practical aspects of numerical simulations of dynamic events-- material interface.pdf

7/27/2019 Practical Aspects of Numerical Simulations of Dynamic Events-- Material Interface.pdf

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ARMY RESEARCH LABORATORY

PracticalAspects of Numerical Simulations of Dynamic Events:

Material Interfaces

by Daniel R . Scheffler and Jonas A. Zukas

ARL-TR-2302

|illIli-l M H H

September 2000

Approved fo r public release; distribution is unlimited.

m s f ist' m m m m > w

2 0 0 0 1 1 0 90 1 3


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The findings in this report are not to be construed as an official Department of the Army position unless so designated by other authorized documents.

Citation of manufacturer's or trade names does not constitute an official endorsement or approval of the use thereof.

Destroy this report when it is no longer needed. Do no t return it to the originator.


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Army Research Laboratory Aberdeen Proving Ground, MD 21005-5066

ARL-TR-2302

eptember 2000

Practical Aspects of Numerical Simulations of Dynamic Events: Material Interfaces

Daniel R. Scheffler Weapons an d Materials Research Directorate, A R L

Jonas A. Zukas Computational Mechanics Consultants, Inc.

Approved fo r public release; distribution is unlimited.


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Acknowledgments

The authors would like to thank Drs. Eugene S. Hertel, Jr., and Raymond L. Bell of Sandia

National Laboratories fo r providing the input decksand examples fo r their

balls-and-jacks problem

that w as used to demonstrate various interface reconstruction algorithms. he authors would also

like to thank Dr. Steven B. Segletes, w ho served as technical reviewer fo r th e original journal paper,

an d M r. Stephen Schraml, w ho served as technical reviewer fo r this technical report version of it.

Their thorough reviews an d comments helped improve the report.

m


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INTENTIONALLYLEFT B LANK.

IV


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Table of Contents

Page

Acknowledgments I List of Figures

List of Tables x1.

ntroduction

2.

agrangian Calculations: nfluence of Contact Surfaces on Solutions 3.

ulerian Calculations: ffects of Material Interfaces on Solutions 5 4.

onclusions

9

5.

eferences

1

Distribution List

7

Report Documentation Page

5


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INTENTIONALLYLEFT B LA N K .

V I


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List of Figures Figure ag e

1 . (a) Lagrangian Computational Grid and (b ) Eulerian Computational Grid

2.

ypical Lagrangian Contact Interface Showing Master- an d Slave-Node

Designations

3. omparison f Eroding lide-Line Options n Numerical Results or a Deep- Penetration Problem

4.

xample of Extreme Distortion in a Lagrangian Calculation

5.

agrangian Calculation Before an d After Rezoning

1

6.

verlay of Computed and Experimental Hole Profiles fo r Steel-Steel Penetration,

Vs = 3.114 km/s

2

7. amage Due to Sphere Impact at 30

3

8.

enetration of a 50-ply Aluminum Target 15 us After Impact

4

9.

tages of Penetration of an IVD = 5 Aluminum R od Striking a Thick Aluminum Target at 6 km/s

6

10 .

esidual Penetration by Eroded Mass Points 7

11 . Typical Plane-Strain HELP Code Simulation Compared With Experiment 9

12 . he Balls-and-Jacks Problem Using the SLIC Algorithm

1

13 .

he Balls-and-Jacks Problem Using Youngs' Interface Reconstruction Algorithm Using Improperly Chosen Material Advection Orders

3

14.

he Balls-and-Jacks Problem Using SMYRA

15.

xample of a Deep Penetration Simulation in Which th e Erosion Products of th e Rod

Come Into Contact With th e Penetrator

5

16. omparison of a Deep Penetration Simulation With an d Without th e BLINT Model

7

17.

omparison of Simulations Using th e Different Strength Options in Mixed Cells .. 8 Vll


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List of Tables

Table

age

1 .

liding Interface Approach in Lagrangian Systems

6

2. omputational Procedure fo r Sliding Interfaces

6

IX


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INTENTIONALLYLEFT BLANK.


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1. ntroduction

In companion papers [1,2], sources of error in calculations involving fast, transient loading due

to various meshing options available in commercial wave propagation codes, th e use of constitutive models,an d use of data at strain rates inappropriate to th e problem are discussed. n this report, the

effects of contact-impact algorithms in Lagrangian codes and the presence of material interfaces in

Eulerian codes are discussed. ttention is limited to conventional production Lagrangian and Eulerian ydrocodes hat re eadily vailable n ndustry nd overnment esearch enters.

Arbitrary Lagrangian Eulerian (ALE) codes and meshless methods (such as th e free Lagrangian or

th e smooth particle hydrodynamics [SPH] technique) are not coveredhere.

The ability to treat problems where adjacent components may independently slide,separate, an d

impact along free surfaces an d material interfaces is crucial in many technical fields. he nuclear

industry nalyzes he mpact of shipping asks ontaining adioactive materials, ipe-to-pipe

impacts, an d soil-structure interaction problems. Crashworthinessof vehicles is another important

area, as is foreign-object-impact damage in aircraft. Erosion and failure of materials of high-speed

aircraft flying through rain an d hail is still a significantproblem. Contact impact an d sliding with

and without friction is as important in metal forming as it is in biomechanics. n weapons design,

relevant roblems nclude he tructural esponse f un-fired rojectiles, arious omb configurations, an d a variety of shaped charge designs.

