourglass control; Material models; Boundary conditions; Initial conditions; Loads; Sets; Contacts; Rigid bodies; Damping; Output control; Restart; Static prestress; Units; Recommendation for control settings.

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Explicit Dynamics with LS-DYNA

Introduction

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What is LS-DYNA: •

•

•

•

Explicit Finite Element Program: • This means: FEM-Program with explicit time integration. • This also means: only transient dynamic analysis are possible. There is also an implicit part in LS-DYNA (several things already possible, but still under development): • Implicit static. • Implicit transient dynamics. • Modal analyses (determination of eigen frequencies and eigen modes). Structural analyses are main field of application: • Coupling with temperature dependent problems possible. • Also fluid-structure interaction (FSI) with eulerian formulation possible (e.g. aquaplaning, airbag inflation, tank sloshing). Topic of this training is 3D structural analyses with explicit time integration.

Explicit Dynamics with LS-DYNA

Introduction

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•

LS-DYNA is developed by LSTC (Livermore Software Technology Corporation) and has its roots in DYNA3D/2D from LLNL (Lawrence Livermore National Laboratories); both are and have been developed by Dr. John Hallquist.

•

LS-DYNA is a pure solver, therefore needs an input file in a specific format and produces results in form of binary and ASCII data.

•

Input file is generated using a pre processor, e.g. LS-PrePost, FEMB, ANSA, ANSYS/LS-DYNA (Classic or LS-DYNA Export), EASi-Crash, FEMAP, HyperMesh, Medina, Oasys Primer, Patran. All pre processors have in common, that they produce a Keyword text file as a input file for LS-DYNA.

Explicit Dynamics with LS-DYNA

Introduction

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•

LS-PrePost version 3.0 can read IGES- and VDA-Files and mesh them with a surface mesh, moreover simple geometric entities can also be generated.

•

Post processing for binary and also ASCII data is typically done using LSPrePost; other post processors are also avaliable e.g. Animator Evaluator (GNS), ANSA, HyperMesh, ANSYS/LS-DYNA, Oasys D3PLOT.

•

LS-DYNA also comes with LS-OPT for optimization using the successive response surface method.

Explicit Dynamics with LS-DYNA

Introduction

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Characteristics of LS-DYNA: Large Element library: - Simple and fast elements for standard applications. - High-order elements available, but costly.

Wide choice of material laws: . plasticity: - Kinematic and isotropic hardening. - Strain rate dependency. - Temperature dependency. - Failure. - Anisotropic plasticity. . Foam. . Composite material: - anisotropic combined with failure. . Rubber. . Viscous. . Fluid. . User defined material via Fortran-interface.

Explicit Dynamics with LS-DYNA

Introduction

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Contact-Algorithm: - With friction. - Contact of deformable with rigid bodies in any combination. - Single surface contact. - Contact with analytical surfaces. - Contact Rigid-Body and Rigid-Body. - Definition quite simple. - Very fast. Rigid Body Dynamics:

- Definition of rigid bodies with elements or nodes. - Joints between rigid bodies. - Deformable to rigid material switching at any time.

Models for gas inflow and gas outflow of airbags. Possibilities to increase the time step (reduce calculation time): Mass Scaling: Local increase of mass, minor changes of the total mass. Subcycling: Grouping of elements according to their time step size.

Explicit Dynamics with LS-DYNA

Fields of application for explicit FE programs STATIC

Structural problems

QUASI STATIC

Metal forming

DYNAMIC

Impact

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Explicit Dynamics with LS-DYNA

Fields of application for explicit FE programs

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Explicit Dynamics with LS-DYNA

Typical application for explicit FE programs

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• Simulation of short time dynamic problems where the frequencies of interest are high (e.g. impact analyses), so that small time steps are also necessary in case of implicit calculation. • Simulation of highly nonlinear problems, which require small time increments (because of contact, large deformations), especially for large model sizes, therefore also for quasi-static problems. Crash- analyses

Metal forming

• Automobile (side-impact); • Automobile (component- and complete models); • Railway construction; • Aerospace industry; • Drop tests.

Turbine

Explicit Dynamics with LS-DYNA

1 DOF System – Equation of motion Equilibrium : Inertia force : Damping force : Elastic force :

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f  f  fs  p i d (t ) .. f  M. u i . f  C.u d f s  K.u

.. . Equation of motion : M. u(t)  C.u(t)  K.u(t)  p(t) Equation of motion depends on time

discretization necessary!

2 possibilities: implicit or explicit time integration

Explicit Dynamics with LS-DYNA

Comparison explicit vs. implicit Implicit time integration :

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e.g. Newmark-method

The equations of motion are evaluated at time tn+1 (i.e. at the end of the current time step):

Explicit time integration :

e.g. Central difference scheme

The equations of motion are evaluated at time tn (i.e. at the begin of the current time step):

Explicit Dynamics with LS-DYNA

Newmark method / linear acceleration method (implicit)

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Assumption : linear change in acceleration . . t .. t .. Velocity : u n 1  u n  u n  u n 1 2 2 2

. t 2 .. t .. Displaceme nt : u n 1  u n  u n t  un  u n 1 3 6

Equation of motion at time tn+1: Displacement at time tn+1: (

6 t

2

M

n 1



3 t

C

n 1

K

n 1

).u

n 1

 p

6

3

M ( 2 u  n 1 n t n t 3

t

C ( u  n t n 2 K

n 1

K

n 1

(u

n 1

. .. un  2un )

.. . un  2un )

)

Problem: stiffness matrix K on left hand side Equilibrium iteration for nonlinear problems necessary, costly solving of system of equation.

Explicit Dynamics with LS-DYNA

Central Difference method (explicit)

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Assumption : linear change in acceleration . 1 Velocity : u n 1/ 2  (u n 1 u n ) t n 1/ 2 .. . 1 . Acceleration : u n  (u n  1 / 2  u n  1 / 2 ) t n

Equation of motion at time tn: Displacement at new time tn+1: (

1 1 2 1 1 Mn  Cn ).u  pn  ( K n  2 M n ) u n  ( 2 M n  C ) u n 1 2 n 1 2t 2t n t t t

If M and C are diagonal, no matrix inversion is necessary, solution is simple and fast!

Explicit Dynamics with LS-DYNA

Comparison explicit vs. implicit Implicit time integration : e.g. Newmark-method

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The equations of motion are evaluated at time tn+1 (i.e. at the end of the current time step) Characteristics:

- Equilibrium must be satisfied at time tn+1. - Thus necessary to solve a large system of equations. - Iteration within time step, convergence may be a problem. - Few but large time steps. - Time step size depending on frequencies of interest. - CPU time per time step depends on equation solver. - One step method, self starting.

Explicit time integration :

e.g. Central difference scheme

The equations of motion are evaluated at time tn (i.e. at the begin of the current time step) Characteristics:

- Equilibrium at time tn, non-equilibrium at time tn+1. - Accelerations calculated to shift the system towards balance. - No large system of equations to solve. - Usually no problems with convergence. - Only conditional stable, time step must be small enough: Time step size depends on highest natural frequency. - Many but very small time steps. - Two step method; not self starting.

Explicit Dynamics with LS-DYNA

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Implicit vs. Explicit time integration

Implicit

Explicit

• The integration method is always stable; independently of the time step used.

• The integration method is only stable if the time step is smaller as the so called critical time step (conditional stable). The critical time step is correlated with the highest eigen frequency of the system and reads for linear systems without viscous damping.

• Usually the time step has to be adapted according to the expected results (eigen frequencies of interest). • In case of nonlinearities the time step must be small enough in order to obtain Convergence.

t  t crit



2

 max

for nonlinear system the time step might be significantly smaller!

Explicit Dynamics with LS-DYNA

Control of time step size

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• LS-DYNA calculates the time step size for each element at each time step automatically (Courand-Levy-Stabilitycriterion): Global time step = Minimum (all element time steps). • The smallest time step size will be used (might change from time step to time step).

• The user can reduce the time step size: • By changing the scaling factor (default: 0.9), which is used in the program to multiply the actual time step size: *CONTROL_TIMESTEP (Control Card 1, tssfac). • By defining a load curve containing the maximum allowed time step size:

*CONTROL_TIMESTEP (Control Card 1, lctm).

Explicit Dynamics with LS-DYNA

Time step control / stability aspects

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Stable time integration: *CONTROL_TIMESTEP $ dtinit tssfac 0.9 tssfac -> Time step scaling factor. Instable time integration: *CONTROL_TIMESTEP $ dtinit tssfac 1.5 values bigger than 1.0 will lead to instability of the time integration procedure

Explicit Dynamics with LS-DYNA

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Control time step

- The time step size is calculated based on wave propagation in the material: Courand-Levy-Stabilit Criterium

t  0.9

l c

l characteristic length of the element c speed of sound

depends on element type

tssfac - Distinguish between:

Solid, Shell and Beam Elements or Discrete Elements l minimum length of the element

Solid-Elements:

c

E (1  )  (1   )(1  2 )

E

Young' s Modulus

 

Poisson ratio Mass density

Explicit Dynamics with LS-DYNA

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Control time step l minimum length of the element Shell-Elements:

l Warped Shell-Elements:

A l max

or l 

c

E (1  )  (1   2 )

A d max

- with *CONTROL_TIMESTEP , isdo

t  Solid-Shell-Elements:

Ve

Ve c.A e, max

c

element vo lume

A e, max greatest element area

E  (1 - 2 )

Explicit Dynamics with LS-DYNA

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Control time step Beam-Elements:

c

E



In general: - Shorter element-edges. - Lower mass density. - Added stiffness.

Reduce time step size by modelling.

• Create mesh as uniform as possible • Mesh refinement increases calculation time Two options to increase the time step size or to reduce calculation time: - Mass Scaling; - Subcycling.

Explicit Dynamics with LS-DYNA

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Mass scaling Mass scaling - User defines the desired time step size: *CONTROL_TIMESTEP, dt2msf

- Program changes the mass density of all elements in such way, that the step size for all elements is equal to the given one. Not useful for dynamic analyses; generally not recommended! - Using a negative value for the time step size, will only change mass density for those elements, whose step size is smaller than the desired one: Also useful for dynamic analyses; Check added mass carefully!

t specified Element l1

l2

l3

n 

l n.min  c

and c 

(t specified ) 2 .E l n .(1  2 ) 2

E  (1 - 2 )

Explicit Dynamics with LS-DYNA

Subcycling

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Subcycling - The time step size is always limited by a single element in the finite element mesh, e.g. due to a small element size, a low mass density or a high Young’s modulus. - In using Subcycling the elements are sorted based on their time step size into groups whose step size is some even multiple of the smallest element step size. Then each group is calculated with its own time step size. *CONTROL_SUBCYCLE - Only recommended for models with very different sizes of elements (mesh refinement) or with extremely different material values (e.g. steel and foam). - Grouping is possible for the following element and contact formulations: • Solid-Elements, Shell-Elements, Beam-Elements, Solid-Shell-Elements; • Penalty-Contacts; • not for Discrete-Elements (spring and damper).

