Autodyn Blast

Computer Modeling of Blast Loading Effects on Bridges Greg Black Lafayette College Easton, Pennsylvania Advisor: Dr. Jennifer Righman University of Delaware Newark, Delaware Submitted to NSF-REU 11 August 2006

Abstract The goal of this report is to evaluate a hydrocode, which is a type of computer program, called AUTODYN for the use of modeling blast loads on bridge sections. Blast modeling is necessary due to the threats posed by terrorist attack and current technology makes computer simulations cheaper than experimental testing. It discusses various options presented by AUTODYN which set it apart from other hydrocodes and other available software. These include the benefits of it graphical interface, modeling options and remapping capabilities. Meanwhile, its large demand on memory for complex models creates issues in the modeling phase, before the models can actually be analyzed. Yet if the user can get past the quirks of the program and work within the memory limits it is possible to obtain fairly accurate results from carefully made models.

Table of Contents ABSTRACT .................................................................................................................................................. 2 1 INTRODUCTION ..................................................................................................................................... 5 2 INTRODUCTION TO BLASTS .............................................................................................................. 5 2.1 EXPLOSIONS ......................................................................................................................................... 6 2.2 CONWEP............................................................................................................................................... 7 3 INTRODUCTION TO HYDROCODES ................................................................................................. 8 3.1 MODELING TECHNIQUES ...................................................................................................................... 9 3.1.1 Structured vs. Unstructured Solvers .......................................................................................... 11 3.1.2 Lagrange Solvers ....................................................................................................................... 13 3.1.3 Euler Solvers.............................................................................................................................. 14 3.1.4 Other Solvers ............................................................................................................................. 16 3.2 INTRODUCTION TO AUTODYN.......................................................................................................... 17 3.2.1 Material Models......................................................................................................................... 18 3.2.2 Parts........................................................................................................................................... 20 4 MODELING AND RESULTS................................................................................................................ 23 4.1 AUTODYN MODELS ......................................................................................................................... 23 4.2 RESULTS AND DISCUSSION ................................................................................................................. 27 4.2.1 Pressure in the Slab ................................................................................................................... 28 4.2.2 Deflection in the Slab................................................................................................................. 32 4.2.3 Effective Strain in the Slab......................................................................................................... 33 4.2.4 Pressure in the Air ..................................................................................................................... 34 4.2.5 Conclusions and Suggestions for Future Investigation.............................................................. 37 5 ACKNOWLEDGEMENTS .................................................................................................................... 38 6 REFERENCES ........................................................................................................................................ 38 APPENDIX – MODELING NOTES ........................................................................................................ 40

List of Figures Figure 2.1 – Charge and Blast Wave...............................................................................................6 Figure 2.2 – Standard Pressure vs. Time Curve for an Explosion...................................................7 Figure 3.1 – Example Grid.............................................................................................................10 Figure 3.2 – Typical Calculation Sequence...................................................................................11 Figure 3.3 – Structured Grid..........................................................................................................12 Figure 3.4 – Unstructured Grid......................................................................................................13 Figure 3.5 – Example Lagrange Grid…………………………………………………………………...13 Figure 3.6 – Example of Normal Mesh and (a)-(d) Examples of Problematic Mesh Distortion…..14 Figure 3.7 – Stationary Euler Grid Example……………………………………………………………15 Figure 3.8 – Example SPH Node Dispersal……………………………………………………………17 Figure 3.9 – Example of Erosion………………………………………………………………………..19 Figure 4.1 – Standard Slab, Air and Charge Model…………………………………………………...24 Figure 4.2 – Standard Slab, Air and Charge Model…………………………………………………...24 Figure 4.3 – (a) Moving Gauges in Slab (b) Fixed Gauges in Air…………………………………...26 Figure 4.4 – Pressure vs. Time for Gauge #1, Same Air Element Size.........................................28 Figure 4.5 – Pressure vs. Time for Gauge #2, Same Air Element Size.........................................29 Figure 4.6 – Pressure vs. Time for Gauge #1, Same Slab Element Size......................................30 Figure 4.7 – Pressure vs. Time for Gauge #2, Same Slab Element Size......................................31 Figure 4.8 – Deflection Comparison for the Back Center of the Slab............................................32 Figure 4.9 – Effective Strain vs. Time for Gauge #2, Same Air Element Size...............................33 Figure 4.10 – Effective Strain vs. Time for Gauge #2, Same Slab Element Size..........................34 Figure 4.11 – Initial Pressure Results for 1000mm from Charge Center.......................................35 Figure 4.12 – Remap of Wedge onto 20mmel Air and 20mmel Slab.............................................36 Figure 4.13 – Comparison of 10mmel Wedge, ConWep and Remapping Results at 1000mm from Center of Charge...........................................................................................................................37

List of Tables Table 4.1 – Models........................................................................................................................27 Table 4.2– Gauge #1 Initial Peak Pressure, Same Air Element Size............................................29 Table 4.3 – Gauge #2 Initial Peak Pressure, Same Air Element Size...........................................29 Table 4.4 – Gauge #1 Initial Peak Pressures, Same Slab Element Size.......................................31 Table 4.5 – Gauge #2 Initial Peak Pressures, Same Slab Element Size.......................................31