Spatial discretization using either finite-differenceor finite-element techniques can be carried

out in a Lagrangian or Eulerian framework (Figure 1 ). n a Lagrangian framework, th e grid is embedded in th e materialand distorts with it so that th e computation tracks th e motion of elements

of mass. n th e Eulerianapproach, th e grid is fixed in space an d material flows through it. Eulerian

codes work well fo r situations where large distortions are encountered, such as in hypervelocity

impact. here re dvantages nd isadvantages o both pproaches. agrangian odes re conceptually straightforward. ince th e grid distorts with th e material, time histories are easily obtained an d material interfaces are sharply defined. However, considerable mesh distortion,


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(a)

g

(b )

Figure 1 . a) Lagrangian Computational Grid and (b) Eulerian Computational Grid.


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entanglement, an d nodal intrusions across slide lines can occur an d special logic is required fo r

modeling deep penetration problems. n Eulerian codes, materialis transported from cell to cell in

the fixed grid. Considerable diffusion can occur, and special logic is required if interfaces are to be

defined with greater precision than one or tw o cell dimensions. Additional information can be found

in Zukas et al. [3], Zukas [4], Walters an d Zukas [5], Hallquist et al. [6], Belytschko and Hughes [7],

Schwer et al. [8], an d Kulak an d Schwer [9].

2. agrangian Calculations: Influence of Contact Surfaces on Solutions

Figure 2 [ 10 ] shows a typical interface setup between tw o contacting bodies, one side designated

as master, th e other as slave. Sliding-interface algorithms can be divided into three broad categories:

(1) he penalty method, r restoring force pproach, articularly popular in tructural dynamics and low-velocity applications, where nodal intrusions are corrected over

several computational cycles;

(2) he put-back" ogic pproach used n most hydrocodes, with or without erosion algorithms, where intruding nodes are repositioned on th e contact surface in a single

computational cycle; an d (3) ovel approaches, such as th e pinball algorithm [11].

In addition to these, there have been various ad hoc approaches used fo r specific problems. ach

of these has proven useful in a specific spectrum of nodal (therefore impact) velocities, but none is

sufficiently general to work in all applications from elastic impact through hypervelocity impact,

where perforations occur an d large debris clouds are formed.

At th e outset of a Lagrangian calculation, where interpenetration of tw o or more bodies can be

expected, th e surface nodes likely to make contact are designated as slave nodes on one of th e bodies

and master nodes on another. With modern contact-impact algorithms, the designation is more or

less arbitrary. hese master an d slave nodes must be designated by the code user. Codes such as


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fcth Slave Zone-

z A

& th Slave Segmen t

Slave Line

Master Line

/th Master Segmen t

Figure 2. Typical Lagrangian Contact Interface Showing Master- and Slave-Node Designations [10].


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ZeuS [ 12] eliminate this nuisance by automatically designating all geometric boundaries and material

interfacesas contact surfaces. The user can remove them if they are not needed but is never required

to specify them. he goal of sliding interface logic (also known as "contact-impact algorithms") is

to prevent intrusion of a slave node through a master surface. ntrusions must be corrected. he procedures are outlined in Tables 1 an d 2.

The most comprehensive contact algorithms of this sort are in the DYSMAS-L code [13].

Following th e scientific method to its logical end, th e authors of the code exhaustively considered

every possibility of slide-line intrusion an d programmed against it. ecause all potential types of

intrusion are checked, considerable time is expended in DYSMAS-L's contact processor at each

cycle, making fo r a slow-running code, but on e without an y significant errors due to the contact

processor. n th e United States, th e approach in codes such as DYNA [14, 5], EPIC [16, 7] , PRONTO [18], ZeuS, an d others has been more pragmatic. hese guard against th e major sources

of error that are likely to occur. Once intrusion of th e master surface is detected, th e offending node

is repositioned in one or another fashion and contact conditions and momentum balance are enforced

locally on th e sliding interface. athological cases are then treated as they occur.

By constrast, with penalty methods, the restoring force on an intruded slave node is very

sensitive to th e stiffness coefficient, which, fo r quite some time in the historyof Lagrangian code development, was a user-defined parameter an d a rather significantsource of error if th e code user

w as not familiar with th e physical problem an d his/her code. he current practice is to determine

th e restoring force modulus from th e properties an d geometry of th e element hosting th e sliding

segment. rior to this, results could be dramatically affected by a poor choice of stiffness constant

an d that choice w as very much matter of experience. y way of example, Goudreau nd Hallquist [19] incorporated procedures in NIKE an d DYNA3D to compute a unique modulus fo r

each slave an d master segment basedon th e thickness an d bulk modulus of th e elementin which it

resides. They state that"... in our opinion, th e lack of user control over this very critical parameter

greatly increases th e success of th e method."


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Table 1 . Sliding Interface Approach in Lagrangian Systems

Designate master an d slave material.

Decompose nto normal and tangential components. In normal direction:

-motion coupled during contact, an d -independent when separated.

In tangential direction: -independent when materials separated or interface frictionless, an d -modified when there is contact or frictional force acts.

Tied sliding - maintain displacement compatibility at abrupt grid changes.

Table 2. Computational Procedure fo r Sliding Interfaces

(1 ) Identify a series of nodes that make up th e master surface.

