proceedings of the 66th shock and vibration symposium, volume ii (1995 ... · ·...

Proceedings of the 66th Shock and Vibration Symposium, Volume II (1995), SAVIAC, 227-248.

227

HYDROCODE METHODOLOGIES FOR UNDERWATER EXPLOSIONSTRUCTURE/MEDIUM INTERACTION

Hans U. MairNaval Surface Warfare Center, Indian Head Division, Code 4610

Silver Spring MD 20903-5640Voice: 301.394.3700; Fax: 301.394.4755 or 301.394.4657

email: [email protected]

The applicability of the general-purpose continuum mechanicscodes, or “hydrocodes,” to underwater explosion structure/mediuminteraction (UNDEX-SMI) is assessed. It is shown that some hydrocodemethodologies are applicable to UNDEX-SMI analysis of thin-walledstructures, but only if the codes employ “structural elements.”

OVERVIEW OF HYDROCODES

Continuum mechanics is a superset of the largely independent fields of solid mechanics(of which structural dynamics is a subset) and fluid mechanics. Computational continuummechanics is a superset of the largely independent fields of computational fluid dynamics (CFD)and computational solid mechanics (CSM, of which computational structural dynamics, or CSD,is a subset). The general-purpose codes (hydrocodes) described herein concern themselves withthe response of solid and fluid materials under such highly dynamic conditions (e.g., detonationand impact) that shock wave propagation is a dominant feature [1,2,3,4,5]. Basically, the general-purpose methods make fewer approximations than either of the more special-purpose CFD orCSM methods. Hydrocodes numerically solve the more fundamental time-dependent equations ofcontinuum mechanics (compared to, for example, the Navier-Stokes equations of fluid dynamics),thereby fulfilling requirements for which neither traditional CFD nor CSM codes are fullysuitable. The ever-expanding scope of CFD, CSM, and hydrocode capabilities has, however,created a semantic difficulty: it is impossible to delineate strictly between hydrocodes and eitherCFD or CSM codes. Hydrocodes are therefore defined as simulation tools for multi-material,compressible, transient continuum (i.e., fluid and/or solid) mechanics. Some hydrocodes haveeven implemented the capability to practically model structural dynamics, allowing an even widerapplicability. This structural analysis capability is crucial to SMI analysis of thin-walledstructures.

Hydrocodes have provided more than simply "hydrodynamic" simulations of materialbehavior for a long time, but in keeping with the common terminology, the misnomer“hydrocodes” is here equated with “general-purpose codes.” An alternate, though less widespread,term is "wavecodes," due to the wave-capturing nature of these codes. Also, the term"hydrocodes" is reserved by some for the Eulerian versions of the general-purpose codes.

The development of hydrocode capabilities has traditionally been driven largely bymilitary requirements, since few non-military applications involve explosives or high-velocityimpact. However, this class of tools has more recently found commercial applicability (andcorresponding development drive) in such diverse fields as automobile and shipping container


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crashworthiness [6,7,8,9], automobile airbag deployment [6,10], automobile and train occupantreaction to crashes [6], bird impact on aircraft [6,11], and sheet metal stamping [12,13].

The Lagrangian, Eulerian, Coupled Eulerian/Lagrangian (CEL), and Arbitrary Lagrangian/Eulerian (ALE) general-purpose methods are described in the sections that follow. A simpleillustration is included for each method, depicting a structure/medium interaction whose geometryis illustrated in Figure 1. It represents a two-dimensional analog of the type of problem that

AirMetal Structure

Water

Cavitation Region

Explosive

ExplosionProducts

(a) (b)

(c) (d)

Figure 1. UNDEX-SMI Analysis Example


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challenges most aspects of underwater explosion structure/medium interaction (UNDEX-SMI): anunderwater explosion that causes large structural distortion and displacement and in which bubblecollapse and cavitation effects are very important. The early expansion of the explosion productssends a strong shock wave into the surrounding water. The shock quickly deforms the structure,resulting in a cavitation region in the water close to the structure. The cavitation region eventuallycloses as the bubble continues to expand, and a water jet is shown to form as the bubble collapses.None of the examples are actual computations; they only illustrate the capabilities and limitationsof the methods. All general-purpose methods are theoretically capable of modeling true SMI sinceno major coupling approximations are made. The methods are, therefore, judged on practicalityinstead of capability. The individual code developers should be consulted for up-to-date codecapabilities and projected improvements.