Explicit Dynamics with LS-DYNA

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Subcycling Exemple Subcycling : E1 = 4 E2 A1 = A2 ρ1 = ρ2

• material 1 is four times stiffer than material 2 • because of : c 

E



and T 

l c

The time step size of material 2 is twice the time step size of material 1. Consequently elements with material 2 are only calculated every second time step

Subcycling is not generally recommended !

Explicit Dynamics with LS-DYNA

Scheme of explicit FE program Loop over all time steps: loop over all integration points IP calculation of strains at IP via deformed geometry (strain tensor at IP from current node position) calculation of stresses at IP with constitutive equation calculation of nodal force contribution of IP

contact algorithm: loop over all contact partners - calculation of penetrations and resulting contact forces sum of all nodal forces including external forces and contact forces) - system of nodes with concentrated masses determined by integration and nodal forces

loop over all nodes: explicit time integration in order to determine the primary variables, i.e. displacements, velocities and accelerations - no system of equation and no stiffness matrix set up (fast)

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Explicit Dynamics with LS-DYNA

Hourglass control

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Hourglassing is a state of strain, which is free of energy (ZEM: Zero Energy Mode) and can emerge in case of one-point-integrated solid- (hexahedrons) and shell elements.

Hourglass modes are mostly caused by: - concentrated loads - contact (contact force at several nodes ) In LS-DYNA there are 2 possibilities to prevent Hourglassing: using the automatic stabilization against this deformation with -*HOURGLASS (input for each part) or - *CONTROL_HOURGLASS (global control) using a fully integrated element type disadvantages: - more computation time - more sensible with respect to large element deformations

Explicit Dynamics with LS-DYNA

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Hourglass control Recommendation for *HOURGLASS and. *CONTROL_HOURGLASS for shell elements for solid elements (in general) for solid elements (foam) for solid elements (elastic) for solid elements (plastic) For solid elements (rubber, viscoel)

ihq=4 (stiffness form, default settings) ihq=5 (stiffness form, default settings) ihq=3 (viscous form, default settings) ihq=6,qm=1.0 (stiffness form) ihq=6,qm=0.01-0.001 (stiffness form) ihq=6,qm=1, qw=1 (stiffness form)

Note: ihq=6 is a special solid element formulation according to Belytschko-Bindeman

Explicit Dynamics with LS-DYNA

Program execution syntax (SMP)

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With the call of LS-DYNA up to 19 parameters can be declared. For a standard execution the following are important: lsdyna i=input file

memory=number_words

ncpu=number_processors

The file input file must contain a complete input data for LS-DYNA. There are two possible formats for the input file: • structured input: - the input data file is structured in using lines and columns - the sequence of input data must be kept - this format is old and not recommended • keyword input: - the input data are described by keywords - the sequence of the data is arbitrarily - in each line the data can be defined either in a tabular format or in a free format (separated by commas)

Explicit Dynamics with LS-DYNA

Program execution syntax (SMP)

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The parameter memory defines the size of the working memory for the program. Number_Words describes the working memory in words. On most platforms the default is Number_Words = 8500000, this is approx. 32 MB. Define e.q. memory=80m to have approx. 305 MB of working memory. An automatic allocation of memory is also possible by definition of an environment variable (LSTC_MEMORY = auto). Use Number_Processors to define the number of CPU’s for parallel processing. Defining Number_Processors as a negative number induces, that the calculation is done in such way that the results are independent of the number processors used (this is related to a somewhat lower performance (see also *CONTROL_PARALLEL). For Distributed-Memory-Paralelisation (MPP) another executable is necessary as well as a different start procedure.

Explicit Dynamics with LS-DYNA

Program execution syntax (MPP)

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The Distributed-Memory-Version of LS-DYNA, MPP-DYNA, is started using a MPIprogram. Thereby slight changes in the argument list compared to SMP is needed. On a linux cluster the program execution could be as follows: mpirun –np ncpu mppdyna i=Inputfile memory=number_words memory2=number_words p=pfile ncpu is the number of CPUs used The parameter memory defines the memory in word for the first processor. The first processor has to do the domain decomposition and therefore needs more memory compared to the other CPUs. The parameter memory2 defines the memory for the remaining processors. In case that memory2 is not given, then all processors will allocate the memory given with memory. An automatic allocation of memory through the definition of an environment variable is also possible (LSTC_MEMORY = auto). The so called pfile defines specific control options for MPP-DYNA. Since the same options are in meantime possible to define in the keyword file directly (*CONTROL_MPP) the pfile is less important in the future.

Explicit Dynamics with LS-DYNA

Program execution using Mechanical APDL Product Launcher

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Mechanical APDL Product Launcher: 2 - Choose Analysis Type

1 - Choose LS-DYNA Solver at Simulation Environment. Select the License.

3 - Browse working directory

If HPC license is available

It’s possible to set the number of CPU’s.

5 - Run

4 - Browse keyword file

Explicit Dynamics with LS-DYNA

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Parallelization Shared Memory Parallelization (SMP)

• shared memory • good speed-up for few CPUs • no domain decomposition necessary • few new coding necessary

Massive Parallel Programming (MMP)

• distributed memory • domain decomposition necessary (controlling is possible) • Extraordinary scalability • new coding in parts necessary

Explicit Dynamics with LS-DYNA

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SMP Main Loop / Time Step

Process Elements

Contact

Constraints

Update Nodes

Explicit Dynamics with LS-DYNA

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MPP Main Loop / Time Step

Process Elements

Contact

Constraints

Update Nodes

Communication

Explicit Dynamics with LS-DYNA

Program execution syntax

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Using LS-DYNA interactive, the run can be controlled with the following key combination: ^C (Control-C) This sends an interrupt to LS-DYNA and the user is prompted to input a sense switch code: sw1 - A restart file is written and LS-DYNA terminates; sw2 -LS-DYNA responds with time and cycle numbers; sw3 -A restart file is written and LS-DYNA continues; sw4 -A plot state is written and LS-DYNA continues; swa -Flush ASCII file buffers. This can be used to stop the calculation at arbitrary time and to continue (restart) later. If the job runs in the back ground, one has to generate a file d3kil in the working directory. The file contains then the above mentioned sense switches. In the next time step LS-DYNA reads the file, deletes it and does the corresponding action.

Explicit Dynamics with LS-DYNA

Description of keyword Input The Keyword input file starts with the line *KEYWORD, followed by all input data in an arbitrary order. A data block begins with a keyword followed by data pertaining to the keyword. Each keyword is started with an “*” in the first column of the line.

The keywords are described in the LS-DYNA Users Manual in alphabetic order.

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Explicit Dynamics with LS-DYNA

General Card format – Keyword input

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For each keyword the required cards have to be defined. Each card is defined in its rigid format form and is shown as a number of fields in an 80 character string. Most cards are 8 fields with a length of 10. An typical description in the Users Manual is shown below:

The type is the variable type and is either ‘F’ for floating point or ‘I’ for integer. The default value is set, if zero is specified, the field is left blank or the card is not defined. In case the card format differs from eight fields of length 10, it is indicated above the card (e.g.*NODE). Free formats may be used with the data separated by commas. When using comma format, the number of characters used to specify a number must not exceed the number which would fit into the equivalent rigid format field. Rigid and free formats can be mixed throughout the deck but not within a card.

Explicit Dynamics with LS-DYNA

Part definition – *PART

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Part *PART

Section *SECTION_

Section ID

Material *MAT_

ElementCross-section- Material formulation Definition for ID SHELL and BEAM Elements (form,integration) )

Material information

Hourglass *HOURGLASS_

Hourglass HourglassID Control-Typ

Explicit Dynamics with LS-DYNA

Part definition – *PART

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in LS-DYNA each element has only one attribute: the PART ID the PART is defined with the Keyword *PART. It contains at least the ID of a material definition (*MAT) and a section definition (*SECTION); optional an equation-of-state ID (*EOS) and a hourglass ID (*HOURGLASS) can be given the section definition includes the element formulation as well as the cross section description in case of shell and beam elements

Explicit Dynamics with LS-DYNA

Element Library – *SECTION_SHELL SECTION_SHELL:

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preferred element type

Shell element: with the nodes I,J,K,L

Triangular Shell element: Shell thickness: - the shell thickness is defined in *SECTION_SHELL, t1 until t4 - additional input is possible in the element card, with *ELEMENT_SHELL_THICKNESS; this overwrites the thickness from section definition - in order to consider thickness change of the shell due to membrane straining one has to set *CONTROL_SHELL, istupd (e.g. for sheet metal forming).

Explicit Dynamics with LS-DYNA

Element Library – *SECTION_SHELL

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Number of integrations points: - most shell elements (other than type 6, 7 and 16) have 1 integration point in plane, shell element types 6, 7 and 16 have 4 integration points in plane - The number of the integration points across the thickness is variable and must be defined in *SECTION_SHELL, nip Default is nip=2, which is not sufficient for most applications. - use the following rules to define the number of integration points throughout thickness: • for membranes 1 integration point • for linear material 2 integration points sufficient Attention: stress output not accurate on shell top- and bottom surface • in case of non-linear material 3 until 5 (or more) integration points are needed - with *DATABASE_EXTENT_BINARY; maxint, declare the number of integration points, for which LS-DYNA writes results to the binary database For maxint =3 (default) the results are written for the middle and the two outermost integration points, available as middle, lower and upper surface.

Shell normal Middle surface NIP=5 ; MAXINT=3

NIP=5 ; MAXINT=5

Explicit Dynamics with LS-DYNA

Element Library – *SECTION_SHELL

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GAUSS integration points across the thickness - usually the Gauss integration rule is used for thickness integration - although the outer integration points are not located on the surface, this method gives accurate results and is commonly used. - thickness integration can be switched from Gauss to Lobatto integration by setting *CONTROL_SHELL, intgrd=1 In this case the inner and outer integration points are located on the shell surface. This feature is only available for 3-10 integration points throughout the thickness

Explicit Dynamics with LS-DYNA

Element Library – *SECTION_SHELL

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Elements formulation in LS-DYNA: EQ.1: Hughes-Liu EQ.2: Belytschko-Tsay -> default EQ.3: BCIZ triangular shell EQ.4: co-rotational C0, triangular shell EQ.5: Belytschko-Tsay membrane EQ.6: S/R Hughes-Liu EQ.7: S/R co-rotational Hughes-Liu EQ.8: Belytschko-Leviathan shell EQ.9: fully integrated Belytschko-Tsay membrane EQ.10: Belytschko-Wong-Chiang EQ.11: fast (co-rotational) Hughes-Liu EQ.12: plane stress (x-y plane) EQ.13: plane strain (x-y plane) Only for 2D analysis EQ.14: axisymmetric solid (y-axis of symmetry) – area weighted EQ.15: axisymmetric solid (y-axis of symmetry) – volume weighted EQ.16: fully integrated shell element with EAS-formulation (very fast) EQ.17: fully integrated DKT, triangular shell element EQ.18: fully integrated linear DK quadrilateral/triangular shell EQ.20: fully integrated linear assumed strain C0 shell Only for linear implicit EQ.21: fully integrated linear assumed strain C0 shell EQ.43: Mesh-free plane strain Only for 2D EFG EQ.44: Mesh-free axisymmetric