(2 ) Identify a series of nodes that make up th e slave surface.

(3 ) Fo r each At, apply equations of motion to both master and slave nodes.

(4 ) Check fo r interference between slave nodes and master surface: -define search region,

-check each slave node no t on master surface, and -if penetration occurs, move slave node to master surface.

(5 ) Once slave nodes are moved onto master surface: -invoke momentum balance, -apply frictional forces, and -open voids (if tensile forces present). (6 ) Repeat (3)-(5) fo r each At


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While this restorative procedure of the penalty method gave a smoothness to th e calculation due

to the fact that restoration of intruding nodes, and therefore element volume changes, was gradual,

th e procedure did not lend itself to impacts at ordnance velocity or hypervelocity because intrusions

could exceed element dimensions. Hence, most existing Lagrangian hydrocodes use th e put-back

logic mentioned previously. The intruding node or nodes are put back onto the master surface in on e

time step, an d momentum balance is invoked. Efficient search procedures fo r slave-node intrusion

are required sincea Lagrangian code is madeor broken by th e accuracy and efficiency of its contact

logic.

Ideally, the operation of th e contact processor should be transparent to th e user. Very much,

however, depends on the gridding in th e vicinity of th e contact surface and th e local time step.

Breidenbach et al. [20] provide a comprehensive discussion of pathological cases that can arise with

slide-line ogic. rove t l. 21], tudying tungsten projectiles penetrating itanium targets, exercised th e various erosion options in EPIC (upon failure of an element, its connectivity is no

longer onsidered nd he nodal masses ssociated with hat element an e etained n he

calculation or ignored) and compared results using th e data fo r th e Johnson-Cook models [22,23]

in th e EPIC materials library with results using strength data reported by Burkins et al. [24]. Results

fo r one of th e calculation sets are shown in Figure 3. he differences between th e calculation sets

are due to a combination of data fo r the selected constitutive model an d the behavior of the sliding interface logic when dealing with free-flying masses.

The Lagrangian codes, which first appeared in th e early 1960s, such as HEMP an d TOODY, had

no means of dealing with the large distortions that ca n occur under impact and explosive loading.

They required that the contact surface, or sliding interface, specified at th e beginning of a calculation

remain unchanged. n effect, an impenetrable membrane w as placed over an d attached to the colliding bodies.

hus, colliding bodies could not fail but could distort ad infinitum.

A dramatic

example of such distortions is shown in Figure 4 [25]. hus, these codes were limited to the study

of th e early stages of impact phenomena. n order to extend th e capability of these codes, rezoning

techniques were invented. n rezoning, a new Lagrangian computational mesh is overlaid on the

distorted mesh. A rezone algorithm maps mesh quantities of th e severely distorted mesh onto the


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120

100 E E

c o MM* B

C L

Q

80

g 60 a.

40

20

0

1

1 1 1 |

-

A 4

- '" .-'' yT

: *;' -*' yS^ LJ ^y

----TYPE = -2 , EPIC

-- -TYPE = -2 , R EPO RT --A--TYPE = -1, EPIC . --X--TYPE = -1 , R EPO RT .

- A TA

t 1.0 1.2 .4 .6 Impact Velocity km/sec) 1.8

Figure 3. omparison f roding lide-Line ptions n umerical esults or a Deep-Penetration Problem. T he Type = -1 Option Retains th e Mass of th e Eroded

Elements at th e Nodes, While he Type = 2 Option Discards Mass Once n Element Erodes. Also Compared Are Simulations With Strength Data Taken From th e EPIC Library to Simulations Using Strength Data Reported Elsewhere. T he Solid Line Represents th e Experimentally Obtained Data [21].


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L A G R A N G IA N Y S T E M

M E S H DISTORTION

L A R G E E S H DISTORTIONS-LARGE R U N C AT I O N R R O R S ,

Figure 4. Example of Extreme Distortion in a Lagrangian Calculation [25].


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new mesh such that conservation of mass, momentum, total energy, an d th e constitutive relationship

are satisfied. Rezoning was, an d remains, a nontrivial process. or deep penetration problems, 30

to 50 rezones are not uncommon. Since, at each rezone, the accumulated history of several elements

is combined into a larger element, frequent rezoning renders th e computational mesh semi-Eulerian

in that large distortions are realized but material history an d location of material boundaries are

diffused. ndeed, if rezoning were to take place at each cycle, th e computations could be effectively

Eulerian. requent rezoning gives computational results a smoothness characteristic of Eulerian calculations. Many codes today, such as DYNA, incorporate automatic rezoners. Despite th e label,

they still require occasional human intervention. This suggests that, despite good intentions, rezoned

calculations can be made to mirror the expectations of th e user monitoring th e process. An example

of a rezoned calculation is shown in Figure 5 [26].

The eroding slide-line concept proved to be a major breakthrough in extending th e capabilities

of Lagrangian codes to do problems involving deep penetration or multiple-plate targets an d other

situations where damage is highly localized. he term "erosion" in this context does not refer to a

physical failure mechanism. ather, t describes bookkeeping procedures that allow dynamic redefinition of master an d slave surfaces when very large distortions occur. The overall result makes

it appear that th e colliding bodies are "eroding." om e examples of th e success achieved with this

technique are shown in Figures 6-8 . igure 6, taken from Kimsey an d Zukas 27], shows the computational grid overlaidon the recovered target from the impact of a long steel ro d onto a semi- infinite armor steel target at a velocity of 3.114 km/s. igure 7 [28] shows debris-cloud formation,

propagation, an d interaction with other components of a space vehicle. igure 8 [29] shows the penetration of a 50-ply aluminum plate by a steel projectile 1 5 us after impact.