1 Introduction The events of 9/11 continue to have a lasting effect on the US and the world. Everyone on the planet has been affected in some way or another. The implications of the vulnerability of the nation’s infrastructure to terrorist attack are a concern that should be shared by all engineers. If bridges and other structures may be subjected to severe loads from explosions or other sources, then it is the engineer’s responsibility to prepare for them. However, before design codes can be better developed or adequate protections can be created it is necessary to gain a better understanding of the complex interactions between structures and explosions. Yet methods for explosive testing are limited due to cost and permissions for experimental results. Therefore, with modern advances in computing technology called hydrocodes may be a better option. This paper will evaluate a hydrocode program called AUTODYN for the use of blast simulation on complex structures, with a focus on hydrocodes as a technology and user interactions with the program as well as the accuracy of the several simulations run in the program. It will also provide the reader with a brief overview of blasts or explosions in order to provide some background on the subject as well as a basis for the comparison of test results.

2 Introduction to Blasts This section will discuss a few of the basic properties of explosions. Once these ideas are understood, the interactions between explosions and structures can be more easily discussed. It will also discuss ConWep, a blast calculation program distributed by

the United States government (Robert, 2007), which will be used to evaluate the performance of AUTODYN.

2.1 Explosions Figure 2.1 depicts a few of the basic characteristics of a simple explosion in air. There is the charge (a), the pressure wave (p) and the standoff distance (r). The main component that any explosion requires is some type of fuel or charge such as TNT. When ignited, this charge rapidly releases energy in the forms such as heat, sound or pressure waves (Robert, 2007). The pressure wave expands out from the charge. The leading edge of this wave is sometimes called the “shock front” and will generally have the highest pressure in the wave at any given point in time (Wilkinson et al., 2003). The standoff distance is basically the distance from the center of the explosion to any object or point of interest.

P r

a Spherical Air Blast

Figure 2.1 – Charge and Blast Wave (Robert, 2007)

The pressure at a specific point in air in the path of an explosion over time will follow the same general pattern, so long as there isn’t any reflection from nearby objects. This pattern, called an overpressure curve (Wilkinson et al., 2003) can be seen in Figure 2.2, below. The main components of the overpressure curve are the detonation (a), arrival time (b), peak pressure (c), and time duration (c to e). The detonation can be

considered as time 0, while the arrival time is the time that it takes for the pressure wave to reach the point of interest (Robert, 2007). Once the peak pressure is reached, it immediately starts to decay and the time it takes the pressure to return to normal is called the time duration (Wilkinson et al., 2003). As the material in the blast wave expands outward it can leave a void, creating a region with pressure lower than normal atmospheric pressure (Robert, 2007). The size, shape and material of the charge, as well as the stand off distance will all determine the magnitude and shape of this curve. In addition to the above factors, the blast wave and the pressure involved can reflect off of surfaces in various directions, and cause further fluctuations in pressure at a single point.

1.0 c

SoD = 1000 mm

Blast Over Pressure, P, MPa

0.9

CONWEP Calculations Explosive: TNT Quantity: 1 kg

0.8 0.7 0.6 0.5 0.4 0.3 0.2

d

0.1 0

a 0

e

b 0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Time, t, ms.

Figure 2.2 – Standard Pressure vs. Time Curve for an Explosion (Robert, 2007)

2.2 ConWep As mentioned above, ConWep is a simple blast program distributed by the United States government. Users can input a charge size and standoff distance and receive

pressure for that point in relation to time as output. It also allows users to receive pressure data after interaction with simple structures such as plates and shells. ConWep is not guaranteed to give a 100% accurate result, but it has been compared to hand calculations and found to be generally correct (Robert, 2007). For phenomena as complex as explosions a generally correct answer may be the best one. A main disadvantage of ConWep comes from the fact that pressure curves can only be obtained for one point at a time. Also ConWep has limited structural interaction capabilities, and certainly cannot evaluate failure or deformation in a structural component.

3 Introduction to Hydrocodes While the damage level produced by blasts is what makes them so critical for examination, it is this same nature that makes experimental studies expensive and difficult. In addition, the dynamic, time dependent nature of the loads produced by blasts increases the complexity further, especially when compared to simple static loads. Large scale tests can require millions of dollars in investments (Zukas, 2004). Therefore, anyone doing experimental blast research needs an almost bottomless source of funding. For the purposes of this project, the costs of destroying a bridge or even simple structure, as well as having the permission to do so, make such testing out of reach. Therefore, anyone interested in examining the effects of an explosion on a structure needs to look into alternatives to experimental testing. One such alternative has been made possible through advanced computer programs called hydrocodes. What is a hydrocode and what is it used for? Zukas defines