Explicit Dynamics with LS-DYNA

Element technique – reduced/selective reduced integration Shear Locking and Hourglassing:

(a) true material behavior (b) fully integrated linear element (shell 4, solid 8 integration points) (c) fully integrated quadratic Element (shell 9, solid 27 integration points) (d) reduced integrated linear Element (shell 1, solid 1 integration points) (e) reduced integrated quadratic Element (shell 4, solid 8 integration points)

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Explicit Dynamics with LS-DYNA

Element Library – *SECTION_SHELL

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Belytschko-Tsay-Shell (Type 2): - standard element with one point integration - very fast - problems in case of warping and large shear deformation -very efficient: moderate accuracy (often sufficient) in combination with high speed C0 Triangular shell (Type 4):

- special triangular element, because degenerated quad elements are very bad - in setting *CONTROL_SHELL, esort=1, all triangular elements use this formulation automatically -only a small number of triads recommended in a quad dominated mesh Fully integrated shell (Type 16): - fully integrated element with EAS-formulation and without Hourglass modes - very fast for a fully integrated element (2.5 times more expensive than type 2) - new standard element of Belytschko-Tsay group for increased accuracy -Bathe/Dvorkin behavior for improvement of transversal shear DKT Triangular Shell (Typ 17): - fully integrated Discrete Kirchhoff Dreieck-Element - better than type Typ 4 triangular, especially in bending; but twice calculation time - appr. 1.9-times calculation time compared to type 2; additionally appr. twice elements

Explicit Dynamics with LS-DYNA

Element Library – *SECTION_SHELL

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Belytschko-Wong-Chiang (Type 10): - slightly slower than type 2 (1.2 times more expensive than type 2) -little bit better results as type 2, especially for warped elements Belytschko-Leviathan (Type 8): - calculation time and accuracy comparable to type 10 (ca. 1.4 times more expensive than type2) - physical Hourglass control, i.e. no input of Hourglass parameters needed -for linear material it should be as accurate as an fully integrated element Hughes-Liu-Shell (Type 1): - developed from continuum model, one point integration - high accuracy (also in case of twisted elements ) -highly expensive (2.5 times more expensive than type 2) selective reduced Hughes-Liu-Shell (Type 6,7): - most costly shell element (10–20 times more expensive than type 2) - only shear part with reduced integration, otherwise 4 integration points in plane thus only one Hourglass mode - use of CSTYP=2 (unique normal orientation) in *CONTROL_SHELL recommended

Explicit Dynamics with LS-DYNA

Element Library – *SECTION_SHELL

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Belytschko-Tsay- Membrane (Type 5): - membrane element without bending stiffness, only 1 integration point throughout the thickness -one integration point in the element plane (Hourglass modes possible) Fully integrated Belytschko-Tsay- Membrane (Type 9): - same as Type 5, but 4 integration points in the element plane (no Hourglass modes)

Explicit Dynamics with LS-DYNA

Element Library – *SECTION_SOLID SECTION_SOLID:

Hexahedron: (favoured solid element)

Tetrahedron: (created by free mesh, less accuracy)

Tetrahedron: - 4-noded without rotation: very stiff, only used for foams - 4-noded with rotation: compromise between effort and accuracy - 10-noded very accurate but also very costly in terms of computation time

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Explicit Dynamics with LS-DYNA

Element Library – *SECTION_SOLID Elements formulation in LS-DYNA: EQ.1: constant stress hexahedron element (default) EQ.2: fully integrated S/R hexahedron EQ.3: fully integrated quadratic 8 node hexahedron with nodal rotations EQ.4: S/R quadratic tetrahedron element with nodal rotations EQ.5: 1 point ALE hexahedron EQ.6: 1 point Eulerian hexahedron EQ.7: 1 point Eulerian ambient hexahedron EQ.8: acoustic hexahedron EQ.9: 1 point corotational hexahedron for *MAT_MODIFIED_HONEYCOMB EQ.10: 1 point tetrahedron EQ.11: 1 point ALE multi-material element, hexahedron EQ.12: 1 point integration with single material and void, hexahedron EQ.14: 8 point acoustic hexahedron EQ.15: 2 point pentahedron element EQ.16: 5 point 10 noded quadratic tetrahedron with mid side nodes EQ.18: 8 point enhanced strain hexahedron element for linear statics only EQ.31: 1 point Eulerian Navier-Stokes Only for fluid analysis EQ.32: 8 point Eulerian Navier-Stokes EQ.41: Mesh-free solid - EFG

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Explicit Dynamics with LS-DYNA

Element Library – *SECTION_SOLID

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standard element (Type 1): - 8-node hexahedron solid element with tri-linear shape functions - reduced integration, i.e. stresses are calculated only in one integration point in the middle of the element -Hourglass modes possible fully integrated quadratic element (Type 2):

- 8-node hexahedron solid element with tri-linear shape functions - fully integrated with 8 integration points - no Hourglass modes - 2-3 times more expensive than type 1 - helpful, if Hourglass modes are a problem - handicap: lower deformations obtained as with type 1 -uses B-bar-method to overcome transversal shear locking

8 integration points

fully integrated quadratic 8 node element with nodal rotations (Type 3):

- 8-node hexahedron solid element with quadratic shape function - 6 degrees-of-freedom per node: translations and rotations - 14 integration points - not useful for plasticity or material with Poisson ratio close to 0.5 - very expensive in cpu time (3 times more expensive than type 2)

Explicit Dynamics with LS-DYNA

Element Library – *SECTION_SOLID

PAGE 51

Solid element - (type 8): - for acoustic simulation (sound distribution within fluids) - nodes only have a pressure degree of freedom 1 point corotational for *MAT_MODIFIED_HONEYCOMB (Type 9): - special hexahedron element for extra large deformations in combination with foam material law 126 (*MAT_MODIFIED_HONEYCOMB)

Pentahedron element (Type 15): - 6-noded element with trlinear displacement behavior and 2 integration points - element typically is generate when triangular surface element is extruded into the depth - with the input: *CONTROL_SOLID, esort=1 all 6-noded solid elements get automatically this element formulation

Explicit Dynamics with LS-DYNA

Element Library – *SECTION_SOLID Tetrahedron element (Type 10): - 4-nodes tetrahedron element with tri-linear shape functions and 1 integration point - in general much too stiff - often used in combination with foam material, then realistic results expected S/R quadratic tetrahedron element with nodal rotations (Type 4): - 4-node tetrahedron solid element with quadratic shape functions - 6 degrees-of-freedom per node: translations and rotations - 5 integration points - very expensive in cpu time (5 times more expensive than type 10) - accuracy better than tetrahedron type 10, but less than hexahedron type 2 - accurate tetrahedron elements must have midside nodes, but impracticable for explicit computations 10-noded tetrahedron element (Type 16): - tetrahedron element with midside nodes and quadratic displacement behavior - 4+1 integration points - needs approx. The same computation time as Type 4 but time step is halfed - for post processing only a constant stress within element available

PAGE 52

Explicit Dynamics with LS-DYNA

Element comparisson - typical bending application modelled with different element formulations - in case of hexahedrons, 4 elements are used across the height - in case of tetrahedrons only 1 element is used across the height

PAGE 53

Explicit Dynamics with LS-DYNA

Element Library – ALE-formulation in Section_Solid;Shell Eulerian- formulation:

- is used in fluid mechanics - mesh of elements is fixed in space - material ‘flows’ through the elements -variable boundary conditions are complicated Lagrangian- formulation: - is used in structure mechanics - material and elements are bonded together -large deformation induces element distortion ALE: Arbitrary- Lagrangian- Eulerian: - both formulations in combination, may be alternated by time - two possible kinds of applications: REZONING: large deformation in structure mechanics; mesh must be corrected FLUID-STRUCTURE-INTERACTION: Airbag inflation

PAGE 54

Explicit Dynamics with LS-DYNA

Element Library – *SECTION_SOLID

PAGE 55

Solid element - ALE (type 5): - 8-node hexahedron element with trilinear displacement behavoir with reduced integration - ALE = Arbitrary Lagrangian Eulerian coupling of lagrangian and eulerian formulation - Eulerian: materials flow through elements - useful for simulations with large element distortion Solid element - (type 6 and 7): - represent fluid elements within an ALE formulation

Solid element - (type 11 and 12): - admit within ALE formulation different materials in one fluid element - use in combination with *ALE_MULTI-MATERIAL_GROUP (11) or in combination with void-definition (12)

Explicit Dynamics with LS-DYNA

Element Library – *SECTION_BEAM SECTION_BEAM:

except for Type 3, 6 and 9 all beam elements need a third node K, which defines the orientation of the local coordinate system. element formulation in LS-DYNA: EQ.1: Hughes-Liu with cross section integration (default) EQ.2: Belytschko-Schwer resultant beam EQ.3: truss (resultant) EQ.4: Belytschko-Schwer full cross-section integration EQ.5: Belytschko-Schwer tubular beam with cross-section integration EQ.6: discrete beam/cable EQ.7: 2D plane strain shell element (xy plane) EQ.8: 2D axisymmetric volume weighted shell element (xy plane) EQ.9: spot weld beam

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Explicit Dynamics with LS-DYNA

Element Library – *SECTION_BEAM

PAGE 57

Belytschko-Schwer-Beam (Type 2):

- efficient in computation - only valid for linear material and for resultant material formulation (plastic hinges) -cross section of the beam is described by area and moments of inertia Hughes-Liu-Beam (Type 1): - expensive in computation - also valid for plastic material - predefined circular and rectangular cross section definition - arbitrary cross section with user defined integration rule (*INTEGRATION_BEAM) Truss-Element (Type 3): - simple element for tension and compression only - described by cross section area

Explicit Dynamics with LS-DYNA

Element Library – *SECTION_BEAM

PAGE 58

Discrete beams (Type 6): - not really a beam, but a stiffness in all 6 directions between two nodes - beam nodes should have (and may have) the same coordinates - element length does not influence the time step - element formulation only for material law 66-68 - *MAT_LINEAR_ELASTIC_DISCRETE_BEAM - *MAT_NONLINEAR_ELASTIC_DISCRETE_BEAM - *MAT_LINEAR_PLASTIC_DISCRETE_BEAM - local beam coordinate system available - input same as beam, output same as beam Cable-Element (Typ 6):

- same input as in discrete 3D-beam, but with element length important - acts as a rod, which can only transmit axial tensile forces - element formulation is exclusively for material law 71: - *MAT_CABLE_DISCRETE_BEAM Spot weld beam (Type 9): - good for description of elastic spot welds alternative to rigid spot welds (*CONSTRAINED_SPOTWELD) - often used in combination with *CONTACT_SPOTWELD to define mesh independent spot welds - only available in combination with the material law 100 (*MAT_SPOTWELD)

Explicit Dynamics with LS-DYNA

Element Library – *SECTION_DISCRETE

PAGE 59

SECTION_DISCRETE: Spring

Damper: Translations

Rotations

Mass: - discrete springs / damper with linear and non-linear characteristic and single mass points -define springs and dampers with *ELEMENT_DISCRETE Those elements do not yet have a mass, the user must take care that the adjacent elements and nodes have sufficient mass - define mass-points with *ELEMENT_MASS and *ELEMENT_INERTIA (in order to represent components which are not modelled in the model)

Explicit Dynamics with LS-DYNA

PAGE 60

Material definition

• description of a material with *MAT_... • the corresponding material ID is then referenced in the corresponding part definition • it should be noted that not all materials are available for each element type • the information, for which elements a material law is valid, is stated in the Keyword Manual in the description of *MAT • often used material laws are: Type Typ Type Type Type Type Type

1: *MAT_ELASTIC 3: *MAT_ELASTIC_PLASTIC 9: *MAT_NULL 20: *MAT_RIGID 24: *MAT_PIECEWISE_LINEAR_PLASTICITY 123: *MAT_MODIFIED_PIECEWISE_LINEAR_ PLASTICITY 57: *MAT_LOW_DENSITY_FOAM

linear elastic plasticity (iso/kin) no effect rigid standard for plasticity improved for shells foam

A FORTRAN interface is available to integrate own material routines. For this material numbers 41-50 are reserved (*MAT_USER_DEFINED).