Eroding slide-line techniques are available in virtually all Lagrangian hydrocodes today. he

name of the proceduremay change (e.g., "advected elements" is popular today), but th e procedure is essentially as described previously. hile very useful, such techniques should be used with caution. nergy is not conserved in most sliding-interface prescriptions. he total energyin each

calculation should therefore be carefully monitored. osses of 4-10% in contact calculations can

be olerated fo r most high-velocity mpact roblems. Anything reater han 0% s sually

10


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Target

(a ) Mesh B efore R ezoning (b ) Mesh After Rezoning

Figure 5. agrangian Calculation Before and After Rezoning [26].

1 1


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.tll-M diele K

TS-

...

teem HTACl Cycle" 58 5

-i. a. .I a. lz.a 16.

u.. r iae- 3.set-os N Dtsm imcT

.a'

-.a-

-a.a.

-12.

Cycle MS

'' ' >**"

-16. -iz.a -e.a -.a T 71 7 i Ti OzO S T

Figure 7. Damage Due to Sphere Impact at 30 [28].

1 3


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Time= .50E-65 tWff lWWWI mmmtuui i

Cycle= 4253

Figure 8 . Penetration of a 50-Ply Aluminum Target 15 \is After Impact [29].

1 4


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indicative of a serious problem an d should prompt a check of both th e computational model and the

data used fo r th e constitutive models.

In penetration problems, a situation often encountered is th e continuation of penetration after

th e projectile has eroded. his is shown in Figures 9 and 10. o many nodes accumulate at the centerline element of the target (close to 180 nodes in this case) that th e element can no longer

withstand th e impacts and fails. As it fails, more nodes fall into th e crater an d th e target appears to

unzip along its centerline. Above this artificialcrack, the crater dimensions an d penetration depth

are about as expected. he cause fo r this behavior is unknown at present, but clues to th e problem

may be found in th e work of Brach [30] and Walsh [31]. ydrocodes are formulated assuming continuum behavior. he impact of single or multiple mass points against an intact elementmay

violate that assumption. Brach gives computational procedures fo r discrete particle impacts against

continuum structures. alsh studies th e effects of the impact of minuscule mass points against continuum targets and found that th e apparent strength of th e target increased by a factor of 4.7 over

pretest-measured strength properties. he formulation of th e slide-line algorithm may also be a factor. ntroducing an analytical formulation fo r th e contact processor in version4.23 of ZeuS (the

calculations shown here are with th e standard version 4.22) helped to considerably reduce the

unzipping effect.

3. Eulerian Calculations: ffects of Material Interface on Solutions

In Lagrangian codes, the mesh moves with th e material, whereas in Eulerian codes th e materials

flow though th e mesh. his is typically donein tw o phases. n th e first phase, th e mesh is allowed

to distort as th e problem is advanced in time (the Lagrangian phase), and, in the second phase, the

distorted mesh is remapped back to th e original mesh (the advection phase). Operator splitting is

typically employed during th e advection phase such that th e remapping occurs one coordinate

direction at a time, an d th e order is reversed each cycle. Fo r example, th e order in which advection

occurs may be in th e x, y, then z directions on e cycle and in reverse order th e next. imilar to th e

contact algorithm in Lagrangian codes, th e advection phase is th e most computationally intensive

1 5


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Ilaa* .MC


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Tine= 3.90E-e5 Cycle= 1768

Figure 10. Residual Penetration by Eroded Mass Points.

1 7


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Kl **+**/'

Xy X

T = 12 is

0' 1

0 1 6 1 8 2 0

Figure 11 . A Typical Plane-Strain H E L P Code Simulation Compared With Experiment.

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Considerable improvements in th e use of Lagrangian particles to define interfaces were made

in he SMITE code 34-37]. n MITE, second-order Eulerian finite-difference code, ach material had its ow n independent grid. hus, the mesh spacing and number of mesh grids in on e material is no t affected by any other material. he extent of each domain w as determined by particles that defined the domain boundary. hese points were moved in a Lagrangian sense by integrating th e ordinary differential equations relating their positions or velocities. dditional particles were dded s eeded o nsure niform pacing hroughout he alculation. he interaction between materials w as through the boundaries. he boundary points were subject to free-surface an d interface conditions an d provided th e only communication between th e various

material domains.

The ext tep n omplexity, f not ecessarily ccuracy, nvolves he se f nterface

reconstruction algorithms. One of th e mostsuccessful (because of its simplicity) material interface

reconstruction algorithms was th e first-order accurate imple line interface calculation SLIC)

algorithm of Noh an d Woodward [38]. The algorithm treats each coordinate direction independently

an d represents material interfaces as straight lines eitherperpendicular or parallel to a coordinate

direction based on the volume fractions of neighboring cells. he order in which each coordinate

direction is treated is reversed each computational cycle. he SLIC algorithm did well when material flow was primarily in a coordinate direction but tended to reorient the material interfaces

if material flow w as not parallel to a coordinate direction. For example,SLICwould tend to reorient

the material interfaces of a circle moving the mesh at 45 such that it would take on a diamondshape.