LAGRANGIAN HYDROCODES

The computational mesh of a Lagrangian model remains fixed on the material, asillustrated in Figure 2. Since the mass within each element remains fixed, no mass flux atinterelement boundaries must be computed; thus the computation is relatively straightforward andfast. Material distortions correspond to Lagrangian mesh distortions, leading to reductions in timesteps and/or breakdown in problem advancement. Mesh rezoning tends to extend the applicationof Lagrangian codes to large distortion problems, but introduces complexities and correspondingsolution inaccuracies. The calculation is also no longer strictly Lagrangian if the mesh is rezoned.The distorted (elongated) elements defining the water at the edge of the bubble in Figure 2 areapparent. These distorted elements (exceedingly thin and wide) would likely cause the time step todrop to unacceptably small values, in effect stopping the calculation. The unfavorable meshevolution is due, in part, to the quadrilateral elements (six-sided "hexahedral" elements in 3D) thatdefine the discretization; were such a mesh composed of triangular elements (four sided"tetrahedral" elements in 3D), more distortion would be allowed since triangular/tetrahedralelements tend to be more robust. This point is illustrated by the fact that shaped charge linercollapse is commonly and effectively modeled using codes that employ triangular/ tetrahedralelements. Even if more robust elements were employed, the Lagrangian method would stillultimately break down as the bubble collapses upon itself, since the mesh that defines theexplosion products cannot simply "get out of the way." The general limitation of most Lagrangianhydrocodes to relatively low-distortion computations limits their applicability to local and globalshock/structure interaction analysis.

Predecessors of modern Lagrangian hydrocodes were HEMP [14], TOODY [15], 2DL[16] and HONDO [17]. EPIC [18], various versions of DYNA [19,20,21,22,23], and PRONTO[24,25,26,27] are the most prominent Lagrangian hydrocodes, but the Lagrangian modules of theCoupled Eulerian/Lagrangian (CEL) codes (described in a subsequent section) are also available.Any Arbitrary Lagrangian/Eulerian (ALE) code (also described below) can also be run in purelyLagrangian mode. Traditional (implicit) Lagrangian solid/structural mechanics codes likeNASTRAN [28], NIKE [29,30], and ABAQUS [31] are not suitable, or not efficient, for highlydynamic analyses in which shock waves are dominant. The EPIC code is based primarily ontriangular elements in 2D and tetrahedral elements in 3D, and is therefore more robust for large


230

distortion problems. Several attempts have been made at coupling the hydrodynamic andstructural capabilities of DYNA3D for UNDEX-SMI analysis [32,33].

Lagrangian hydrocodes have been successfully coupled and linked to Eulerian hydrocodessuch that large distortion fluid dynamics calculations can be made within an Eulerian framework.These types of codes are described in a following section. The Arbitrary Lagrangian-Eulerian(ALE) method, described in a following section, can be considered a variant of the Lagrangianmethod; in effect, the Lagrangian method is a subset of the ALE method.

Plate Elements

Void

Plate Element Nodes

Water

Explosion Products

Cavitation Region

Figure 2. Lagrangian Hydrocode UNDEX-SMI Example


231

Other Lagrangian methods that have potential application to UNDEX-SMI analysis but arenot as mature as the standard method include the Free Lagrange Method (FLM) [34,35] andSmoothed Particle Hydrodynamics (SPH) [36,37,38]. A Free Lagrange mesh distorts as thematerial distorts, but the connectivity of the elements changes as the mesh distorts. This concept isillustrated in Figure 3, which could illustrate the mesh distortions accompanying shear banding.The elements that define the domain are redefining their connectivity as the mesh distorts; this isnot possible in a standard Lagrangian code. Research codes that are examples of FLM includeCAVEAT-GT [39] and TRIX [40]. In SPH, Lagrangian "particles" dynamically interact with nofixed, permanent connectivity (as in FLM), as shown in Figure 4. Lagrangian hydrocodes thathave implemented SPH concepts as analysis options include EPIC [41,42] and PRONTO [43].Both FLM and SPH are particularly attractive for large shear distortion problems, overcoming themain limitation of traditional Lagrangian hydrocodes. An UNDEX-SMI event would probably bemodeled using Lagrangian particles, or Free-Lagrange elements, to trace fluid motions andcontinuously interact with fully Lagrangian structural elements (Figure 4), thus creating a coupledSPH/Lagrangian or FLM/Lagrangian method. Since the "mesh" of SPH and FLM codes is notrigidly interconnected, the methods do not break down as an underwater explosion bubblecollapses upon itself. UNDEX-SMI problems have been attempted with the PRONTOSPH/Lagrangian approach [43].