a hydrocode as “a computer program for the study of very fast, very intense loading on materials and structures”(2004). Developed in the 1960’s, hydrocodes originally performed calculations by assuming hydrodynamic behavior in the materials, and therefore ignoring material strength, which is the origin of the term hydrocode. This method was used because the pressures generated by experiments often greatly surpassed the strength of the materials (Zukas, 2004). Also, while many of the calculations performed by hydrocodes could be done by hand or even with the use of a calculator, the shear number of calculations involved in even simple problems makes the use of powerful computers invaluable. Modern hydrocodes, including AUTODYN do a great deal more than model the hydrodynamic behavior of materials, but the name has stuck. They can make use of a variety of methods to model different material behaviors. In addition to their use in blast modeling, hydrocodes have been used to evaluate structures for aircraft impacts, to simulate vehicle crashes and even design sports equipment (Zukas, 2004). The following sections will detail some of the methods hydrocodes use in modeling, with a focus on Lagrangian and Eulerian models in particular.

3.1 Modeling Techniques The systems used for modeling in hydrocodes are based on finite element and finite difference techniques. How these techniques are implemented may vary, just as the computer code used to write these programs will not be exactly the same. However, there are many similarities due to their common basis. It is these common aspects which will be discussed below. Usually the first step in modeling is to divide the problem up

into a finite system of nodes and elements as seen below in Figure 3.1. The configuration of these systems, as well as how properties such as mass, energy and material strength are dealt with is the main way of distinguishing between various methods. Lagrangian codes and Eulerian codes are the two basic methods which are implemented in hydrocodes such as AUTODYN.

Figure 3.1 – Example Grid (AUTODYN, 2005b)

Hydrocodes make use of a set of differential equations called equations of state (EOS) which are based in classical continuum dynamics. An EOS “relates the density (or volume) and internal energy (or temperature) of the material with pressure”(Anderson, 1987). It does this by applying the principles of conservation of mass, momentum and energy. For example, uniform gases would typically be modeled with an EOS based on the Ideal Gas Law. Other relationships help to describe the nature of the material to be modeled by relating the stress and strain to each other based on material properties. These can incorporate strain rate, work hardening, thermal softening and other things which can affect material properties and behavior. A typical order for calculations can be seen below (Figure 3.2).

Figure 3.2 – Typical Calculation Sequence

Using these relationships, the modeling program will advance the calculations forward a short period, called a timestep, and then perform this sequence of calculations again. Since the timestep is an important variable, the program will often have a method to calculate it on its own. This calculation incorporates the speed of sound in the material (soundspeed), element size and some type of safety factor to prevent the timestep from becoming to large (Zukas, 2004). Smaller safety factors result in smaller timesteps and therefore more accurate the calculations. Smaller timesteps will require the performance of more calculations to reach the same point in time. Therefore element size not only determines the complexity of the problem spatially but temporally as well.

3.1.1 Structured vs. Unstructured Solvers As has already been mentioned, the setup of the grid of elements and nodes is critical to the modeling process. Generally, smaller element sizes will allow for more accurate calculations, while larger element sizes sacrifice accuracy for rapidity and

simplicity in the calculation process. Size is not the only factor to consider in mesh generation though. This is where the differences in structured and unstructured solvers become involved. The distinguishing feature of a structured mesh is its organization. The lines which form the elements and nodes are set up in a way to ease calculations with a regular numbering scheme (Mathis et al., 2005). In addition, the elements formed will tend to be quadrilaterals (at least in 2D). AUTODYN, for example, uses a coordinate system in which each line is assigned a number in structured parts (Figure 3.3). In fact, any part generated directly in AUTODYN will be a structured part. This system makes progressive calculations easier to perform, since related nodes and elements are next to each other in this numbering scheme.

Figure 3.3 – Structured Grid

Unstructured meshes lack organization. The lines which form the elements and nodes do not have a regular numbering scheme. The elements formed can have any shape, although triangles seem to be a favored. The main advantage of unstructured meshes seems to be their ability to accurately represent both the surface geometry and macrostructure of a material (Mathis et al., 2005). However, since they lack the organization of structured meshes, more time is spent determining which nodes and

elements are related. The only way to use an unstructured mesh in AUTODYN is to import it from another program.

Figure 3.4 – Unstructured Grid (Mathis et al. 2005)

Therefore, unstructured grids are generally preferred where complex geometries or macrostructures are involved, while structured grids are preferred when the geometry is simple.

3.1.2 Lagrange Solvers As mentioned above, Lagrange solvers are one of the basic models used in hydrocodes. One of the distinguishing features of a Lagrange code is that the grid it uses is created so that cell boundaries occur at free surfaces and material boundaries. Another is that during calculations, the mesh will distort to match the distortion of the material, as seen in Figure 3.5 below. In a typical Lagrange mesh, coordinates, velocities, forces, and masses are associated with the corner nodes, while stresses, strains, pressures, energies and densities are centered within the cells (Birnbaum et al., 1999).