An example of th e algorithm is provided in the "balls-and-jacks" problem shown in Figure 12 in

which tw o balls (resembling a "figure eight") and tw o jacks are moved throughthe mesh at 45 with

x and y velocity components of 100 km/s.

Most modern production Eulerian hydrocodes use a second-order-accurate material interface reconstruction scheme. One such scheme is Youngs' interface reconstruction algorithm [39]. he

Youngs' algorithm also uses lines (o r planes in three dimensions) to represent the material interfaces;

however, th e lines can be at any angle. A problem with th e Youngs' algorithm is that th e code user

is required to input th e order in which materials will advect. The wrong choice of material advection

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3- s o

0

0

2D R lock X em ) Two-Dlmsnslorwl dvc1ion st SLIC) BJJCAP 02/10/99 9:22:48 THGEN

(a) 0 TimB=Q.

> -

2D R lock cm ) Two-Dimensional dvction ss t S LI C) BJJCAP 02/10/99 9:22:48 THGEN

(b ) 0 Ti me = Q.

100

Figure 12. he Balls-and-Jacks Problem Using th e SLIC Algorithm, a) Material Interface Plot Shows th e Initial and Final Configurations of th e Balls and Jacks. he Interfaces A re Reoriented in he Direction f Motion, b) Material Volume Fraction Plot Shows That Small Fragments of Material Are Left Behind.

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order can lead to strange results, as shown in th e balls-and-jacks problem in Figure 13 . n very complex problems involving many materials, considerable skill is needed in choosing th e material

advection order. dditionally, the advection order of materials in a complex problem is rarely uniform over the entire computational domain. The problems with the choice of material advection

order were largely solved with th e Sandia modified Youngs' reconstruction algorithm (SMYRA)

[40] sed in th e C TH code [41], which is essentially Youngs' lgorithm, but material volume

fractions of neighboring cells are used to determine the advection order in mixed cells. An example

of th e balls-and-jacks problem using SMYRA is shown in Figure 1 4 . A more comprehensive review

of material reconstruction algorithms can be found in the workby Benson [42].

Even with a perfect material reconstruction algorithm, problems can occur when objects with

th e same material identity come into contact. he interface in this case will simply disappear, and

th e material behaves as though it were bonded together. This occurs because material interfaces can

only be determined between different materials or materials and void, not like materials (meaning

materials that are assigned th e same material number). An example is shown in Figure 1 5 fo r a deep

penetration problem involving a tungsten alloy projectile penetrating a steel target. n this case, th e

erosion products of th e long-rod penetrator came in contact with th e penetrator an d th e interface

between the penetrator an d erosion products can no longer be distinguished. The end result was that

th e simulation underpredicted final penetration due to the penetrator being decelerated from th e contact.

Velocities in most Eulerian hydrocodes are either face centered or node centered, while other

cell quantities are cell centered. Therefore, materials in a mixed cell all have th e same velocity field.

Thus,a cell moves as a distorting block implyinga no-slip condition. herefore, Eulerian codes do

not handle problems very well where sliding between materials occursor where materials separate.

Unfortunately, liding ccurs n most roblems. ttempts ave een made o orrect his shortcoming. For example, Silling [43] developeda boundary layer algorithm fo r sliding interfaces (BLINT) fo r two-dimensional problems. The algorithm creates a "slip layer" in a user-defined "soft"

material. he strength of th e cells in th e slip layer is se t to zero, allowing sliding to occur outside

of th e mixed cells. The model has been used with some success in modeling

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0

0

2D R lock cm ) Two-Dimensional dVection es t SMYRA-SO)

BJHDZP 02/10/99 7:44:53 THGEN

Time=0.

(a )

0

0

2D R lock cm ) Two-Dimensional oVection es t S M Y R A - S O ) BJHDZP 02/10/99 7:44:53 THGEN

Time=0.

(b )

100

Figure 13 . he Balls-and-Jacks Problem Using Youngs' Interface Reconstruction Algorithm Using Improperly Chosen Material Advection Orders, (a) Material Interface Plot Shows That th e Algorithm Does a Better Job Keeping Track of th e Material Interfaces Than he L IC Algorithm f Figure 2(a). b) Material Volume Fraction Plot Reveals That Material Incorrectly Advected Is Being Left Behind.

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0

0

2D R oc k cm ) Two-Dimensionol dvectic-n est SMYRA)

BJHCZO

02/10/99

7:33:35 T H G E N

(a )

0 Time=0.

2D R lock cm ) Two-Dimens!orKil dvection es t SMYRA) BJHCZO 02/10/99 7:33:36 THGEN

(b )

100

0 Ti m e = Q .

Figure 14. he Balls-and-Jacks Problem Using SMYRA. a) Material Interface Plot Shows Results Similar to th e Youngs' Algorithm of Figure 13(a). b) Material Volume Fraction Plot Reveals That No Material Fragments A re Being Left Behind.