Explicit Dynamics with LS-DYNA

Material definition – Plasticity

PAGE 61

*MAT_ELASTIC or *MAT_001:

• simple material law for linear elastic behaviour of material, available for (almost) all element types Example input :

MID: RO: E: PR:

Material ID Density E-Modulus Poisson ratio

Explicit Dynamics with LS-DYNA

Material definition – Plasticity

PAGE 62

*MAT_PLASTIC_KINEMATIC (*MAT_003) • material law to describe isotropic materials with plastic hardening behavior (isotropic or kinematic hardening) • strain rate effects can be considered • available for Shells, Solids, Beams

Example input :

MID: RO: E: PR:

Material ID Density E-modulus Poisson ratio

SIGY: Yield strength FS: Failure strain ETAN: Tangent-modulus BETA: Hardening parameter iso/kin SRC/SRP: Strain rate parameters

Explicit Dynamics with LS-DYNA

Material definition – Plasticity

PAGE 63

*MAT_PIECEWISE_LINEAR_PLASTICITY or *MAT_024: • standard material law to describe an elastic-plastic material behavior • the stress-strain curve is either bilinear with a yield stress (sigy) and the tangent modulus (etan) or can be specified with an input table of a stress-strain curve (either in the fields eps{n} and es{n} or as a load curve lcss with *DEFINE_CURVE • the true stress in relation to the logarithmic plastic strain must be entered Example input :

Explicit Dynamics with LS-DYNA

Material definition – Engineering X True nominal strain:

L  eng  L0

nominal stress:

F  eng  A0

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Explicit Dynamics with LS-DYNA

Material definition – Engineering X True Logarithmic strain (natural strain)

engineering

 eng 

L L0

incremental

 

L L

With integration

 L   L0  L  dL   ln 1   eng   log    ln L  ln L0  ln   ln L  L0   L0  L0 L

 tot   el   plas

  plas   tot  E

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Explicit Dynamics with LS-DYNA

Material definition – Engineering X True

PAGE 66

true stress

F  A Constant volume

L0 1 A  A0  A0 L0  L 1   eng F F    1   eng    eng 1   eng  A A0

true stress belongs to true strains

V  AL0  L  A0 L0  V0

Explicit Dynamics with LS-DYNA

Material definition – Plasticity *MAT_PIECEWISE_LINEAR_PLASTICITY or *MAT_024: •To enter strain rate effects for plasticity: a) constants C and P for Cowper&Symonds b) TABLE-input via lcss c) Load-Curve (lcsr) defining yield stress scaling factor vs. strain rate Example input for TABLE-Option:

Important for TABLE-Input: -lcss is a TABLE-ID

- for any strain rate in the TABLE a *DEFINE_CURVE must follow immediately

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Explicit Dynamics with LS-DYNA

Material definition – Plasticity Specific load curves (*DEFINE_CURVE), which are used in material models, LS-DYNA does an internal rediscretisation of the input curve. Thereby the new curve is described with 100 x-y pairs, which have the same increment on the abscissa.Starting from the smallest input value to the largest value, the internal used increment on the abscissa is:

x  ( x  x ) / 99 end

in

Using internally a strain increment of 0.01 for the hardening curve, one has to define in *DEFINE_CURVE for the first strain value 0 and for the last 0.99.

PAGE 68

Explicit Dynamics with LS-DYNA

Material definition – Plasticity This is done for stress-strain curves e.g. in: *MAT_024 and *MAT_123 (both only in case of TABLE input) *MAT_120 (always) This is done for almost all force curves of discrete beams: *MAT_..._DISCRETE_BEAM It is not done for stress-strain curves e.g. in: *MAT_024 and *MAT_123 (both only if no TABLE input is used) *MAT_36 (always) It is not done for all force curves in discrete elements: *MAT_SPRING_.. Recommendation: Largest value on abscissa as small as possible; material curves will be linearly extrapolated. End values must be chosen in such way that important inner pairs are well represented.

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Explicit Dynamics with LS-DYNA

Material definition – Plasticity

PAGE 70

Many plasticity material models allow the usage of a viscoplastic formulation, activated with the input: VP=1 This feature needs some more computation time, but leads to a smoother and more realistic stress curve. It is generally recommended. In the standard strain rate formulation (VP=0), the effective strain rate is calculated once based on the components in the current strain rate tensor. In the viscoplastic strain rate formulation (VP=1), the effective strain rate is calculated only based on the plastic part of the strain rate tensor. In this formulation you need to do iteration on the effective plastic strain rate during the corrector state of the backward euler integration scheme typically used in material models for metals.

Explicit Dynamics with LS-DYNA

Material definition – Plasticity *MAT_MODIFIED_PIECEWISE_LINEAR_PLASTICITY or *MAT_123: • description of an elastic-plastic material behaviour; same as Type 24, but with extended failure criteria • only available for shell elements Exemple input:

PAGE 71

Explicit Dynamics with LS-DYNA

Material definition – Null

PAGE 72

*MAT_NULL or *MAT_009: -shell elements and beam elements with this material definition neither have a stiffness nor need any significant computation time -application: - “Null shells” for description of contact surfaces on solid elements or between beams - “Null beams” for description of contact edges with *CONTACT_AUTOMATIC_GENERAL - visualisation of stonewalls, springs or draw beads (for invisible elements) - in combination with solid elements also for fluids in tanks, when the mass of the fluid is relevant. An additional *EOS definition is necessary. The mass of the fluid comes from *MAT_NULL and the compressibility comes from the *EOS definition

Explicit Dynamics with LS-DYNA

Material definition – Rigid

PAGE 73

Type 20 (*MAT_RIGID): • with this material any element can become a rigid body • the Young's modulus, which should be in the same order than the surrounding material, is used only to compute the contact stiffness if the rigid body interacts in a contact definition; neither element length nor material data have an influence on the time step size • a part with MAT_RIGID is one rigid body and has only 6 degrees of freedom for calculation • elements of one rigid body must not be connected. Nevertheless they move like a single body (Attention !). For independent rigid bodies different parts are necessary and must be defined • nodes connected with rigid bodies may have no additional boundary conditions or constraints • define boundary conditions for rigid bodies in the material definition, this applies to the centre of gravity • the centre of gravity, the mass and the moments of inertia are calculated by the shape of the elements, this can be overwritten by *PART_INERTIA

Example input:

Explicit Dynamics with LS-DYNA

Material definition – Foams Fundamental Behavior 1. Cell walls carry loads: ~linear elastic (first region) 2. Cell walls buckle: - few stress increase (horizontal plateau) - air in pore carry little load or decelerates - with or without failure 3. Material is compacted: significant stress increase; densification is obtained

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Explicit Dynamics with LS-DYNA

Material definition – Foams There is a distinction between elastic and crushable foams (plastic)

PAGE 75

Explicit Dynamics with LS-DYNA

Material definition – Foams Material models available in LS-DYNA: • elasto-viscoplastic material models with failure (so-called crushable foams) • Viscoelastic formulation for foams with hysteretic behavior • Isotropy or anisotropy

Differences of the models: • Input of curves for stress-strain relationship • Input of material parameters • Consideration of strain rate effects Similarities of the models: • Material behavior is controlled with volumetric strain • Stresses and strains input is positive for compression • Elastic foam has no transverse contraction

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Explicit Dynamics with LS-DYNA

Material definition – Foams

PAGE 77

Overview Elastic Foams: distinction in strain rate effect *MAT_057 *MAT_073 *MAT_083

- viscoelastic with one term (most simple model) - viscoelastic with 6 terms (seldom used) - table input of stress strain curves; not viscoelastic but rate dependent (often used)

Overview Crushable Foams: distinction in anisotropy and plasticity *MAT_026 *MAT_126 *MAT_063 *MAT_163 *MAT_075 *MAT_142

- for strongly anisotropic foams (Honeycomb), one-dimensional uncoupled plasticity - modification of MAT_026, one-dimensional uncoupled plasticity - isotropic, one-dimensional plasticity (principal stresses) - isotropic, one-dimensional plasticity (principal stresses); strain rate dependent - isotropic, three-dimensional plasticity - anisotropic, three-dimensional plasticity

Explicit Dynamics with LS-DYNA

Material definition – Elastic foam *MAT_LOW_DENSITY_FOAM or *MAT_057 • For highly compacted foams with low densities (e.g. seat cushion) • Very stable, viscoelastic formulation (no permanent deformation) • Similarities to a Kelvin element • Input of engineering strains and -stresses • Unloading with hysteretic option (HU) • Form and amount of unloading hysteresis controlled with parameters (HU and SHAPE) • Most simplest strain rate dependency(1 parameter); corresponds to a Maxwell element • Optional tension cut off for tensile stress; otherwise linear elastic behavior with E-Modulus without transverse contraction under tensile loading • Optional input of reference geometry in order to calculate the initial stress stress state • The time step is calculated based on the steepest tangent in the stress strain curve under consideration of the CURRENT density • If KCON is input, the time step is calculated according to this value

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Explicit Dynamics with LS-DYNA

Material definition – Elastic foam Type 57 (*MAT_LOW_DENSITY_FOAM): - simple material law for highly compressible low density foams - for compression a stress-strain-curve has to be defined - in tension linear behaviour up to failure Exemple input:

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Explicit Dynamics with LS-DYNA

Material definition – Elastic foam

PAGE 80

Determination of the stress strain curve from quasi-static or dynamic compression tests. Needed values: engineering stresses over strains (strain measure depends on used material model) In order to avoid localization, the stress strain curves have to fulfill the following conditions:

 0  0

0

For each stress strain curve

 0  2

0

2

0



0

.



