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.

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

r

P

Spherical Air Blast

a

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.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

SoD = 1000 mm

b e

d

c

a

CONWEP CalculationsExplosive: TNTQuantity: 1 kg

Time, t, ms.

Blas

t Ove

r Pre

ssur

e, P

, MPa

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.

Air

Concrete Slab

TNT

Y

X

Air

Concrete Slab

TNT

Y

X

Figure 4.1 Standard Slab, Air and Charge Model 3400

1700 1700

12201220

2440

2000

2000

4000

1220

300

300

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 Cycles

Run Finish

Time (ms) Fixed

Gauges Additional Variables Notes

2000mm long 10mmel air wedge 400 0.473406 yes - 190mm charge radius

1200mm long 1mmel air wedge 1800 0.176983 - - 188mm charge radius,

used for remaps 5mmel air + 40mmel slab 2000 0.524316 no no

5mmel air + 20mmel slab 2000 0.52499 no no



5mmel air + 5mmel slab with erosion 8000 2.050421 no no Retained inertia of

eroded nodes 5mmel air + 5mmel slab with crack softening

1300 0.411723 no no Failure mode switched to crack softening

5mmel air + 2mmel slab 8500 1.303755 yes yes



10mmel air + 2mmel slab with additional variables

8000 1.254802 yes yes

10mmel air without slab with normal charge

800 0.722242 yes no

10mmel air without slab with circular charge

759 0.592869 yes no 190mm charge radius

20mmel air + 20mmel slab with wedge remap

10000 11.842196 yes yes

3D 20mmel air + 20mmel slab with wedge remap

600 1.152533 no no 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.

0

10000

20000

30000

40000

50000

60000

0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80

Time (ms)

Pres

sure

(kPa

)

5mmel air +2mmel slab




5mmel air +40 mmel slab

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

0

50000

100000

150000

200000

250000

0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60

Time (ms)

Pre

ssur

e (k

Pa)






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

Model Peak Pressure at about .43ms (kPa)

Percent Difference (%) from 5mmel air + 2mmel slab

5mmel air + 2mmel slab 24297 N/A 5mmel air + 5mmel slab 23733 2.32 5mmel air + 10mmel slab 22984 5.40

5mmel air + 20mmel slab 21927 9.76

5mmel + 40mmel slab 20361 16.20

Table 4.3 – Gauge #2 Initial Peak Pressure, Same Air Element Size

Model Peak Pressure at about .3ms (kPa)

Percent Difference (%) from 5mmel air + 2mmel 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.

0

10000

20000

30000

40000

50000

60000

0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80

Time (ms)

Pres

sure

(kPa

))




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

0

50000

100000

150000

200000

250000

0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60

Time (ms)

Pres

sure

(kPa

) 2mmel air +2mmel slab



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

Model Peak Pressure (kPa)

Percent Difference (%) from 2mmel air 2mmel slab


Table 4.5 – Gauge #2 Initial Peak Pressures, Same Slab Element Size

Model Peak Pressure (kPa) Percent Difference (%) from 2mmel air


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.

0

5

10

15

20

25

0 0.1 0.2 0.3 0.4 0.5 0.6

Time (ms)








Figure 4.8 – Deflection Comparison for the Back Center of the Slab

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

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Time (ms)

Effe

ctiv

e St

rain






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

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Time (ms)

Effe

ctiv

e St

rain




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.

0

10000

20000

30000

40000

50000

60000

0.19 0.21 0.23 0.25 0.27 0.29 0.31 0.33 0.35

Time (ms)

Pres

sure

(kP

a)

10mmel Air + 2mmel Slab2D Planar Square Charge

10mmel 2000mm Wedge

10mmel Air No Slab 2DPlanar Spherical

10mmel Air No Slab 2DPlanar Square Charge

ConWep

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

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

0.19 0.21 0.23 0.25 0.27 0.29 0.31 0.33 0.35

Time (ms)

Pres

sure

(kPa

)

10mmel 2000mmWedge

ConWep

20mmel air + 20mmelslab Wedge Remap

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.

Documents

Autodyn Blast