Figure 3.5 – Example Lagrange Grid (Birnbaum et al. 1999)

The main problems with Lagrange solvers occur when large deformations are involved. Severe distortion of the mesh can result in inaccuracies, negative densities and extremely small timesteps (Figure 3.6). In order to avoid this it is may be necessary to eliminate the overly deformed cells by manually redrawing the mesh or “rezoning” (Birnbaum et al., 1999). Therefore they are typically not used for models which involve flow or large distortion.

Figure 3.6 – Example of Normal Mesh and (a)-(d) Examples of Problematic Mesh Distortion (AUTODYN, 2005b)

One of the advantages of a Lagrange mesh is that it moves with the material. Therefore, the movement of a single section or point in an object is easy to track. Lagrange solvers are often used in impact models (where two solid objects collide), as both target and projectile.

3.1.3 Euler Solvers Euler solvers, the other basic hydrocode model, differ from Lagrangian solvers in a few basic ways. Instead of confining the grid to only the objects being modeled, Euler

solvers place a grid over the space in which the materials can move. As the calculation progresses, the material of interest will move while the grid remains stationary (Figure 3.6). Individual nodes and cells are basically observing as the material being modeled flows by. In a typical Euler model, the centers of the cells are used as interpolation points for all variables, unlike Lagrange models as described above (Birnbaum et al., 1999).

Figure 3.7 – Stationary Euler Grid Example

The main problems with Euler codes are with the amount of elements they require, and their poor handling of geometry. Since you are not only modeling the object of interest, but the space around that object, more elements and therefore more memory and more time can be required than a standard Lagrange model. Also since the grid does not distort with the object of interest, it becomes more difficult to track the various components of a part, and therefore observe how a single piece behaves over time. Therefore, Euler models are typically not used to model solid objects. The advantage of Euler solvers is that they do not deform and therefore are not subject to the limitations imposed by deformation in Lagrange solvers. They can also

allow the mixing of different materials inside the cells. Therefore the shape of material surfaces is not completely limited by element size. They are used when a problem involves high levels of deformation or fluid flow (i.e. gases and liquids), while Lagrange solvers are normally used to model solids which don’t experience severe deformation.

3.1.4 Other Solvers Since the two basic solvers listed above each can have difficulty in modeling some situations, scientists and computer programmers have developed alternatives. These alternatives become particularly useful in modeling situations in which Euler and Lagrange models have difficulty. Arbitrary Lagrange Euler (ALE) solvers are a combination of the two basic solvers. They make use of an “automatic rezoning” technique in which the deformation of the grid is limited (Birnbaum et al., 1999). The different parts of an ALE will act more like a Lagrange or more like a Euler solver depending on the limitations the user puts in. The main problems with ALE solvers are the amount of user input required and their handling of contact surfaces. They perform well in modeling solids, fluids or gases so long as large flows are not involved. Structural solvers (note this is a different term from the structured solvers mentioned earlier), such as STAAD, which are made to handle beams, rods, and shells, can also be used. These models are formulated to deal with specific geometries and therefore handled the calculations more easily than a Lagrange or Euler solver could. Shell solvers, for instance, are designed to handle thin structures. Therefore, it is assumed to be in a biaxial state of stress, ignoring the component along its thickness, and

the timestep is only controlled by the length of the cells (Birnbaum et al., 1999). Since the timestep just depends on the length, the program can run through the calculations more easily, and with fewer cycles. There are other gridless techniques which avoid the issues that occur with large deformations. Smooth Particle Hydrodynamics (SPH) is one such technique which has its basis in Lagrange solvers (meaning its nodes move as the part moves). The SPH solver does not use cells or elements. Instead, as the name implies, SPH materials are treated as if they are made up of a group of particles. This is similar to what a Lagrange solver would be if it was made up of nodes only, or can alternatively be seen as a completely unstructured solver. An example can be seen below (Figure 3.7). The main disadvantage of SPH solvers is that they are a relatively new method, and therefore less developed than other techniques (Birnbaum et al., 1999).

Figure 3.8 – Example SPH Node Dispersal (Hayhurst et al., 1996)

3.2 Introduction to AUTODYN Various programs have their own particular way of putting together and implementing the techniques mentioned above, while retaining many of the basic principles. The main benefit that can be attributed to AUTODYN (at least among

hydrocodes) is its graphical user interface (GUI) for creating the models, running the simulations and observing the results. Other programs can model complex situations just as well as, or even better than, AUTODYN. However, for users not accustomed to inputting and receiving data via lines of code, AUTODYN becomes a useful tool. This section will detail some of the specifics of using AUTODYN in general terms, without going into the technical details, such as specific equations.