0

0

For a bunch of stress strain curves in a TABLE definition

Explicit Dynamics with LS-DYNA

Material definition – Elastic foam *MAT_LOW_DENSITY_FOAM or *MAT_057: • influence of HU (hysteretic unloading parameter) • influence of SHAPE (shape factor for hysteretic unloading)

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Explicit Dynamics with LS-DYNA

Material definition – Elastic foam *MAT_LOW_DENSITY_FOAM or *MAT_057:

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Explicit Dynamics with LS-DYNA

Material definition – Elastic foam *MAT_LOW_DENSITY_VISCOUS_FOAM or *MAT_073 • Enhancement to *MAT_LOW_DENSITY_FOAM • For highly compressible low density foams with large strain rate effects

• Input of engineering stresses and strains for strain rate Independent part • Extensive viscoelastic formulation • Strain rate effect either determined with a relaxation curve or with pairs of shear modulus and exponent (Prony-Serie) > those input parameters are typically not easy to determine, consequently seldom used.

PAGE 83

Explicit Dynamics with LS-DYNA

Material definition – Elastic foam *MAT_FU_CHANG_FOAM or *MAT_083 • For foams with low density • Input of engineering stresses and strains • Consideration of strain rate effects using a TABLE definition (simple input if experimental data are available, therefore often used) • Optional input of engineering strain rate or logarithmic strain rate (SFLAG) • Optional input of stress strain relation or linear behavior for tensile (TFLAG) • Calculation type of strain rate can be changed (RFLAG) • Additional input of load curves to define the hydrostatic compression over volumetric strain (PVID) • Hysteretic behavior during unloading • Time step calculated from Ed; if Ed=0 then from E; time step does not follow the steepest tangent > E or Ed must be large enough density change is not considered for calculating the time step > Attention: for highly compacted foams and used mass scaling large increase in mass might occur.

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Explicit Dynamics with LS-DYNA

Material definition – Elastic foam

PAGE 85

Explicit Dynamics with LS-DYNA

Material definition – Elastic foam *MAT_CRUSHABLE_FOAM or *MAT_063 • For foams with failure and permanent deformations • Isotropic, one-dimensional plastic formulation

• Plasticity uncoupled in terms of principal stresses, yield surface is a cube • Unloading with elastic E-modulus • Input of unaxial stress over volumetric strain

*MAT_MODIFIED_CRUSHABLE_FOAM or *MAT_163

• Same model as *MAT_063 • Additional strain rate dependency: input with TABLE option for different stress strain curves for different strain rates

PAGE 86

Explicit Dynamics with LS-DYNA

Material definition – Elastic foam

PAGE 87

Explicit Dynamics with LS-DYNA

Material definition – Plastic foam *MAT_BILKHU/DUBOIS_FOAM or *MAT_075 • For foams with failure and permanent deformation • Isotropic 3D plasticity formulation

• Unloading with elastic E-modulus • Input of unaxial stress over volumetric strain (from uniaxial experiment) • Input of pressure at yield over volumetric strain (from triaxiality experiment) • Elliptical yield surface i.e. 3D plasticity • Optional with transverse contraction in the plastic region

PAGE 88

Explicit Dynamics with LS-DYNA

Material definition – Honeycomb *MAT_HONEYCOMB or *MAT_026 • For Honeycomb materials with highly anisotropic behavior • One dimensional formulation with permanent deformations • Plasticity uncoupled for the single material axes • Unloading with elastic E-modulus • Input of stress volumetric strain curves for each material direction; also for shear components *MAT_MODIFIED_HONEYCOMB or *MAT_126 • For honeycomb materials with highly anisotropic behavior • One dimensional formulation with permanent deformations • Plasticity uncoupled for the single material axes • Unloading with elastic E-modulus • Input of stress volumetric strain curves for each material direction; also for shear components • Small strain option available • Option for 3D plasticity available

PAGE 89

Explicit Dynamics with LS-DYNA

Material definition – Honeycomb Input of material direction is done with AOPT definition on material card:

AOPT=0.0: local orthotropic material cosy defined by the element node numbering; only useful for structured meshes with equal or predefined orientation of element cosy AOPT=1.0: local orthotropic material cosy defined by element center and vector to origin P; only for solid elements AOPT=2.0: global orthotropic material cosy defined by two vectors a and d; only useful for flat or minimal curved structures (plates) AOPT=3.0: local orthotropic material cosy defined by element normal and vector v; also useful for curved structures AOPT=4.0: local orthotropic cylindrical material cosy defined by point P and vector v; only for solid element

PAGE 90

Explicit Dynamics with LS-DYNA

Boundary conditions

PAGE 91

• boundary conditions are used to fix displacements or rotations of nodes • boundary conditions can be defined in two different ways > - at the end of the lines in the nodes definition (*NODE) - this boundary condition always acts in the global coordinate system - it is not possible to output the corresponding reaction forces > - with *BOUNDARY_SPC_... - this boundary condition may act in an arbitrary coordinate system (the coordinate system „0“ is the global coordinate system) - the reaction forces are print to the ASCI file spcforc • nodes connected to rigid bodies may not get such boundary conditions > define boundary conditions for rigid bodies at their centre of gravity in the material description (*MAT_RIGID) or define a joint (*CONSTRAINED_JOINT) > translate center of gravity using *PART_INERTIA and new values

Explicit Dynamics with LS-DYNA

Initial conditions

PAGE 92

- for time transient calculations initial conditions for displacements and velocities are necessary, default is zero for all - the acceleration is set to zero at time t=0 - initial velocities can be set with *INITIAL_VELOCITY, -for rigid bodies define initial velocities in the part definition with *PART_INERTIA > but then, all mass parameters of the rigid body (centre of gravity, mass, moments of inertia) must be defined too - to define initial displacements (e.g. for a prestressed structure) different ways are possible a) calculation of prestress deformation with LS-DYNA using dynamic relaxation b) define initial displacements (for beams and shells also initial rotations) for each node from a external file (may be created by an implicit code like ANSYS) > define *CONTROL_DYNAMIC_RELAXATION, idrflg =2 (initialisation to a prescribed geometry) and set m=filename as parameter on the command line to start LS-DYNA c) run the prestress calculation in LS-DYNA using the implicit solver - initial temperatures can be defined in the same way as initial displacements - initial stresses and initial strains can be defined in the same way as initial displacements, e.g. *INITIAL_STRESS_OPTION and *INITIAL_STRAIN_OPTION

Explicit Dynamics with LS-DYNA

Loads

PAGE 93

possible loads: -- nodal forces (*LOAD_NODES ; *LOAD_RIGID_BODY) > defines concentrated forces on nodes or on the centre of gravity of rigid bodies > possibility to modify the force direction with the deformation (follower forces), e.g. shell with water loading

-- element pressure (*LOAD_SEGMENT) -- prescribed displacements, velocities or accelerations (*BOUNDARY_PRESCRIBED_MOTION_...) > defines the displacement, the velocity or the acceleration as a function of time > for rigid bodies only displacements or velocities at centre of gravity can be defined > the use of prescribed velocity is recommended to get a smooth process > the reaction forces are reported to the ASCII file bndout

Explicit Dynamics with LS-DYNA

Loads

PAGE 94

-- acceleration field (e.g. gravitation) (*LOAD_BODY) > this describes an acceleration of the ground -- the quantity of the load is generally provided as a function of time by pairs {time; value} in form of so-called “load curves“: *DEFINE_CURVE

-- load curves are also used for many other reasons: > e.g. for the input of a time-dependent damping > for the input of stress-strain-relation in the material description > for the input of time dependent output frequency > for the input of an arbitrary line in case of generating a axisymmetric body as geometric contact entities

Explicit Dynamics with LS-DYNA

Sets

PAGE 95

-SETS are needed to define contact, loads, boundary conditions or initial velocities, where a number of nodes, elements or parts must be specified -a set describes a group of nodes, parts, elements or segments with the reference of a set ID - *SET_BEAM_OPTION (options: GENERATE ; GENERAL) - *SET_DISCRETE _OPTION (options: GENERATE ; GENERAL) - *SET_NODE _OPTION (options: LIST; COLUMN; LIST_GENERATE; GENERAL) - *SET_PART _OPTION (options: LIST; COLUMN; LIST_GENERATE) - *SET_SEGMENT _OPTION (options: GENERAL) - *SET_SHELL _OPTION (options: LIST; COLUMN; LIST_GENERATE; GENERAL) - *SET_SOLID _OPTION (options: GENERATE ; GENERAL) - *SET_TSHELL _OPTION (options: GENERATE ; GENERAL) - possible options are:

GENERATE - generate a block of entities between a starting nodal ID and an ending nodal ID number GENERAL - combine a series of options, see Keyword-Manual LIST - define a list of entities LIST_GENERATE - generate a block of entities between begin and end COLUMN - define additional attributes for nodes/parts/elements

Explicit Dynamics with LS-DYNA

Contact

PAGE 96

- the contact algorithm prevents the penetration of nodes into element (contact) segments - contact segments can be element faces of solid elements or the element area of shell elements; if necessary together with an offset of half the shell thickness - for a contact definition, parts of the model coming in contact must be described as socalled master and slave side. If it is not possible to describe two contacting model parts a single surface contact can be used instead and only a slave side has to be defined

Explicit Dynamics with LS-DYNA

Contact

PAGE 97

- the contact partners can be defined by direct input of the nodes and segments or by a list of PART numbers and geometric box dimensions - internally LS-DYNA uses always nodes and segments, where segments are element areas (shell elements or faces of solid elements) -in some contact types the normal direction of the contact plane is important. In solid elements the normal is always outward directed, for shell elements the element normal is used -> it is generally recommended to create connected meshes with uniform normal orientation

Explicit Dynamics with LS-DYNA

Contact

PAGE 98

3 Types of Contact: 1) Sliding Interfaces (*CONTACT_...) 2) Stonewalls (*RIGIDWALL) 3) Geometric Contact Interfaces(*CONTACT_ENTITY)

1) Sliding Interfaces (*CONTACT_...) - this is the most general formulation for contact between rigid and deformable bodies in arbitrary combination - in most cases a penalty-method is used, i.e. inner pairs of forces are applied at those locations where penetrations are observed - the pair of forces are calculated based on penetration depth and contact stiffness - this procedure is neutral in energy (theoretically)

Explicit Dynamics with LS-DYNA

Contact – Contact stiffness - penalty force:

F = k ×g

with k - contact stiffness g - penetration depth - for shell elements the contact stiffness is determined by: k = slsfac × sf ×K×A/ d

With:

slsfac - global scale factor given in *CONTROL_CONTACT sf - local scale factor given in *CONTACT_, Card 3 (sfs,sfm) K - bulk modulus A - element area d - thickness or shortest diagonal

and for solid elements: k = slsfac × sf ×K×A² /V With:

slsfac - global scale factor given in *CONTROL_CONTACT sf - local scale factor given in *CONTACT_, Card 3 (sfs,sfm) K - bulk modulus A - segment area V - volume of element

PAGE 99

Explicit Dynamics with LS-DYNA

Contact – Contact stiffness

PAGE 100

- according to this, the contact formulation is identical to a spring under compression

- the contact stiffness is computed for each segment on the master and slave side; in case of contact the smaller value is used - if these two values differ about a factor of more than 100, the mean value is computed and a warning message is given -the biggest disadvantage of the penalty method is, that a contact stiffness has to be defined, which might be not optimal for all cases: > if the stiffness is too low, the penetration will be too high > if the stiffness is too high, high frequency vibrations are activated and the explicit time integration procedure may become unstable