The natural applicability of Lagrangian hydrocodes with structural analysis capability tohighly dynamic problems spawned the automobile crashworthiness simulation industry. Manyexplicit codes are currently applied to, and/or developed explicitly for, automotivecrashworthiness; LS-DYNA3D [21], ABAQUS/Explicit [44], and PAM-CRASH [45] areexamples. Two features of crash simulation codes are advanced contact algorithms (for structuralmembers folding upon themselves) and Adaptive Mesh Refinement (AMR) algorithms, sincemany plastic hinges form.

EULERIAN HYDROCODES

Eulerian hydrocodes advance solutions in time on a mesh fixed in space, as illustrated inFigure 5, instead of a mesh fixed on the material, as is done in a Lagrangian solution. Byadvancing the solution on a computational mesh fixed in space and time, Eulerian codes avoid theLagrangian problem of mesh distortions. Correspondingly, and unlike Lagrangian simulations,time steps can remain roughly constant during simulations, and bubble jetting simulations becomefeasible. The difference between Eulerian computational fluid dynamics (CFD) codes and

time 0 time 1 time 2 time 3

Figure 3. A Free-Lagrange Mesh Motion Example


232

Eulerian hydrocodes is primarily the inclusion of material strength (flow of solids) andmultimaterial capability in the hydrocodes. Furthermore, Eulerian hydrocodes are strictly transientdynamics solvers; they are not designed to solve steady-state fluid flow problems.

The usual sequence of logic within Eulerian hydrocodes, unlike traditional CFD codes,consists of a Lagrangian computation at every time step, followed by a remap (advection) phasewhich restores the slightly distorted mesh to its original state.

Lagrangian Plate Elements

Water Particles Explosion Products Particles

Cavitating Particles

Figure 4. SPH/Lagrangian Hydrocode UNDEX-SMI Example


233

Cells (or elements) containing more than one material are common in Eulerian hydrocodecomputations; the presence of multiple fluid and/or solid materials within a cell is the main reasonthat these codes are computationally expensive, and sets them apart from more traditional CFD

Void Eulerian Cells

Cavitation Region

Mixed Water/Steel/Void Cells

Water-Filled Cells

Mixed Water/Explosion Products Cells

Figure 5. Eulerian Hydrocode UNDEX-SMI Example


234

codes. This situation calls for numerical algorithms that prevent artificial material diffusion (themixing of materials across a material interface) within these mixed cells. The convergence to acommon state parameter (e.g. pressure) within a multimaterial cell can also result in considerableexpense, particularly if the higher order accuracy of the Lagrangian phase is to be retained. Theadditional computational effort expended in the remap phase is largely responsible for thediscrepancy in comparative Eulerian versus Lagrangian computational expense.

Since solid materials are defined within Eulerian cells whose properties must be uniform,several modeling limitations present themselves. Several cells must define the thickness of anyplate structure to capture its bending stresses; this necessitates prohibitively fine zoning.Furthermore, structural properties of a solid will be “smeared” with the fluid properties of anyadjacent water within a mixed cell. Combined, these facts result in Eulerian UNDEX-SMI (localand global shock- and bubble/structure interaction) computations being highly impractical.

The most prominent Eulerian hydrocodes are CTH [46,47,48,49,50,51,52,53,54,55,56,57,58,59] and MESA [60], although the Eulerian modules of the Coupled Eulerian/Lagrangian(CEL) codes, described below, are also commonly used. Other Eulerian hydrocodes includePAGOSA, PCTH and RAGE (SAGE) [61]. Also, the more general type of ArbitraryLagrangian/Eulerian (ALE) codes (see below) can be run in purely Eulerian mode. Sincecomputational structural dynamics analysis is highly impractical in an Eulerian frame, noexamples of Eulerian UNDEX-SMI analysis exist.