3.2.1 Material Models The Materials button gives access to a range of options which basically allow the user to specify which types of materials they wish to model and what type of situation is expected. The user can input the information for a new material or make use of the preexisting materials provided by AUTODYN. In either case it is possible to modify the properties of the material in question, such as density or soundspeed. Here it is very important to stress that the user understand what type of behavior they expect the material to encounter and therefore understand which particular material model(s) may be appropriate. Real life data, including duplicable experiments, is critical to establishing accurate models. In the Modify section, the user can specify the equation of state for the material and specify the appropriate variables for that substance. This allows the user to determine whether the material is a gas, metal, porous material, explosive, polymer, etc and input the properties of that particular substance. A strength subsection lets the user input properties of a structural nature such as tensile strength. The Failure subsection deals with how that particular material will fail as well as how AUTODYN will display that failure. Of particular importance in this case is how

the model deals with damage. Concrete for example has its own particular failure model which can make use of a crack softening model in addition to other failure modes. Damage in concrete is rated on a scale from 0 to 1 in relation to the strain at failure, with 0 being a fully intact cell and 1 being a fully failed cell (AUTODYN, 2005b). Users can employ a visualization technique in Plots under Mater Status which will display which cells have reached a selected failure level. The next subsection deals with erosion of the material. It allows the user to determine whether or not an element will erode and at what point it will do so. When an element reaches a specified strain limit, it is “eroded.” This means that the element is “either discarded, or…transformed from a solid element to a free mass node disconnected from the original mesh”(Birnbaum et al., 1999). Basically, the element breaks down and either disappears or breaks off from the rest of the part and behaves like a particle (Figure 3.9). This option is noteworthy because it is one method the program uses to prevent the errors that normally result when Lagrange parts suffer from large distortions.

Figure 3.9 – Example of Erosion, Note: Eroded nodes are in yellow (Birnbaum et al. 1999)

In most of these sections the user can define their own governing equations or constants for the material. So it seems that there is a great deal that AUTODYN can do for those wishing to develop new materials from material models.

3.2.2 Parts The Part section of AUTODYN is actually where most of the “modeling” takes place. A part is basically any distinct component of the system the user wishes to model. Other sections will allow the user to define things such as initial conditions and boundaries, but they won’t actually apply it to the model until they are assigned in the parts section. In the Part section, the user creates a part by either going through the process of importing an object from another program, or by creating a whole new part. To create a new part, first, the user specifies the type of solver they wish to use (i.e. Lagrange or Euler). Next, the use creates the overall shape and mesh, which is the system of elements and nodes which make up the part. The last thing the user does is to decide what type of material the part is made of. As already mentioned, AUTODYN does allow the user to import parts from other programs such as LS-DYNA. The manuals that come with the program provide the user with examples as to how this is done. However, this further complicates the process, since the user would need to learn another program. Since one of the benefits of AUTODYN is the comparative ease in which models are created, it seems unlikely that an inexperienced user would prefer another program. Therefore, unless the user is more experienced with the use of another program or wishes to make an unstructured part, as much of the model as possible should be created in AUTODYN.

One other point should be made when discussing the choice of solver, while using AUTODYN. Different solvers interact with the various options in AUTODYN in different ways. For instance in order to create an explosion from a charge it is necessary to use a Multimaterial Euler solver, which can be used with most materials instead of the Ideal Gas Euler solver, which can only be used with gas materials. Another example would be the case of boundary conditions. Euler solvers automatically treat their boundaries as rigid walls, so it is necessary to specify boundary conditions if the user wishes to allow material and other data to flow out of an Euler grid. AUTODYN also gives the user the option of collecting data over time for certain locations via gauges, while automatically doing so for parts or for materials as a whole. Gauges can be placed anywhere on the model and can either be fixed or moving. A fixed gauge will stay in one spot during the calculation no matter what the parts or materials are doing. Meanwhile a moving gauge will stay fixed to the material or element it starts at and record data as that material moves and deforms. Here it is important for the user to know what type of data they are interested in since certain variables require the user to specify them in the output section of AUTODYN. AUTODYN also has the capability to “remap” the results of one model onto another. This is beneficial since the user can take the results from a small part with a relatively fine grid and basically load data such as pressures, and velocities into a larger part with a coarser grid. Therefore, this larger model should then have more accurate results than if it was run from the same starting point as the smaller model. Yet there are limits to AUTODYN’s remapping capabilities. It only works for certain solvers, and although it works for the purpose of transferring a 1D Euler Multimaterial wedge to a 2D

or 3D part of any type, it is impossible to remap the results of a small 3D model made of anything but Euler Ideal gas. How well remapping actually performs is evaluated later, in the Results and Discussions section of this report. Here it is important to note some of the capabilities of AUTODYN, at least on a computer with 3.25 GB of RAM and a 3.60GHz Xeon CPU. Any attempt to make a part with more than about 2 million elements either caused the program to shut down with a “Memory allocation error”, or caused it to be too slow for it to be used. In addition, models with parts approaching 2 million elements left the user with limited visualization options. Basically, clicking rather simple options in the plots section such as contours, grid, or nodes and elements, caused the program to either freeze with a “Memory allocation error” or be so slow that the user must sit and wait before they can do anything. Also, it should be noted that the slide and movie generation capabilities of AUTODYN are fairly inconsistent from day to day. Often attempts to create an image or animation from AUTODYN results simply produce fuzzy pictures, while other times these built in functions will work fine. Usually, there is no obvious reason as to why these functions do or do not work. Run times for AUTODYN models also vary a great deal depending on the complexity of the model. A simple wedge model could probably run for thousands of cycles in a matter of minutes. Meanwhile a more complicated 3D or even large 2D part could take a day or two to run for a few hundred. AUTODYN does offer the option of using “parallel processing” which would allow a network of computers to work on solving a single problem. This would allow calculations to be performed more rapidly, and thus the running of the model would take

less time. However, it appears that the limiting factor is in the creation and visualization of the model and the displaying of results, which can only be done on a single computer. Therefore, it seems unlikely that “parallel processing” would be beneficial at this point in time unless the user desires to run a particularly complicated model for an extended period time.