Explicit Dynamics with LS-DYNA

Contact – Contact stiffness

PAGE 101

- at the beginning of a calculation LS-DYNA computes and prints the needed time step size for contact stability (surface time step) into an output file. Those step sizes must be compared with the used time step size and should be almost equal

> if the contact time step size is smaller than the time step size used for the calculation, the contact is too stiff - a reduction of the contact stiffness would be reasonable > if the contact time step size is larger, then the contact might be to soft - the contact stiffness may be increased -the contact stiffness can be changed in setting scale factors *CONTROL_CONTACT, slsfac *CONTACT, sfs/sfm

- acts global for all contact definitions - acts only for this contact

Explicit Dynamics with LS-DYNA

Contact – Contact stiffness

PAGE 102

 soft constraint - this is another option for the determination of the contact stiffness - activated with *CONTACT,optional card A, soft=1 - then the contact stiffness is independent of material data and element length, but depends on the actual time step size used > for the contact stiffness the highest possible value is used, to keep the simulation stable:

k  sofscl. With

ms t 2

sofscl - local scale factor from *CONTACT_,optional card A ms - mass of slave node t - time step size - this stiffness can be scaled with the factor sofscl (*CONTACT) - sofscl=0.5 to 1.0 gives a very stiff contact with only small penetrations - this formulation is recommended for single surface contact situations in large models, where different materials with huge stiffness differences (e.g. foam and steel) are in contact with each other, because nearly the same contact stiffness is used for all segments - also useful for bulk metal forming applications with high surface pressure - be careful by using this option in combination with foam material, because the high contact stiffness may produce high contact forces which may lead to self penetration of solid elements (error message: negative volume in brick element …)

Explicit Dynamics with LS-DYNA

Contact – Alternative contact formulation

PAGE 103

Segment Based Contact, Alternate Penalty, Pinball Algorithm > new development: alternative contact formulation SOFT=2 -this new version of contact search is an extended version of the so-called pinballalgorithm - penalty formulation is used but not penetration of single node into contact segment is checked, but always segment area with segment area is checked (segment based contact) - this alternative contact formulation is activated in setting *CONTACT_, optional card A, soft=2 and uses as soft=1 a contact stiffness which is calculated via the global time step; scaling factors are sfs/sfm - only available for SURFACE_TO_SURFACE, ONE_WAY_SURFACE_TO_SURFACE, SINGLE_SURFACE contact defintions with and w/o AUTOMATIC- and ERODING-option

Explicit Dynamics with LS-DYNA

Contact – Friction

PAGE 104

> Friction - a Coulomb friction can be defined between pairs in contact i.e. a friction force is calculated: with: Fr - friction force F  .F Fn - normal force r n  - coefficient of friction -the coefficient of friction  is calculated by:

    (s   )e cv d d

with: 



s

- static coefficient of friction (FS)

d - dynamic coefficient of friction (FD)

c - factor for velocity (DC) > the coefficient of friction has to be defined in *CONTACT, card 2 > the use of the dynamic coefficient of friction FD is only meaningful in combination with DC

Explicit Dynamics with LS-DYNA

Contact – Sliding interfaces

PAGE 105

The most important contact type Contact type 5: one-sided contact (*CONTACT_NODES_TO_SURFACE)

- slave nodes are tested whether they penetrate into the master segments - the simplest and most robust contact formulation - can also be used, if no element segments exist on the slave side, e.g. beams - master side must consist of segments; direction of normal only relevant for master side - graphical representation of contact stress in interface force file only for master side and not for slave side (missing control possibility) - recommendation: finer discretized side should be slave; rigid bodies must be master

Explicit Dynamics with LS-DYNA

Contact – Sliding interfaces

PAGE 106

Contact type 10: one-sided contact (*CONTACT_ONE_WAY_SURFACE_TO_SURFACE) -slave nodes are tested for penetration into the master segments - same procedure as type 5, but segments must exist on slave side too (better visualisation) - very effective and sufficiently accurate, if slave side has a finer discretisation than the master side - slave side also depicted in interface force file Contact type 3: symmetric contact (*CONTACT_SURFACE_TO_SURFACE) - slave nodes are tested for penetration into the master segments and master nodes are tested for penetration into the slave segments - in fact, this is the same than two definitions of contact type 10 with exchanged master and slave side - accurate, but more time consuming - depending on contact situation not always the best choice

Explicit Dynamics with LS-DYNA

Contact – Sliding interfaces

PAGE 107

 Contact type 13: single surface contact  (*CONTACT_AUTOMATIC_SINGLE_SURFACE) - only slave side is defined - all nodes are tested for penetration into all elements - complicated contact situations describable, e.g. buckling and folding - most expensive contact type - no resultant contact forces in rcforc file

 Contact type 13a: airbag contact (*CONTACT_AIRBAG_SINGLE_SURFACE)

- same formulation as type 13, but a more expensive contact search for thin multilayer structures

Explicit Dynamics with LS-DYNA

Contact – Sliding interfaces

PAGE 108

Contact type 26 (*CONTACT_AUTOMATIC_GENERAL) - the most general form of single surface contact - contains additional EDGE-TO-EDGE contact (cylinders with shell thickness along shell edges, so elements are bigger) - contains additional BEAM-TO-BEAM contact - not as stable as contact type 13 - not recommended "generally“, but helpful if edge-to-edge or beam-to-beam contact necessary Contact type 22 (*CONTACT_SINGLE_EDGE) - contact is included between edges of shell elements - the contact occurs at the element edges without any offset - automatic input will only find external shell edges

Explicit Dynamics with LS-DYNA

Contact with or without AUTOMATIC WITH AUTOMATIC Segment orentation

- normal direction of elements meaningless

PAGE 109

WITHOUT AUTOMATIC - contact direction is based on normal direction of the segments (for shell elements the element normal)

Shell tickness

- shell thickness is always used in contact since shell elements more or - define with *CONTROL_CONTACT, less treated as solid elements shlthk , whether the shell thickness is > contact is always on top and bottom of taken into account or not in the contact the shell element

Contact depth

- a node is released if the penetration is more than penmax * shell thickness penmax=0.4 for most contact types -contact is not found if a node penetrates the full shell thickness in one time step > problem by using very thin shells

Options, to influence the scan depth

- with *CONTACT, optional card B, penmax

- a node is released if the penetration is more than xpene * shell thickness xpene=4.0 for most contact types (sufficient)

- *CONTROL_CONTACT, xpene

Explicit Dynamics with LS-DYNA

Contact with or without AUTOMATIC

PAGE 110

Explicit Dynamics with LS-DYNA

Contact – Tied contacts

PAGE 111

Contact type 2 (*CONTACT_TIED_SURFACE_TO_SURFACE) Contact type 6 (*CONTACT_TIED_NODES_TO_SURFACE) - connection of different meshes - only displacements are tied, no rotations; constraint method is used and therefore not to be used with rigid bodies - distance between slave and master must be zero (LS-DYNA moves nodes)

Contact type 2 (*CONTACT_TIED_SURFACE_TO_SURFACE_OFFSET) Contact type 6 (*CONTACT_TIED_NODES_TO_SURFACE_OFFSET) - connection of different meshes - only displacements are tied, no rotations; penalty method is used and can be used with rigid bodies - distance between slave and master should not be too large

Explicit Dynamics with LS-DYNA

Contact – Tied contacts Contact type 7 (*CONTACT_TIED_SHELL_EDGE_TO_SURFACE) - both translations and rotations are tied - using _OFFSET (Penalty-method) and without (Constrained-method)

Contact type 8 (*CONTACT_TIEBREAK_NODES_TO_SURFACE) - same as type 6, but with failure criteria > after failure same behaviour as *CONTACT_NODES_TO_SURFACE

Contact type 9 (*CONTACT_TIEBREAK_SURFACE_TO_SURFACE) - such as type 2, but with failure criteria > after failure same behaviour as *CONTACT_SURFACE_TO_SURFACE

PAGE 112

Explicit Dynamics with LS-DYNA

Contact – Tied contact with OFFSET

PAGE 113

- usually a tied contact implies, that slave nodes lie exactly on the element surface of the master segments - in using *CONTACT_TIED_... it is possible to introduce a distance between the contact pairs, which is given by the option _OFFSET - without the _OFFSET option the slave nodes are shifted during contact initialisation onto the master surface and will be kept there due to constraint equations - with _OFFSET they remain at their original positions relative to the tied surface and are kept with the help of penalty forces

tied contact without _OFFSET > Node is moved onto master segment

tied contact with _OFFSET > Node remains at its original position

Explicit Dynamics with LS-DYNA

Contact – Spot weld

PAGE 114

Contact type 7 (*CONTACT_SPOTWELD) - to connect mesh independent elastic spotweld elements onto shell surfaces - only in combination with *MAT_SPOTWELD and Spotweld-beams *SECTION_BEAM, elform=9 - automatic generation of Spotweld beams using *ELEMENT_BEAM_PID possible - translations as well as rotation are connected, but no rotation about the shell element normal - alternative to rigid spotweld using *CONSTRAINED_SPOTWELD - Slave side composed of part-ids of spotweld beams - Master side composed of part-ids of those shell elements to be connected -can be also used in combination with solid elements to model spotwelds Contact type s7 (*CONTACT_SPOTWELD_WITH_TORSION) - same as Typ 7, but additionally connection of rotations about the shell normal

Explicit Dynamics with LS-DYNA

Contact – Sliding interfaces

PAGE 115

Contact type 14,15,16 (*CONTACT_ERODING_...) - this contact formulation is only useful for solid elements - during contact initialisation only the outermost surfaces of all solid elements are used as contact segments - in case of failure and subsequent eroding of elements in the contact area, new contact segments will be generated on the surfaces of the elements below

Contact type 1 (*CONTACT_SLIDING_ONLY) - the contact partners are connected to each other permanently, merely their surfaces can slide on top of each other - therefore sliding of a fluid at a surface without the eventuality of vortex shedding is possible

Explicit Dynamics with LS-DYNA

Contact – Sliding interfaces Contact type m10, m3, m5 (*CONTACT_FORMING_...) - special contact formulation for sheet metal forming simulation - good for disconnected meshes of tool parts - necessary to control adaptive mesh refinement based on tool curvature - Lagrange multiplier option available instead of penalty method

Contact type 23 (*CONTACT_DRAWBEAD) - not really a contact formulation - used as a simplified draw bead model without the need to mesh the draw bead geometry

PAGE 116

Explicit Dynamics with LS-DYNA

Contact – Stonewalls

PAGE 117

Stonewalls (*RIGIDWALL) - stonewalls are not penetrable and in general not visible and not movable planes - in order to keep the contact condition, the relative velocity of the penetrating node is set stepwise to zero (energy absorbing) - the energy dissipated hereby is monitored in the rigidwall energy - nodes to get in contact with rigidwalls are either defined direct or by using a box definition - by default, rigid bodies are not allowed to get into contact with stonewalls - an option is available to handle also rigid bodies with the help of penalty forces *CONTROL_CONTACT, rwpnal=1 - if the keyword input is used, LS-DYNA internally creates for visualisation reasons a single shell element in the plane of the stonewall