Eulerian hydrocodes are related to the more traditional computational fluid dynamics(CFD) codes, some of which have even demonstrated their ability to model underwater explosionbubbles [62,63]. Eulerian hydrocodes have been successfully coupled to Lagrangian hydrocodessuch that detailed structural calculations can be made within a Lagrangian framework. TheArbitrary Lagrangian-Eulerian (ALE) method, described in a following section, can be considereda variant of the Eulerian method; in effect, the Eulerian method is a subset of the ALE method.

COUPLED EULERIAN/LAGRANGIAN (CEL) HYDROCODES

Coupled Eulerian/Lagrangian (CEL) hydrocodes employ both Eulerian and Lagrangianmethods in their most advantageous modes in separate (or overlapping) regions of the domain. Asillustrated in Figure 6, the Lagrangian shell elements continuously interact with the Eulerian fluiddomain; the communication between the two coordinate systems is accomplished through"interface elements." A recommended practice concerning the application of the CEL method is todiscretize solids (materials in which the material strength plays a dominant role) in a Lagrangianframe, and materials exhibiting primarily fluid behavior (little or no strength) in an Eulerianframe. The Eulerian and Lagrangian regions continuously interact with each other, allowing truecoupling of a fluid and a structure. A typical CEL code is actually comprised of a family of threecodes: Eulerian, Lagrangian and Coupling modules. The coupling module handles the informationthat is passed continuously between the Eulerian and Lagrangian modules (in both directions), inone of two ways.


235

In the first coupling method, "interface elements" are employed that coincide with theexterior surfaces of the Lagrangian model, forming a surface in a three dimensional model (a linein a two-dimensional model). The interface elements determine the volume of Eulerian cells that

Lagrangian Plate Elements, and Coincident Interface "Elements"

Eulerian Grid

Void Eulerian CellsPartially Water-Filled Eulerian Cells

Cavitation Region

Figure 6. Coupled Eulerian/Lagrangian Hydrocode UNDEX-SMI Example


236

are partially covered by the Lagrangian mesh. Since the surface of the Lagrangian mesh isgenerally not flat, this determination can be very difficult. The presence of an arbitrarily shapedLagrangian model usually creates some small volumes in partially covered Eulerian cells; suchcells are “blended” with neighboring cells to avoid the severe time step restrictions on small cells.This coupling method is used in DYSMAS/ELC [64], PISCES [65,66] and DYTRAN [67,68].

The second coupling method avoids the difficulty of calculating partially filled cells byincluding the Lagrangian material within the Eulerian calculation. Since the dynamics of thinmaterials cannot be calculated practically within an Eulerian mesh, this coupling method is notapplicable to UNDEX-SMI analysis. This method is applicable to high-velocity impact analyses;it is employed in HULL [69] and the coupling of CTH with EPIC through ZAPOTEC [70].

All CEL codes can compute in a strictly Lagrangian or Eulerian mode. A feature of someCEL codes is the capability to rezone a Lagrangian mesh into an Eulerian mesh. An example ofthis is to begin the computation of a shaped-charge liner in a Lagrangian frame, and to convert theliner into an Eulerian computation after material distortions have made the continuation ofLagrangian computations impractical.

An UNDEX-SMI event that a CEL code would find difficult or impossible to modelproperly would be where thin structural members extend out into the fluid, as illustrated in Figure7. A CEL code must define the interface between the Lagrangian region (structure) and Eulerianregion (fluid), but a Lagrangian structural element (no spatial thickness) can easily "see" a singleEulerian fluid cell on both sides. Thus two separated fluid regions would be described within asingle Eulerian cell - an unphysical situation. The employment of Lagrangian continuum elementsfor the structure would tend to overcome this problem, but then the disadvantages of usingcontinuum elements where structural elements are more appropriate come into play.