4 Modeling and Results This section will discuss the development of the AUTODYN models used in this research. It will also cover the results of those models and their implications for computer models as part of the overall project in blast research.

4.1 AUTODYN Models The standard AUTODYN model that was used is seen below in Figure 4.1 while exact dimensions can be seen in Figure 4.2. This model was developed to be representative of a lateral bridge cross section, approximately 8 feet long by 8 inches thick slab that is fixed on both ends. The charge is based on a 100lb TNT charge as representation of a vehicular bomb at a standoff distance of about 4 feet. The charge was assumed to be a cube and then dimensions calculated based on a TNT density of 1.63g/cm3. Note that the center of the charge is located at the origin and is also the point of detonation.

Concrete Slab

Air TNT

Y X Figure 4.1 Standard Slab, Air and Charge Model 3400 1700

1700

2440 1220

1220

2000 1220

300 4000 300

2000

Figure 4.2 – Standard Slab, Air and Charge Model (Dimensions in mm) (Robert, 2007)

In each instance the slab, air and charge were made out of square elements. The air part that surrounds the slab was created to make sure that the explosion would be able to take place, and interact with the entire slab. It was modeled as a Multimaterial Euler part so that the explosion could be generated from a charge. The air is also at standard atmospheric pressure, and about 15 degrees Celsius at the start of the calculation. The boundary condition transmit was applied to all four sides of the air part to allow the flow created by the explosion to pass through. The only 2D slab model that had different dimensions for the air part consisted of 2mm elements in the slab and 2mm elements in the air. In that model the air of the lower half is shortened to only 400mm below the origin and only 1600mm on each side. A 3D model made of 20mm elements in the slab and in the air was also generated which was shortened to only 1000mm below the origin. This was done to keep the model size under 2 million elements in each case. Models which had a remapped wedge simply did not have the regular 300mm charge in the model. The remapped wedge itself is an axial symmetric Multimaterial Euler part 1200mm long with the origin set as the detonation point. The concrete slab was modeled using the standard material properties of 35MPa Concrete provided by AUTODYN. The standard properties include a porous density of 2.314g/cm3, and porous soundspeed of 2920m/s. It should also be noted that the concrete is not reinforced. The slab was created as a Lagrange part since AUTODYN allows Euler parts to interact with Lagrange parts. In addition, the slab had boundary conditions were applied to the end nodes. These boundary conditions were constant, zero velocities in both the x and y directions in order to simulate fixed ends in 2D.

Moving gauges were placed in the slab as seen in Figure 4.3 (a). Gauges #1 and #3 are each 100mm from the edge while Gauge #2 is in the center of the slab. All three gauges are centered vertically. These gauges were placed so that there would be no interference from the boundary conditions and so they would remain within the slab in the event of surface failure.

Figure 4.3 – (a) Moving Gauges in Slab (b) Fixed Gauges in Air

Some models also contain fixed gauges located at 1000mm (Gauge #4), 1200mm (Gauge #5) and 1220mm (Gauge #6) vertically above the detonation point (Figure 4.3 (b)). These gauges were placed when it became apparent that the planar models were producing peak pressures higher than anticipated by either past ConWep or hand calculations (see Results and Discussion section). A full list of the relevant models is provided below (Table 4.1). For more details on model generation see the Appendix.

Table 4.1 – Models Model 2000mm long 10mmel air wedge 1200mm long 1mmel air wedge 5mmel air + 40mmel slab 5mmel air + 20mmel slab 5mmel air + 10mmel slab 5mmel air + 5mmel slab 5mmel air + 5mmel slab with erosion 5mmel air + 5mmel slab with crack softening 5mmel air + 2mmel slab 2mmel air + 2mmel slab 10mmel air + 2mmel slab 10mmel air + 2mmel slab with additional variables 10mmel air without slab with normal charge 10mmel air without slab with circular charge 20mmel air + 20mmel slab with wedge remap 3D 20mmel air + 20mmel slab with wedge remap

Cycles Run

Finish Time (ms)

Fixed Gauges

Additional Variables

400

0.473406

yes

-

190mm charge radius

1800

0.176983

-

-

188mm charge radius, used for remaps

2000

0.524316

no

no

2000

0.52499

no

no

1976

0.51835

no

no

2000

0.521504

no

no

8000

2.050421

no

no

Retained inertia of eroded nodes

1300

0.411723

no

no

Failure mode switched to crack softening

8500

1.303755

yes

yes

8500

0.765133

no

no

10582

1.387083

no

no

8000

1.254802

yes

yes

800

0.722242

yes

no

759

0.592869

yes

no

10000

11.842196

yes

yes

600

1.152533

no

no

Notes

190mm charge radius

Model depth of 3040mm, Ideal Gas Euler used for air part

4.2 Results and Discussion This section will discuss the results of the models run in AUTODYN and their implications to future computer modeling. It covers the examination of three separate

variables: pressure in the slab and the air, effective strain and deflection. This section will also discuss some results of the attempts to use a different failure model (crack softening). Finally it will also discuss the outcomes of the remapping attempts.