Explicit Dynamics with LS-DYNA

Contact – Geometric contac entities

PAGE 118

Geometric Contact Entities (*CONTACT_ENTITY) - describes the contact of nodes of deformable elements to geometrically described rigid bodies - Geometric Contact Entities can be: - predefined primitives (sphere, cylinder, ellipsoid,...) - bodies generated by rotating a polygon about an axis - bodies from a CAD-description (VDA-FS or IGES) - in all of these cases the contact surface is smooth (while the contact surface is always facetted by the use of finite elements)

- a rigid material definition (*MAT_RIGID) is necessary for Geometric Contact Entities - Geometric Contact Entities are invisible by default; with *CONTACT_ENTITY,go=1, a dummy mesh is created for visualisation reasons

Explicit Dynamics with LS-DYNA

Rigid body and rigid connections

PAGE 119

- there are two possibilities to define areas of the finite element model as rigid: > rigid bodies composed of finite elements with material type 20 (*MAT_RIGID) > nodal constraints, spot welds or nodal rigid bodies (*CONSTRAINED_...) > Important for all of these rigid bodies: no node is permitted to be a part of two rigid bodies *CONSTRAINED_... *CONSTRAINED_NODE_SET - coupling of nodal displacements (no rotations possible) - not possible for rigid nodes - be careful if the coupled nodes have different coordinates because this yields to rotational constraints

Explicit Dynamics with LS-DYNA

Rigid body and rigid connections

PAGE 120

*CONSTRAINED_LINEAR_OPTION (OPTION: GLOBAL, LOCAL) - translational and rotational DOFs are coupled with linear functions (but always only one DOF)

*CONSTRAINED_INTERPOLATION - extended formulation of *CONSTRAINED_LINEAR -the motion of the single node depend on the motion of several independent nodes *CONSTRAINED_POINTS - two shell elements at nodes (not element nodes) with predefined coordinate are coupled (Translation & Rotation) - used e.g. for spot weld definition - definition of failure possible

Explicit Dynamics with LS-DYNA

Rigid body and rigid connections

PAGE 121

*CONSTRAINED_SHELL_TO_SOLID - connection between shell edge and solid element edge

*CONSTRAINED_LAGRANGE_IN_SOLID - couples lagrangian-mesh (slave) of shells, solids or beams with eulerian-mesh (master) - e.g. for fiber reinforced material or reinforcement in concrete, FSI

Explicit Dynamics with LS-DYNA

Rigid body and rigid connections

PAGE 122

*CONSTRAINED_RIVET - rigid and mass less rivet between two nodes modelled with a rigid truss - the nodes must not have the same coordinates - distance of nodes is kept

*CONSTRAINED_SPOTWELD_OPTION - defines a mass less spot weld between two nodes; modelled with a mass less rigid beam - displacements and rotations of nodes are coupled *CONSTRAINED_GENERALIZED_WELD_OPTION - more flexible than *CONSTRAINED_SPOTWELD because an arbitrary number of nodes can be connected, e.g. spot weld through 3 sheets

Explicit Dynamics with LS-DYNA

Rigid body and rigid connections

PAGE 123

*CONSTRAINED_TIE-BREAK - defines a bonded connection of two shell edges - connection can locally fail, if surrounding shell elements exceed plastic strain limit -e.g. opening of a weld line respectively seam line can be modeled

*CONSTRAINED_TIED_NODES_FAILURE - defines a connected node-set, which may fail due to exceeding plastic strains - location of the defined nodes must be coincide - if plastic failure strain is reached, a crack forms, which runs through the whole mesh

Explicit Dynamics with LS-DYNA

Rigid body and rigid connections

PAGE 124

*CONSTRAINED_NODAL_RIGID_BODY - an arbitrary number of unconstrained nodes (defined by *SET_NODE) can be set to rigid, i.e. combined to a rigid body

*CONSTRAINED_EXTRA_NODES - connect nodes of a deformable body with a rigid body without the necessity of mesh connectivity - nodes of the deformable body are tied to the rigid body, i.e. the connected nodal coordinates of the deformable body are triggered by the rigid body motion

Explicit Dynamics with LS-DYNA

Rigid body and rigid connections

PAGE 125

*CONSTRAINED_RIGID_BODIES - this keyword merges two rigid bodies to one rigid body in case they share common nodes - it can be also used to merge two completely separated rigid bodies to one rigid body - the resulting rigid body only has the mass properties, boundary conditions and loads of the master rigid part; all data from the slave parts are lost -nevertheless the slave parts can be used for contact definitions

*CONSTRAINED_RIGID_BODY_STOPPERS - simple modelling of a limit stop for rigid bodies: the motion stops, if the displacements or the coordinates exceed certain given limit values - for free moveable rigid bodies a maximum velocity can be defined; this is useful to prevent undesirable dynamic effects in a quasi-static analysis

Explicit Dynamics with LS-DYNA

Rigid body and rigid connections *CONSTRAINED_JOINT_OPTION - defines a joint between two rigid bodies - possible options are:

PAGE 126

SPHERICAL REVOLUTE CYLINDRICAL PLANAR UNIVERSAL LOCKING TRANSLATIONAL_MOTOR ROTATIONAL_MOTOR GEARS RACK_AND_PINION PULLEY SCREW - to impose the kinematic conditions a penalty method is used. Consequently the joints have a stiffness, which is set as large as possible regarding the time step size. But very high loads might destroy the joints - an implicit Lagrange multiplier option is available, where the joints are completely rigid, but this may not be stable for all cases *CONTROL_RIGID, lmf=1 An alternative to those joints is the usage of discrete beams ( *SECTION_BEAM, elform=6) in combination with *MAT_GENERAL_JOINT_DISCRETE_BEAM Those joints exclusively use the penalty method and can be used to connect elastic as well as rigid bodies.

Explicit Dynamics with LS-DYNA

Rigid body and rigid connections

PAGE 127

Explicit Dynamics with LS-DYNA

Joint – Cylindrical joint

PAGE 128

“Door hinge”: rotation and translation only possible in the direction of axis N1-N2.

joints can be only defined between rigid bodies. Consequently rigid spiders are often used. a) *MAT_RIGID b) *CONSTRAINED_NODAL_RIGID_BODY Nodes for joints can be connected with *CONSTRAINED_EXTRA_NODES to existing rigid bodies

Explicit Dynamics with LS-DYNA

Joint – Cylindrical joint Joint, as constructed in LS-DYNA

PAGE 129

Joint extracted for better visualization and easier checking.

The nodal pairs N1/N2 and N3/N4 must be coincide, i. e. they must have the same nodal coordinates. In contrast, it is positive if the single nodal pairs are far apart, for a optimal joint operation. recommended: • small mass points applied to each joint node, in order to omit warning message „mass less nodes“.

Explicit Dynamics with LS-DYNA

Joint – Spherical joint Sperical joint: rotation in all directions. joints can be only defined between rigid bodies. Consequently rigid spiders are often used. a) *MAT_RIGID b) *CONSTRAINED_NODAL_RIGID_BODY Nodes for joints can be connected with *CONSTRAINED_EXTRA_NODES to existing rigid bodies

PAGE 130

Explicit Dynamics with LS-DYNA

Joint – Spherical joint Joint, as constructed in LS-DYNA

PAGE 131

Joint extracted for better visualization and easier checking.

The nodes N1/N2 must be coincide, i. e. they must have the same nodal coordinates.

recommended: • small mass points applied to each joint node, in order to omit warning message „mass less nodes“.

Explicit Dynamics with LS-DYNA

Joints

PAGE 132

Gear drive:

nodal pairs (1,3) and (2,4) define axis orthogonal to the plane of the gear, nodal pairs (1,5) and (2,6) define vectors lying in the plane of the gear

Rack drive:

nodal pairs (1,3) define a vector orthogonal to the plane of the gear, nodal pairs (1,5) define a vector lying in the plane of the gear and nodal pair (2,4) define the motion direction of the second body

Explicit Dynamics with LS-DYNA

Joints *CONSTRAINED_JOINT_STIFFNESS_OPTION - defines a curve for force vs displacement and stop angles of joints, which are defined using *CONSTRAINED_JOINT_OPTION

e.g. *CONSTRAINED_JOINT_STIFFNESS_GENERALIZED defines in addition to a joint - torsional moment versus angle change - damping moment versus angle change velocity - frictional moment due to angle change - stop angle (elastic)

PAGE 133

Explicit Dynamics with LS-DYNA

Rigids and rigid connections

PAGE 134

*CONSTRAINED_ADAPTIVITY - using adaptiove meshing produces new nodes which do not have a connection to adjacent nodes (hanging nodes); those nodes are then connected to the adjacent element edge - the coupling is done automaticall; all 6 DOF are connected

Explicit Dynamics with LS-DYNA

PAGE 135

Damping Rayleigh – Damping - equation of motion:

.. . M. u (t)  C. u (t)  K.u(t)  p(t)

- Rayleigh-damping:

C  α.M  β.K

- attenuation factor:

 

with M as mass matrix and K as stiffness matrix

   2 2

0

with

0

>mass proportional damping:

>stiffness proportional damping

with C as damping matrix

 

 

 2



0

– Eigen frequency and   2f

0



0

2

the mass proportional damping affects mainly lower frequencies - for the highest eigenfrequency  it is almost zero - global velocities are damped, i.e. a free flying body is decelerated due to mass proportional Damping.

Explicit Dynamics with LS-DYNA

Damping

PAGE 136

The stiffness proportional damping affects mainly higher frequencies - relative velocities in the material are damped - for a damping value, which has been chosen to damp low frequencies significant, it might happen, that for high frequencies the damping is already overcritical. On the other hand the high frequencies govern the critical time step, such that overcritical damping might lead to instabilities in the explicit time integration. Therefore use stiffness proportional damping with care! - since LS-DYNA version 960 the input value for *DAMPING_PART_STIFFNESS is no longer ß, but a factor for the critical damping of the highest eigenfrequency.