24


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2D C lock cm ) WAIIoy s em i H A : s=1300 n/s = 7 2 9 m =24.3 m =5.917 g G J S A G N 07/11/98 4:52:14 TH 9478 Tim8=6.00007x10-4

Figure 15 . xample of a Deep Penetration Simulation in Which th e Erosion Products of th e

R od Come Into Contact With the Penetrator. A t th e Point of Contact, an Interface Is Indistinguishable. he Contact Caused th e Penetrator to Decelerate More Rapidly Than Usual, Causing th e Simulation to Underpredict Penetration.

25


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rigid-body penetrations [44-46] an d has recently been extended to three dimensions. An example

problem comparing simulations with an d without the BLINT model is shown in Figure 16 . Walker

an d Anderson [47] attempted to overcome the problem by developing a model fo r multimaterial

velocities in mixed cells. he model defined a cell-centered velocityand allowed each material to

have its ow n velocity, which w as advected as a state variable. he model w as strictly geometrical.

The authors attempted to model a rigid-body penetrator problem using th e model with only limited

success.

Because th e cell stress increments are calculated from velocity gradients, using th e face-centered

or node-centered velocities, a single yield strength must be calculated fo r mixed cells. ome Eulerian hydrocodes allow th e user to select th e formulation fo r determining th e yield strengthof a

mixed cell. s an example, th e CTH hydrocode gives th e user three choices on how th e yield strength of a mixed cell is determined. hey include (1 ) setting th e strength of a mixed cell to zero;

(2) multiplying th e yield strength of each material by its volume fraction an d adding them; and

(3 ) multiplying th e yield strength of each material by its volume fraction, umming them and

dividing by th e total volume fraction f all materials within th e cell. ll these methods or determining th e yield strength in a mixed cell can lead to calculating unrealistic results when th e

materials within a mixed cell have vastly different strengths. Figure 17 compares simulations using

the previously mentioned strength treatments fo r mixed cells. or each strength formulation, th e penetrator did not perforate th e target, when, experimentally, it was determined it should. he reason is partly due to the strength treatment artificially weakening th e penetrator material in mixed

cells an d partly due to th e fracture model chosen. If a solid were in a mixed cell with a gas, th e solid

can undergo unrealistic deformation. The strength treatment used in mixed cells is one reason most

Eulerian codes cannot model rigid-body penetration.

Mixed cells can also cause thermodynamic problems. This occurs because most Eulerian codes typically etermine he hermodynamic tate f he ixed ell n ubcell evel. he thermodynamic state of neighboring cells is not used to determine th e state of materials within a

mixedcell. Assumptions must therefore be made to give a closed se t of equations to determinethe

state within a mixed cell. The assumptions most often used include (1) all materials are at the same

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Figure 16. Comparison of a Deep Penetration imulation With and Without th e BLINT Model, a) BLINTM odel Simulation Shows th e Ogival-Nose R od Penetrating as a Rigid Body. he White Layer Around th e R od Shows th e Slip Layer Where Sliding Occurs, b) Simulation Without th e BLINT Model Incorrectly Shows the Ogival-Nose R od Eroding.

27


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pressure and temperature; (2) all materials are at the same pressure, but th e temperature of each

material may vary; or (3 ) all materials may have their ow n pressure and temperature. Assuming that

all materials have the same pressure as in th e first tw o assumptions is obviously incorrect. While

pressures ay ventually quilibrate, his sually appens ver ime, ot nstantaneously. Additionally, assuming all materials have the same pressure can cause problems to arise when

fracture is to be modeled using a tension criteria in a cell containing a solid an d fluid. he solid will

never fail because fluids do not support tension. Assuming thermal equilibrium implies an infinite

thermal conductivity. his assumption w as used in th e CSQH code [48]. he assumption that all

materials have their ow n temperature and pressure on the surface is the most correct; however,

additional approximations have to be made. hese include assuming the volumetric train is constant among all materials in a mixed cell. his means, in a mixed cell containing a solid an d a

gas, the solid would have to accept th e same amountof volumetric strain as the gas in spite of th e

fact that th e gas is much more compressible. he approximation correctly allocates PdV work to

materials only when compression occurs parallel to a material interface. his assumption is used

in he MESA, CTH, nd KRAKEN 49] odes. nother pproximation sed or multiple temperatures an d pressures in a mixed cell is that all materials experience equal pressure change.

This approximation correctly allocates PdV workamongmaterials only when a cell is compressed

perpendicular o he material nterfaces nd epresents n pposite imiting ase o onstant

volumetric strain approximation. This approximation was recently added to th e CTH code as a user selectable option [50].

4. Conclusions

Various actors elated o material nterfaces n agrangian nd ulerian hock wave propagation codes, which can lead to disagreement between computations an d experience, have been

discussed. or Lagrangian codes, interfaces are well defined; however, special logic is needed to

prevent interpenetration of tw o or more bodies. hese slide-line algorithms can have user-defined

parameters or options that, when incorrectly applied, can lead to considerable error in a computation.

For Eulerian codes, interfaces are not well defined an d special logic is needed if the interface is to

29


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be known to greater than one cell dimension. Several means of tracking the interfaces and problems

associated with them have been discussed. dditionally, Eulerian codes have difficulty treating sliding or material separation. aterial properties in mixed cells are treated in an ad hoc manner. Code users should be aware of th e problems that can arise in th e treatment of material interfaces

when they occur so as not to attribute them as reality or new physics.