The original Coupled Eulerian-Lagrangian code was CEL [71]. MSC/DYTRAN (formerlyPISCES-3DELK) [67,68], MSC/PISCES (formerly PISCES-2DELK) [65,66], HULL [69],DYSMAS/ELC [64], AUTODYN-2D [72] and the coupling of CTH with EPIC throughZAPOTEC [70] are the primary CEL hydrocodes in use. All except the HULL and CTH/EPICcodes have some practical thin-plate structural analysis capability in 2D or 3D. Only

Lagrangian Plate Elementsand Coincident Interface "Elements"

Split Eulerian Cell

Figure 7. A Difficult Coupling Problem for CEL Codes


237

MSC/DYTRAN and DYSMAS/ELC have 3D coupled capability using “interface elements”, withsubstantial structural analysis capability. They are therefore the only CEL codes currently capableof practical, comprehensive UNDEX-SMI analysis (local and global shock/structure andbubble/structure interaction analysis) in 3D. The capability for modeling the interaction betweenan underwater explosion (primarily shock) and naval structures has been demonstrated with theCEL method using DYSMAS/ELC [73,74,75,76] and MSC/DYTRAN [77,78]. The capability tomodel combined shock/structure and bubble/structure interaction in 2D has been demonstrated byPISCES-2DELK [79] and DYSMAS/ELC [80,81].

ARBITRARY LAGRANGIAN/EULERIAN (ALE) HYDROCODES

Arbitrary Lagrangian/Eulerian (ALE) hydrocodes share aspects with both Lagrangian andEulerian hydrocodes; Lagrangian motion is computed every time step, followed by a remap phasein which the spatial mesh is either not rezoned (Lagrangian), rezoned to its original shape(Eulerian) or rezoned to some more "advantageous" shape (between Lagrangian and Eulerian). Inthis way the spatial description of the mesh is neither restricted to following material motions(Lagrangian) nor remaining fixed in space (Eulerian). ALE mesh motions are based primarily onthe preservation of a uniform mesh, not the capture of physical phenomena.

The ALE method provides a way of coupling fluid dynamics to structural dynamicswithout interfacing two separate coordinate systems as is done in the CoupledEulerian/Lagrangian method. The efficiency to be gained by straightforward coupling (theavoidance of a separate coordinate coupling module) is probably significant. In cases wherestructural elements can be incorporated directly within the ALE framework, the coupling is trivial.In cases where the ALE numerical method cannot incorporate structural elements, the couplingcan be effected through a continuous transfer of boundary conditions without the coordinatesystem interactions required in the CEL method.

Two levels of ALE technology exist. One allows ALE behavior only within a material(forcing material boundaries to remain Lagrangian); an example of this "single material” or“Simple” ALE (SALE) type is illustrated in Figure 8. The material boundary between theexplosion products and the water remains Lagrangian, and the mesh that defines the water remainsuniform (unlike the fully Lagrangian water in Figure 2). The distinction between the meshmotions of this example and those of the purely Lagrangian example lies primarily in the elementsthat define the water region adjacent to the expanding bubble, as illustrated in Figure 9. In thepurely Lagrangian case, those elements become exceedingly thin as the bubble expands. In thesingle material ALE case, those water elements are continuously rezoned such that a much moreuniform mesh evolves; this has the advantage that the time step does not drastically drop as it doesin the purely Lagrangian case. A disadvantage of rezoning includes the computational expenseinvolved in rezoning from which purely Lagrangian computations are spared. This method, likethe fully Lagrangian case, ultimately breaks down as the bubble collapses upon itself, since themesh that defines the explosion products cannot simply "get out of the way."


238

The second level of ALE technology allows multimaterial elements to form and istherefore more generally applicable; an example of this "multimaterial ALE" is illustrated inFigure 10. In this example, most of the mesh remains fixed in space (Eulerian), but the regionadjacent to the deforming structure deforms with the structure (Lagrangian). The elements thatrepresent the region between the structure and the stationary mesh are therefore neitherLagrangian nor Eulerian; they form a bridge between the two regions. Since the mesh in the

Lagrangian

Water

Void

Plate Element Nodes

Cavitation Region

Explosion Products

Plate Elements

Figure 8. Single Material ALE Hydrocode UNDEX-SMI Example


239

bubble region is largely Eulerian, this method does not break down as the bubble collapses uponitself.