4.2.1 Pressure in the Slab Initial models kept the air elements a constant size (5mm), while varying the size of the slab elements. Figures 4.4 and 4.5 are graphs which display the pressure results for Gauge #1 and Gauge #2 of these initial tests while Tables 4.2 and 4.3 compare the initial peak pressures. Gauge #3 showed similar results to Gauge #1. Note that mmel stands for millimeter elements. These results seem to indicate that the calculations diverge as slab element size increases. However, they do not do so to a significant degree until 20mm elements are used. A cursory examination of the graphs also seems to indicate that larger slab elements will smooth over the sharper peaks obtained from the finer meshes. 60000

5mmel air + 2mmel slab

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Figure 4.4 – Pressure vs. Time for Gauge #1, Same Air Element Size

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Figure 4.5 – Pressure vs. Time for Gauge #2, Same Air Element Size Table 4.2 – Gauge #1 Initial Peak Pressure, Same Air Element Size Peak Pressure at Percent Difference (%) from Model about .43ms (kPa) 5mmel air + 2mmel slab 24297 N/A 5mmel air + 2mmel slab 23733 2.32 5mmel air + 5mmel slab 5mmel air + 10mmel 22984 5.40 slab 5mmel air + 20mmel 21927 9.76 slab 20361 16.20 5mmel + 40mmel slab

Table 4.3 – Gauge #2 Initial Peak Pressure, Same Air Element Size Peak Pressure at Percent Difference (%) from Model about .3ms (kPa) 5mmel air + 2mmel slab 141527 N/A 5mmel air + 2mmel slab 144418 2.04 5mmel air + 5mmel slab 5mmel air + 10mmel 144754 2.28 slab 5mmel air + 20mmel 146853 3.76 slab 5mmel air + 40mmel 132268 6.54 slab

Three models used varied the air element sizes while keeping the size of the slab elements constant (2mm). Figures 4.6 and 4.7 are graphs which display the pressure results for Gauge #1 and Gauge #2 of these models while Tables 4.4 and 4.5 compare the initial peak pressures. Again, Gauge #3 shows similar results to Gauge #1. This data appears to show that as the element size of the air changes, the calculations become very inconsistent. The peaks of the two models with smaller elements are different magnitudes while the peak for the 10mm element air model fluctuates more than seems reasonable compared to the other models.

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Figure 4.6 – Pressure vs. Time for Gauge #1, Same Slab Element Size

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Figure 4.7 – Pressure vs. Time for Gauge #2, Same Slab Element Size

Table 4.4 – Gauge #1 Initial Peak Pressures, Same Slab Element Size Peak Pressure Percent Difference (%) from 2mmel air Model (kPa) 2mmel slab 20153 N/A 2mmel air + 2mmel slab 23733 17.76 5mmel air + 2mmel slab 10mmel air + 2mmel 24300 20.58 slab

Table 4.5 – Gauge #2 Initial Peak Pressures, Same Slab Element Size Peak Pressure Model Percent Difference (%) from 2mmel air (kPa) 217839 N/A 2mmel air + 2mmel slab 141527 35.03 5mmel air + 2mmel slab 10mmel air + 2mmel 220626 1.28 slab

Comparing the Figures 4.6 and 4.7 to Figures 4.4 and 4.5 suggests that the size of the air elements effects the calculations much more dramatically than the size of the slab elements. This is unfortunate, since as the largest part the air already requires more elements. If the air elements need to be fairly small in order to obtain accuracy, then this

will limit the size of the model that AUTODYN can make due to the memory issues presented earlier. Therefore, it is critical to examine other variables in order to see what level of effect this inconsistency in pressure may have on the ultimate behavior of the slab. If this obstacle can be avoided, then it will make creating larger, more complicated models easier.

4.2.2 Deflection in the Slab The graph of the results of the deflection analysis can be seen in Figure 4.8. The graph contains data from models with various element sizes in both the air and the slab. Visual analysis of this graph seems to agree with results of the pressure analysis. While the deflections for the models with the same air appear to be almost uniform, the deflections in models with different air diverge over time. 25

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4.2.3 Effective Strain in the Slab The results of the analysis of this third variable (effective strain) agree with those presented by the analysis of pressures and deflections. Figure 4.9 and 4.10 are graphs which display the pressure results for Gauge #2. The results for Gauge #1 and Gauge #3 agree with the results for Gauge #2. They all show that the size of the air elements affects the AUTODYN models to a much greater degree than the size of slab elements. 0.1 0.09

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Figure 4.9 – Effective Strain vs. Time for Gauge #2, Same Air Element Size

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Figure 4.10 – Effective Strain vs. Time for Gauge #2, Same Slab Element Size

4.2.4 Pressure in the Air Further investigations into the effects of air on the modeling used the results of the fixed gauges. The main focus of this is on the results produced by gauges located 1000mm from the charge center. The results of these studies can be seen below in Figure 4.11.