30


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5. References 1. ukas, J. A ., and D. R . Scheffler. Practical Aspects of Numerical Simulation of Dynamic

Events: ffects of Meshing." nternational Journal of Impact Engineering, to be published.

2. ukas, J. A ., and D . R . Scheffler. Practical Aspects of Numerical Simulation of Dynamic Events: onstitutive Models an d Data." n progress. 3. ukas, J. A., T. Nicholas, L. B . Greszczuk, H. F. Swift, an d D. R . Curran. mpact Dynamics .

N ew York: Wiley-Interscience, 1982, Reprinted Melbourne, FL : Krieger Publishing Co., 1992.

4. ukas, J. A. (editor). High Velocity Impact Dynamics . New York: Wiley-Interscience, 1990. 5. alters, . ., nd . . ukas. undamentals f haped harges. ew ork:

Wiley-Interscience, 1989, reprinted in Baltimore, MD: MCPress, 1997. 6. allquist, J. O., G . L. Goudreau, and D. J. Benson. Sliding Interfaces With Contact-Impact in Large-Scale Lagrangian Computations." Proceeding of the Third International Conference

on Finite Elements in Nonlinear Mechanics (FENOMECH '84), Stuttgart, West Germany, 1984.

7. elytschko,T ., and T. J. R . Hughes (editors). Computational Methods for Transient Analysis. Amsterdam: orth-Holland, 1992.

8 . chwer, L. E., N. J. Salamon, and W . K. Liu (editors). "Computational Techniques for Contact, Impact,Penetration an d Perforation of Solids." AMD-vol . 103. N ew York: American Society of Mechanical Engineers, 1989.

9. ulak, R . ., nd L. E. chwer (editors). omputational Aspects of Contact, Impact and Penetration. ausanne: lmepress International, 1991. 10. allquist, J. O. A Numerical Treatment of Sliding Interfaces an d Impact." omputat ional

Techniques for Interface Problems, AMD-vol . 30, pp. 117-134, K. C . Park an d D . K. Gartling (editors), N ew York: American Societyof Mechanical Engineers, 1978.

11. eal, M. . Contact-Impact y he inball Algorithm With enalty, Projection, nd Augmented Lagrangian Methods." hD dissertation, Northwestern University, 1989 .

12. ukas, J. A ., and S. B . Segletes. euS Technical Description and User's Manual . owson, MD: omputational Mechanics Consultants, Inc., 1989.

13. iekhoff, . ., . iessler, . ausmann, . charpf, nd . . chittke. nternal Documentation, Industrieanlagen-BetriebsgesellschaftmbH, Ottobrunn, Germany.

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26. eickert, C . A. "Evaluation of Selected Computer Codes fo r Impact and Explosive Detonation Calculations." Memorandum 1059, Defence Research Establishment, Suffield, 1983.

27. imsey K. D., nd . A. Zukas. Contact urface Erosion or Hypervelocity Problems." BRL-MR-3495, U.S . Army Ballistic Research Laboratory, Aberdeen Proving Ground , M D ,

1986.

28 . ukas, . A., nd . B. egletes. Hypervelocity Impact On pace tructures." Dynamic Response of Structures to High-Energy Excitations, AMD-vol . 127/PVP-vol. 225, T. L. Geers and Y. S. Shin (editors), New York: merican Society of Mechanical Engineers, 1991.

29. egletes, S. B ., and J. A. Zukas. T he Contact/Erosion Algorithm in th e ZeuS Hydrocode." Contact Mechanics: omputational Techniques, M . H. Aliabadi and C. A. Brebbia (editors), Southampton: omputational Mechanics Publications, 1993.

30. rach, . . echanical mpact Dynamics: igid ody ollisions. ew ork: Wiley-Interscience, 1991.

31. alsh, J. M. Personal communication. anta Fe, N M , September 1996. 32. agliostro, D. J. , D . A . Mandell , L. A. Schwalbe, T. F. Adams, and E. J. Chapyak. MESA 3-D

Calculations of Armor enetration y rojectiles With Combined Obliquity nd Yaw." International journal of Impac t Engineering, vol. 0, nos. -4 , pp. 81-92,1990.

33. alsh, J. M . HELP, A Multiple-Material Eulerian Program for Compressible Fluid an d Elastic-Plastic Flows in T w o Space Dimensions an d Time." SR-350 , Systems, Science an d Software, 1970.

34. urstein, S. Z., H. S. Schechter,an d E. L. Trkei. A SecondOrder Numerical Mod e l for High Velocity mpact Phenomena." RL-CR-239, U.S. Army Ballistic Research aboratory, Aberdeen Proving Ground, M D, 1975.

35. urstein, S. Z., H . S. Schechter, an d E. L. Trkei. SMITE - A Second OrderEulerian Code fo r Hydrodynamic and Elastic-Plastic Problems." BRL-CR-255 , U.S. Army Ballistic Research Laboratory, Aberdeen Proving Ground, M D , 1975.

36. urstein, . Z., nd H . . chechter. A econd Order Numerical C o d e or Plane lo w Approximation of Oblique Impact." BRL-CR-294 , U.S. Army Ballistic Research Laboratory,

Aberdeen Proving Ground, M D , 1976.

37. ustein, S. Z., and H . S. Schechter. Fracture Modeling in th e SMITE Code." BRL - CR- 295 , U.S. Army Ballistic Research Laboratory, Aberdeen Proving Ground, M D , 1976.