Due to the current lack of practical structural analysis capability, some ALE hydrocodesare currently not applicable to the analysis of local and global shock/structure and bubble/structureinteraction. ALE technology, however, has much potential for UNDEX-SMI analysis. Unlike theCoupled Eulerian/Lagrangian (CEL) codes, the ALE codes are each only one program, so thestructure/medium coupling would be more straightforward and efficient. In fact, an ALE codewith structural analysis capability would potentially be able to solve the problem shown in Figure7, which a CEL code would find difficult or impossible to model properly. However, the couplingof fluid and structural regions through matching of element nodes creates another problem. Asillustrated in Figure 11, elements that must remain Lagrangian (e.g., plates) cannot be allowed tocollapse upon each other if material is entrained between them. This is the same limitation thatprevents the Lagrangian and Single-Material ALE (SALE) methods from being applied to bubblejetting problems: the mesh that defines the entrained fluid cannot simply “get out of the way” of aLagrangian interface, even if the fluid itself could.

The first attempts at creating ALE hydrocodes can be seen in the Lagrangian hydrocodesthat implemented "automatic rezoning" options within material boundaries (single material ALE,or SALE). Such codes include ARTOO (based on TOODY) [82] and DYNA2D [19].VEC/DYNA3D, LS-DYNA3D [21], and AUTODYN-3D [72] include SALE capability.

Prominent multimaterial ALE hydrocodes include CALE [83], CAVEAT [84], ALE3D[85], ALEGRA (also known as RHALE) [86] and MSC/DYTRAN [68]. ALE3D, ALEGRA andDYTRAN include Lagrangian structural elements and are therefore applicable to thecomputational analysis of UNDEX-SMI. Multimaterial ALE UNDEX-SMI analyses have beenattempted with ALE3D [87] and DYTRAN [77].

Thinner Elements in Lagrangian Computation than in ALE

Lagrangian Single-Material ALE

Figure 9. Comparison of Lagrangian and Single-Material ALE


240

The ALE method can be considered a superset of both the Eulerian and Lagrangianmethods, since both types of mesh motions are incorporated within an ALE scheme. The ALEmethod cannot, however, be considered a superset of the Coupled Eulerian/Lagrangian (CEL)method, since the ALE method makes no provision for allowing an Eulerian region to interactdirectly with a Lagrangian interface. ALE hydrocodes are more general than ALE CFD codes, inthat ALE hydrocodes allow simulations of materials with strength.

Lagrangian

Void

Cavitation Region

Plate Element Nodes

Plate Elements

Water

Explosive

Figure 10. Multimaterial ALE Hydrocode UNDEX-SMI Example


241

SUMMARY

Many simulations of structural response must include the dynamics of the surroundingmedium. Such are the intended capabilities of the general-purpose methods, or “hydrocodes.” Thehydrocodes are computational tools that make minimal assumptions about the physicalphenomena exhibited by the many classes of problems they are applied to. Detonation physics,shock wave propagation, bubble dynamics, and large-strain structural plasticity and failure aresome of these classes; underwater explosion structure/medium interaction is a combination.

Several general-purpose (hydrocode) methods are in general use: Lagrangian, Eulerian,Coupled Eulerian-Lagrangian (CEL) and Arbitrary Lagrangian-Eulerian (ALE) hydrocodes andtheir derivatives. All general-purpose methods are theoretically capable of solving problems instructure/medium Interaction (SMI). However, the lack of infinite computer resources and theavailability of Lagrangian “structural elements” allow the assessment of methods to be based onpracticality rather than capability. Only those codes that include structural elements (i.e., thinplates, etc.) as well as fluid dynamics modeling capability (including detonation physics) arecapable of practical SMI analysis of thin-walled structures; prominent three-dimensionalhydrocodes are so categorized in Table 1.

General capabilities of the various hydrocode methods are summarized in Table 2. Sincehydrocodes (like most other analytical tools) provide no measure of accuracy, analysis capabilityis defined as the possibility to generate a model that will produce accurate results.

Lagrangian hydrocodes with structural elements, though applicable to structure/mediuminteraction, are not suited to model the large material distortions prevalent in longer-duration,bubble/structure interactions, and are therefore of limited utility.

Lagrangian Plate Elements

Water (Continuum) Elements

Plate/Continuum Element Nodes

Problem: Pinch-Off Region

Initial Configuration Later Configuration

Figure 11. A Difficult Coupling Problem for ALE Codes


242

Eulerian hydrocodes, though practical for modeling large distortion continuum dynamics,can be dismissed as impractical for UNDEX-SMI analyses, due to their inability to practicallymodel thin-plate structures.