 

 2

0

Explicit Dynamics with LS-DYNA

PAGE 137

Damping 5 types of damping are available a) *ELEMENT_DISCRETE b) *DAMPING_GLOBAL

> discrete damper element > a mass proportional system damping (Rayleigh damping) defined globally for all nodes of deformable bodies and for the mass centre of mass of rigid bodies c) *DAMPING_PART_MASS > a mass proportional damping only for the defined parts d) *DAMPING_PART_STIFFNESS > a stiffness proportional damping (Rayleigh damping) for the defined parts e) *DAMPING_RELATIVE > a mass proportional damping relative to the movement of a rigid body -the types b) to e) correspond to the Rayleigh-damping:

C  α.M  β.K

the term

α.M

damps low frequencies (vibration period large)

the term

β.K

damps high frequencies (vibration period small)

Explicit Dynamics with LS-DYNA

Output controls

PAGE 138

Four different kinds of result files are created in LS-DYNA: > binary plot files d3plotnn > binary time history database d3thdtnn > ASCII database > BINOUT (binary data basis for ASCII-Files) > binary interface force files Binary plot file d3plot - contains for all nodes the displacements, velocities and accelerations - contains for all elements the stresses and strains - predominantly used for visualisation and animation of deformations, stresses and strains, e.g. with the postprocessor LS-POST - the output frequency must be defined in *DATABASE_BINARY_D3PLOT care should be taken to produce not to much data > usually 20 to 100 states are written during a simulation - with *DATABASE_EXTENT_BINARY the extent of output data can be controlled - it is a nice option to set *DATABASE_EXTENT_BINARY, ieverp=1 ; thus every output state is written to a separate file with the name d3plotnn ; after the first postprocessing, all unnecessary files might be deleted

Explicit Dynamics with LS-DYNA

Output controls

PAGE 139

Time history file d3thdt - contains some global results (energies, rigid body displacements) - contains displacements, velocities and accelerations only for selected nodes - contains stresses and strains only for selected elements - with *DATABASE_HISTORY_... the desired nodes and elements must be specified - with *DATABASE_BINARY_D3THDT the desired output frequency must be specified -since this file contains only the results of some nodes and elements, a smaller output increment can be chosen > usually in-between 1000 and 10000 time steps within a calculation - post processing can be done with LS-POST

Explicit Dynamics with LS-DYNA

Output controls

PAGE 140

ASCII files -in addition to the two binary result files there is still a family of ASCII result files: > GLSTAT - contains the total energy balance > MATSUM - contains the energy for all parts separately > NODOUT - contains the displacements of selected nodes > ELOUT - contains the forces and stresses of selected elements > DEFORC - contains the forces of all discrete spring and damper elements > RBDOUT - contains the displacements of all rigid bodies > RCFORC - contains the resultant forces for each contact definition > NCFORC - contains the single node forces for each contact definition > SPCFORC - contains the reaction forces for nodes having SPC boundary conditions > JNTFORC - contains the forces in joints > BNDOUT - contains forces and energies for external load definitions - the output increment is defined with *DATABASE_... (e.g. *DATABASE_GLSTAT) - the number of output steps might be in-between 100 and 10000; a unique number for all files cannot be given, since the size of these files can differ significantly, e.g. the file rcforc is very compact, while the file rbdout can be much larger, even with the same number of output steps (depending on how much rigid bodies exist) - for the files nodout and elout the desired nodes and elements must be specified with *DATABASE_HISTORY_... - LS-POST is able to plot this data

Explicit Dynamics with LS-DYNA

Output controls

PAGE 141

- besides the already mentioned ASCII files, there are additional ones: > GCEOUT: - contains the contact forces on geometric contact entities > SLEOUT: - contains the energies of contact surfaces > SECFORC: - contains the cross section forces (*DATABASE_CROSS_SECTION) > SBTOUT: - contains the forces and stresses of seat belts (*ELEMENT_SEATBELT) > RWFORC: - contains the contact forces of the rigid walls (*RIGIDWALL) > NODFORC: - contains the forces of defined groups of nodes (*DATABASE_NODAL_FORCE_GROUP) > ABSTAT: - contains Airbag statistics > SWFORC: - contains forces in spot welds (*CONSRAINED_SPOTWELD) > TPRINT: - contains thermal output from a thermal or coupled structural-thermal Analysis -post processing of all ASCII data is done using LS-PrePost MPP-DYNA can not produce ASCII data, except GLSTAT. Instead a binary file dbout.nnnn is written. nnnn is the processor number, i.e. there are as many dbout.* files as processors used. The files dbout.* must be translated at the end of an mpp run with an additional program dumpbdb in order to generate the ASCII files: cat dbout.* > dbout dumpbdb dbout

Explicit Dynamics with LS-DYNA

Output controls

PAGE 142

BINOUT Since version 970 all ASCII files can be written to a binary file. This binout file can be directly read by LS-PrePost (currently not recommended). A small additional program l2a converts the binout file again into ASCII files: l2a binout* The binout file is typically used in MPP-DYNA as a newer alternative to the dbout-Files; it is also available for SMP-Version On the *DATABASE_option card one can set with the parameter binary, whether ASCII data directly or binout has to be generated. Using binary=3 both methods are written (ASCII-Files and binout); this is recommended for MPP runs. The SMP version writes per run only one binout-File, the MPP versionn typically more than one (e.g.. binout0000, binout0004)

Explicit Dynamics with LS-DYNA

Output controls

PAGE 143

Interface force file - contains contact forces for all contact segments - by default this file is not created, use the parameter s=d3intf on the command line of LS-DYNA to create this file (d3intf is an arbitrary file name)

- by default the output increment is the same as for d3plot - the ooutput frequency is input using *DATABASE_BINARY_INTFOR - in the contact definitions one has to specify whether or not the output for this contact is included in the Interface-Force-File (*CONTACT_, card 1, spr, mpr) - the evaluation of the Interface-Force-Files takes place with LS-POST analogue to the evaluation of the plot-files

Explicit Dynamics with LS-DYNA

Output controls Message file is a type of error file and contains all warnings and error messages like initial penetrations, contact reorientation, nodes with no mass, …

D3HSP file (High Speed Printer) contains an report, how the input data is interpreted by LS-DYNA

PAGE 144

Explicit Dynamics with LS-DYNA

Restart

PAGE 145

- in case that a calculation is stopped with the ‘sense switch’ code or terminated normally due to endtime, a restart file is written with the name d3dumpnn . This restart file can be later used to continue (restart) the calculation - 3 types of restart are available: > the simple restart > the so-called „little restart“ > the „big restart“ (full restart) - instead of d3dumpnn the so called “running restart file” runrsf could be also used - with *DATABASE_BINARY_RUNRSF the output frequency for this file can be defined and the previous file is overwritten - only one file runrsf exists, so it can be written more often than the d3dumpnn - rename this file before using it as a restart file

The simple restart - the simple restart is used to continue a stopped calculation without any modifications: -restart the simulation with lsdyna r=d3dumpnn

Explicit Dynamics with LS-DYNA

Restart The “little” restart -small changes in the model input are possible: > change of the termination time and the output frequencies > deletion of contact surfaces > deletion of elements or parts > switch deformable bodies to rigid bodies and vice versa > change of velocities > change of load curves - the restart input file contains only this changes, e.g. for termination time: *KEYWORD *CONTROL_TERMINATION 120.0 *END -continue the calculation with lsdyna i={restart inputfile} r={restart file} - all output files will be appended, nothing overwritten

PAGE 146

Explicit Dynamics with LS-DYNA

PAGE 147

Restart The following keywords can be used in a “little” restart: *CHANGE_OPTION_ -> possible options are:

*CONTROL_DYNAMIC_RELAXATION *CONTROL_TERMINATION *CONTROL_TIMESTEP *DAMPING_GLOBAL *DATABASE_OPTION *DATABASE_BINARY_OPTION *DELETE_OPTION *INTERFACE_SPRINGBACK *RIGID_DEFORMABLE_OPTION *TERMINATION_OPTION *TITLE *KEYWORD *CONTROL_CPU

BOUNDARY_CONDITION CONTACT_SMALL_PENETRATION CURVE_DEFINITION RIGID_BODY_CONSTRAINT RIGID_BODY_STOPPER STATUS_REPORT_FREQUENCY THERMAL_PARAMETERS VELOCITY VELOCITY_NODE VELOCITY_RIGID_BODY VELOCITY_ZERO

*SET_OPTION

*DEFINE_OPTION

Explicit Dynamics with LS-DYNA

Restart

PAGE 148

The “big” restart -a „big” restart is necessary for those changes, which are not possible with a „little“ restart - the restart input file contains now a complete input file and the additional input line *STRESS_INITIALIZATION (identification for the “big” restart). This will describe, how the „ old” results are transferred to the „new” model - initial velocities in the input file are ignored; in order to set velocities at the beginning of the restart, use *CHANGE_VELOCITY_...

-the new calculation starts at the time step where the old has ended - all output-files, e.g. d3plot or glstat are created new, i.e. the old result files would be overwritten

Explicit Dynamics with LS-DYNA

Static prestress

PAGE 149

Dynamic relaxation - dynamic relaxation is a method to obtain a static solution respectively a static prestress in LS-DYNA although an explicit time integration used. - the difference to a transient calculation is, that the program uses the critical damping for all nodes in order to get the static solution as fast as possible; the static solution is reached, if the kinetic energy falls below a certain tolerance -dynamic relaxation can be carried out before a transient analysis in order to model a static prestress Initialisation to a prescribed geometry another way to start a explicit simulation with a prestressed model: - perform an implicit calculating using an arbitrary program and write out all displacements - set *CONTROL_DYNAMIC_RELAXATION , idrflg =2 - start LS-DYNA and include the input of these displacements with the command line option: m=filename > LS-DYNA will calculate the stresses based on the given displacements and use it for the further calculation (displacements applied linearly in 100 steps such that history variables calculated as well)

Explicit Dynamics with LS-DYNA

PAGE 150

Units in LS-DYNA Mass Length Time kg m sec kg cm sec kg cm ms kg cm ms kg mm ms gm cm sec gm cm ms gm mm sec gm mm ms ton (1000 kg) mm sec lbf-sec^2/in in sec slug ft sec

Force N 1e-02N 1e+04N 1e+10N kN dyne 1e+07N 1e-06N N N lbf lbf

Stress Pa

Energy Joule

GPa dyne/cm^2 Mbar Pa MPa MPa psi psf

kN-mm erg 1e7Ncm N-mm N-mm lbf-in lbf-ft

(steel) 7.83e+03 7.83e-03 7.83e-03 7.83e-03 7.83e-06 7.83e+00 7.83e+00 7.83e-03 7.83e-03 7.83e-09 7.33e-04 1.52e+01

E(steel) 2,07E+11 2,07E+09 2,07E+03 2,07E-03 2,07E+02 2,07E+12 2,07E+00 2,07E+11 2,07E+05 2,07E+05 3,00E+07 4,32E+09

* 1 slug = 32.18 kg; 1 ft = 0.3048 m = 12*2.54 cm; 1 N = 105dyne = 1 lbf/4.4482; 1 Mbar = 1012 dynes/cm2; 1 bar = 14.7 psi = 1.0 atm= 105 Pa; 1 kg/m3 = 10-3 gm/cm3 = 0.9112 slug/ft3

Explicit Dynamics with LS-DYNA

Units in LS-DYNA

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Recommendations for *CONTROL

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Recommendations for *CONTROL

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Recommendations for Shell Elements Simplest Belytscko Tsay, fast:

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Recommendations for Shell Elements Simplest Shell-Element Belytscko Tsay, more accurat (20% slower):

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Recommendations for Shell Elements Higher Shell-Element Fully integrated, default:

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Recommendations for Shell Elements Higher Shell-Element Fully integrated, more accurate (20% slower):

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Recommendations for Contacts Contact:

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LS-DYNA related links http://www.lstc.com LSTC’s Homepage

http://www.dynasupport.com/ Tutorials, Howtos, FAQ, Manuals, Release Notes http://www.topcrunch.org Benchmarking for Hardware, car model Neon & 3-cars http://www.ncac.gwu.edu/vml/models.html Freely available car models, Barriers http://www.feainformation.com Latest information on LS-DYNA and related things http://www.feapublications.com LS-DYNA Newsletter respectivly FEA-Newsletter

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