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38 . oh , W. F. , an d P. Woodward. SLIC Simple Line Interface Calculation)." ecture Notes in Physics. . I. Van de Vooren and P. J. Zandbergen (eds.), vol. 59, pp . 330-340, Berlin: Springer-Verlag, 1976.

39. oungs, D. L. An Interface Tracking Method fo r a 3-D Eulerian Hydrodynamics Code." AWRE/44/92/35, U K Atomic Weapons Establishment, 1987.

40 . ell, R. L., and E. S. Hertel Jr. "An Improved Material Interface Reconstruction Algorithm fo r Eulerian Codes." AND92-1716, Sandia National aboratories, Albuquerque, NM, 1992.

41 . cGlaun, J. M., S. L.Thompson, an d M. G. Elrick. "CTH: A Three-Dimensional Shock Wave Physics Code." Internationaljournal of Impact Engineering, vol. 10 , nos. 1-4, pp. 351-360, 1990.

42 . enson, D. J. Computational Methods in Lagrangian an d Eulerian Hydrocodes." Computer Methods in Applied Mechanicsand Engineering, vol. 99 , pp . 235-394,1992.

43 . illing, S. A. CTH Reference Manual: oundary Layer Algorithm fo r Sliding Interfaces in Tw o Dimensions." AND93-2487, Sandia National Laboratories, Albuquerque, NM, 1994.

44. metyk, L. N., an d P. Yarrington. CTH Analyses of Steel Rod Penetration Into Aluminum an d Concrete Targets With Comparisons to Experimental Data." AND94-1498, andia National Laboratories, Albuquerque, NM, 1994.

45 . cheffler, D. R. CTH Hydrocode Simulations of Hemispherical an d Ogival Nose Tungsten Alloy Penetrators Perforating Finite Aluminum Targets." tructures Under Extreme Loading Conditions, PVP-vol. 325, pp . 25-136, Y. S. Shin an d J. A. Zukas (editors), New York: American Societyof Mechanical Engineers, 1996.

46 . cheffler, D. R., and L. S. Magness Jr . Target Strength Effects on th e Predicted Threshold Velocity or Hemi- nd Ogival-Nose enetrators erforating inite Aluminum argets." Structures Under Shock and Impact V (SUSI98), pp. 285-298 , N. Jones, D. G. Talaslidis, C. A. Brebbia, nd G. D. Manolis editors), outhampton: omputational Mechanics Publications, 1998.

47. alker, J. D., nd C. . Anderson Jr . Multi-Material Velocities or Mixed Cells." n High-Pressure Science and Technology -1993, pp. 1773-1776, S. C. Schmidt, J. W. Shaner, G. A. Samara, an d M. Ross (editors), Woodbury, NY: merican Institute of Physics, 1994.

48 . hompson, . L. CSQII - An Eulerian Finite Difference Program fo r Two-Dimensional Material Response - Part 1 . Material Sections." S AND77-1339, Sandia National Laboratories, Albuquerque, NM, 1979.

49. eBar, R. B. Fundamentals of th e KRAKEN Code." UCID-17366, University of California Lawrence Livermore National Laboratory, Livermore, CA, 1974.

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50 . arnsworth, A. V., Jr. "CTH Reference Manual: ell Thermodynamics Modifications and Enhancements." SAND95-2394, Sandia National Laboratories, Albuquerque, NM, 1995.

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September 2000 Final, May-Dec 99 4. TITLEA N DSUBTITLE

Practical Aspects of Numerical Simulationsof Dynamic Events: Material Interfaces

6. A U T H O R ( S )

Daniel R. Scheffler an d Jonas A. Zukas*

5. F U N D I N G N U M B E R S

622618

A H 8 0

7 . P E R F O R M I N G O R G A N I Z AT I O N N A M E ( S ) A N D A D D R E S S ( E S )

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11 . S U P P L E M E N TA RY N O T E S

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13 . A B S T R A C T (Maximum 200 words)

T he use of finite-difference and finite-element computer codes to solve problems involving fast, transient loading is commonplace. large number of commercial odes xist an d re pplied to roblems anging from airly lo w o extremely ig h amage evels e.g., esign of ontainment tructures o mitigate ffects of ndustrial ccidents; protection of buildings nd people ro m last nd mpact oading; oreign-object mpact amage; esign of pace structures to withstand impacts of small particles moving at hypervelocity, a case where pressures generated exceed th e material strength by an order of magnitude). ut, wh a t happensif code predictions d o not correspond with reality? his report discusses various factors related to material interfaces in Lagrangian an d Eulerian shock wave propagation codes (hydrocodes), which an ead o isagreement between omputations nd experience. ompanion reports ocus on problems associated with meshing and constitutive models an d th e use of material data at strain rates inappropriate to th e problem. h is report is limited to problems involving fast, transient loading, which can be addressed by commercial finite-difference an d finite-elementcodes.

This report h as been accepted for publication in a future volume of th e International Journal of Impact Engineering

14 . S U B J E C T T E R M S

high-velocity mpact , as t ransient oading, umerical ethods, aterial nterfaces, Lagrangianmethods,Eulerain methods, finite difference, finite elements

15 . N U M B E R O F PA G E S

50 16 . PR IC EC O D E

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