The Coupled Eulerian/Lagrangian (CEL) hydrocodes were developed for structure/medium interaction calculations, specifically fluid/structure interaction, in which both thestructure and its surrounding medium are modeled within their traditional frames of reference:

Code Lagr

angi

an (

trad

ition

al)

Sm

ooth

ed P

artic

le H

ydro

dyna

mic

s (S

PH

)

Fre

e-La

gran

ge M

etho

d (F

LM)

Eul

eria

n

Cou

pled

Eul

eria

n/La

gran

gain

(C

EL)

Sin

gle-

Mat

eria

l Arb

itrar

y La

gran

gian

/Eul

eria

n (S

ALE

)

Mul

ti-M

ater

ial A

rbitr

ary

Lagr

angi

an/E

uler

ian

(MM

ALE

)

Thi

n-pl

ate

Str

uctu

ral D

ynam

ics

Sm

all d

isto

rtio

n co

ntin

uum

dyn

amic

s

Larg

e di

stor

tion

sing

le-m

ater

ial c

ontin

uum

dyn

amic

s

Larg

e di

stor

tion

mul

ti-m

ater

ial c

ontin

uum

dyn

amic

s

ALE3D l l l l l l l lALEGRA l l l l l l l l

AUTODYNE-3D l l l l lCTH l l l l

CTH-EPIC l l l l l lDYNA3D l l l

DYSMAS/ELC l l l l l l lEPIC l l l l lHULL l l l l l l

LS-DYNA3D l l l l l MESA l l l l

MSC/DYTRAN l l l l l l l l lPRONTO3D l l l l l l

Table 1. Descriptions and Potential SMI Applicabilities of Prominent 3D Hydrocodes


243

Eulerian for fluid dynamics and Lagrangian for structural dynamics. CEL hydrocodes withstructural elements are therefore practical for UNDEX-SMI analyses; such models have beendemonstrated.

The Arbitrary Lagrangian/ Eulerian (ALE) hydrocodes, developed with many of the samegoals as the CEL codes, overcome some difficulties inherent in the CEL codes associated withcoupling the Eulerian and Lagrangian coordinate systems, but introduce others. MultimaterialALE (MMALE, as distinguished from Single-material ALE (SALE)) hydrocodes with structuralelements are potentially applicable to UNDEX-SMI analyses, though few models have been

Method Thi

n-pl

ate

stru

ctur

al d

ynam

ics

Sm

all-d

isto

rtio

n co

ntin

uum

dyn

amic

s

Larg

e-di

stor

tion

sing

le-m

ater

ial c

ontin

uum

dyn

amic

s

Larg

e di

stor

tion

mul

ti-m

ater

ial c

ontin

uum

dyn

amic

sLagrangian hydrocodes with structural elements

Traditional Lagrangian l l Smoothed Particle Hydrodynamics (SPH) l l l l

Free-Lagrange Method (FLM) l l l l

Eulerian hydrocodes l l l

Coupled Eulerian/Lagrangain (CEL) hydrocodes with structural elements

l l l l

Arbitrary Lagrangian/Eulerian (ALE) hydrocodes with structural elements

Single-Material ALE (SALE) l l l Multi-Material ALE (MMALE) l l l l

Table 2. Potential SMI Applicabilities of Hydrocode Methods


244

demonstrated with this relatively new method.In summary, the simulation of underwater explosion structure/medium interaction with

hydrocodes is practical. Of the four hydrocode methodologies (Lagrangian, Eulerian, CoupledEulerian/Lagrangian, and Arbitrary Lagrangian/Eulerian), only the Eulerian method is notpractical for UNDEX-SMI analysis. All other methods are applicable to various extents, and thenonly if the codes under consideration employ structural elements (i.e., thin plates and beams). Themost versatile methods are the CEL and Multi-Material ALE.

ACKNOWLEDGMENTS

This work was sponsored by the Office of Naval Research, through the UnderseaWarheads and Explosives Project (Dr. Judah Goldwasser). The author is indebted to numerousreviewers; in particular, Stephen Zilliacus of the Carderock Division of the Naval Surface WarfareCenter, and Vera Revelli of Sandia National Laboratories, Livermore, California.

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