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Figure 4.11 – Initial Pressure Results for 1000mm from Charge Center

The results of these tests were not promising at first but it may be better to explain how and why the tests were performed, chronologically. First, the results of the “10mmel air and 2mmel slab” model were compared to those from ConWep, the established blast program mentioned earlier. Although the arrival times are fairly close, the peak pressure from the AUTODYN model is 5 times as large as the ConWep value. The presence of the slab could have caused the higher pressure if it built up on the surface, yet the results of the 10mmel air model without the slab match the one with the slab almost perfectly. The shape of the charge may have been another factor since ConWep normally deals with spherical blasts. However, the results of a model with a charge with a circular cross section show that, do not match either the square charge results or the ConWep results. Figure 4.11 also shows the results of the simple 1D 10mmel wedge, which

actually matches the ConWep peak pressure nicely. This suggests that perhaps it is simply the planar models in AUTODYN which have trouble matching the expected results. Therefore, it seems important to study the effects of remapping a wedge onto a planar model. Figure 4.12 shows the results of a remap of a 1200mm long 1mmel wedge onto a 20mmel air and 20mmel slab model. Figure 4.13 is a comparison of the results of the model with the remapped wedge with the ConWep and 10mmel wedge results at a distance of 1000mm from the charge center. The wedge is remapped onto a model with larger air elements than all of the other 2D planar models and yet the results of this model match much better (~6.5% difference from ConWep) to expected results than those models. This suggests that remapping is the may the best way to obtain accurate, confirmable results from AUTODYN.

Figure 4.12 – Remap of Wedge onto 20mmel Air and 20mmel Slab Model

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Figure 4.13 – Comparison of 10mmel Wedge, ConWep and Remapping Results at 1000mm from Center of Charge

4.2.5 Conclusions and Suggestions for Future Investigation First and foremost it appears that a fine mesh for the air is required to achieve accurate results. However, due to the limits in model size imposed by AUTODYN, a fine mesh will restrict models to small sizes. In addition it appears that may produce inaccurate results when modeling a charge with a planar cross section. Remapping, however offers a potential solution to both of these problems. Future work with the intention of developing bridge models should look more closely at remapping as an option. In addition, future models should begin to incorporate other materials, and parts such as the girders themselves. The options for failure models for concrete and whatever other parts are brought in need to be further examined for appropriateness and accuracy. Finally, real experimental data should be obtained to more adequately assess the accuracy of the program.

5 Acknowledgements This material is based on work supported by the National Science Foundation under Grant No. EEC-0139017, “Research Experiences for Undergraduates in Bridge Engineering,” at the University of Delaware. In addition to the advisor for this project Dr. Jennifer Righman, the author would also like to thank Renee Robert and Evan Brodsky for working with him on this project, as well as Dr. Jack Gillespie and Dr. Bazle Gama, of the University of Delaware Center for Composite Materials, for their assistance and advice.

6 References Anderson, Charles E. Jr. (1987). “An Overview of the Theory of Hydrocodes.” Int. J. Impact Engng. Vol. 5, pp. 33-59. AUTODYN (2005a). “SPH User Manual & Tutorial: Revision 4.3.” Century Dynamics AUTODYN (2005b). “Theory Manual: Revision 4.3.” Century Dynamics. Birnbaum, Naury K., Francis, Nigel J., & Gerber, Bence I. (1999). “Coupled Techniques for the Simulation of Fluid-Structure and Impact Problems.” Computer Assisted Mechanics and Engineering Sciences. Vol. 6, n. 3-4, pp. 295-311. Hayhurst, Colin J. Clegg, Richard A., Livingstone, Iain H. & Francis, Nigel J. (1996). “The Application of SPH Techniques in AUTODYN-2D to Ballistic Impact Problems.” 16th International Symposium on Ballistics. San Francisco.

Mathis, Mark M. & Kerbyson, Darren J. (2005). “A General Performance Model of Structured and Unstructured Mesh Particle Transport Computations.” The Journal of Supercomputing. Vol. 34, pp. 181-199. Robert, Renee (2007). Unpublished Master’s thesis, University of Delaware. Wilkinson, C. R. & Anderson, J. G. (2003). An Introduction to Detonation and Blast for the Non-Specialist. Edinburgh, Australia: Australian Government Defence Science and Technology Organization. Zuka, Jonas A. (2004). Introduction to Hydrocodes. Amsterdam: ELSEVIER

Appendix – Modeling Notes This appendix contains a collection of notes made while the AUTODYN models were being created and run. There are notes for most models and recordings of errors, but they are not extensive.