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Research ArticleModeling Large Deformation and Failure of ExpandedPolystyrene Crushable Foam Using LS-DYNA

Qasim H. Shah and A. Topa

Department of Mechanical Engineering, Faculty of Engineering, International Islamic University Malaysia, Jalan Gombak,Kuala Lumpur, Malaysia

Correspondence should be addressed to Qasim H. Shah; [email protected]

Received May ; Accepted October ; Published January

Academic Editor: Dimitrios E. Manolakos

Copyright Q. H. Shah and A. opa. Tis is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.

In the initial phase o the research work, quasistatic compression tests wereconducted on the expanded polystyrene (EPS) crushableoamor material characterisation at low strain rates (8.3103 8.3102 s1) to obtain thestress straincurves. Te resulting stressstrain curves are compared well with the ones ound in the literature. Numerical analysis o compression tests was carried out tovalidate them against experimental results. Additionally gravity-driven drop tests were carried out using a long rod projectile withsemispherical end that penetrated into the EPS oam block. Long rod projectile drop tests were simulated in LS-DYNA by usingsuggested parameter enhancements that were able to compute the material damage and ailure response precisely. Te material

parameters adjustment or successul modelling has been reported.

1. Introduction

Crushable oams are suitable solution in the eld o shockmitigation and impact absorption applications because otheir incombustibility, cost, complex compression behavior,and high energy absorption capabilities []. In saety appli-cations, accurate predictions o behaviour o shock absorbermaterials are extremely important because the experimentalwork is a resource hungry process.

Troughout the past years, the range o applications ocrushable oams has become wider and larger as engineersand designers keep altering the microstructure o the oammaterials in order to achieve the desired mechanical proper-ties andbehaviour that ull the requirements regarding theirapplications. Crushable oams are mainly used in cushioning,impact mitigation, energy absorption, and comort applica-tions [].

One way to increase the car body stiffness and crash-worthiness is the utilization o local reinorcements with syn-thesized polyurethane oam. Te crushable oams have sev-eral advantages over other reinorcement materials becauseo their high energy absorbing capabilities, coupled with theirlow cost and weight [].

Another important application o the crushable oamsis the aircraf runway arrestor systems. Te aircraf mightoverrun the available runway area during take-off or landing.Crushable oam arrestor bed systems mitigate the overrunwhich prevents accidents involving aircraf damage and losso lie [].

In automotive saety, the crushable oams are used in thenew Steel And Foam Energy Reducing (SAFER) barriers.In many NASCAR racetracks, simple crushable polystyrene

insulation oam blocks are placed between the outer steeltube, and the inner concrete wall. Tis SAFER barrier is verylow in cost and weight and easy to abricate [,].

Another application or the crushable oams is in oil wellcasing. Heat is generated due to the normal drilling andproduction applications. As temperature rises, the trappeduids tend to expand and potentially can create a veryhigh pressure. Te most effective mitigation solution or thispressure build-up is the application o crushable oam wrap.Tis will allow the uid trapped within the casing annulusto expand. Te crushable oam wrap is predetermined tocollapse beore any potential dangerous pressure may exist[].

Hindawi Publishing CorporationModelling and Simulation in EngineeringVolume 2014, Article ID 292647, 7 pageshttp://dx.doi.org/10.1155/2014/292647
http://dx.doi.org/10.1155/2014/292647http://dx.doi.org/10.1155/2014/292647

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Modelling and Simulation in Engineering

Extensive experimental work has been conductedto determine the mechanical properties o expandedpolystyrene oams. Difficulties arise in modelling these typeso materials because they are stain rate dependant. Previousstudies show that the rate dependant behaviour is linear withthe logarithm o the strain rate []. Moreover, the mechanical

properties o polymeric oams depend on their density [,].Tereore, developing the material model depends on thedensity o the oams and their applications.

Te complexity o the mechanical behaviour o thecrushable oams is a consequence o its cellular structure.Compression is the most common mode o deormationor crushable oams as they are weak in tension and shear.However, tension and shear deormation can occur due toconcentrated compressive loads or the geometry o crushableoams [].

In pure compression, there are three regions in the stress-strain relationship: linear compression, stress plateau, andnon-linear compression. Poissons ratio is negligible in purecompression. In pure tension, the material behaves linearly inlow deormation. However, nonlinear behaviour is observedat large deormations [,].

In previous work, material models or EPS oams weredeveloped. Tese models were proved to be successul inthe cases o uniorm compression loading and low velocitylocalized damage [,,,]. However, during high velocitylocalized compression, the material undergoes a combinedmode o compression and tension. Brittle rupture and crackinitiation are experimentally observed in the material [, ].Tereore, these material models need to be improved toinclude the brittle ailure behaviour.

2. Experimental Work

.. QuasiStatic Compression est. Te quasistatic compres-sion tests were conducted on cubic specimens o EPS crush-able oam with the side length o mm. Te average density

o the specimen was measured as . kg/m3. Te specimenwas compressed until % o its initial length. Te compres-sion test was carried out at three different compression rates: mm/min, mm/min, and mm/min and the strainrates or these three compression rates were calculated as./s, ./s, and ./s, respectively.

Upon examining the specimen during the compressiontest, no lateral elongation was observed as seen in Figure .

Tis proves that EPS crushable oams have zero Poissonsratio. Te volume o the material is not conserved duringcompression. Instead, the density increases while the materialis compressed. Poissons ratio plays an important role in stressstrain diagrams. Te initial and nal cross section areas o theEPS crushable oams in compression remain constant. Tus,the engineering and true stress strain diagrams are identical.

When the compressive load was removed, the specimenelastically recovered to approximately % o its initial length.Tis is due to the elastic component (matrix material) opolymeric oams. However, a permanent damage is observedbecause o the oam cells collapsing in the stress plateauregion.

F : Quasistatic compression test o EPS crushable oam.

0

0.1

0.2

0.3

0.4

0.5

0.6

0 10 20 30 40 50 60 70 80 90

Stress

(MPa

)

Strain (%)

500mm/min

250mm/min

50mm/min

F : Rate dependency o EPS crushable oam.

: Effects o strain rate on yield stress, Youngs Modulus, andabsorbed energy.

Strain rate Yield stress Youngs Modulus Absorbed energy

(s) (MPa) (MPa) (J)

. . . .. . . .

. . . .

Te results o the compression test are plotted in Figure .Te three regions o deormation are observed in EPScrushable oams. However, the transition point between thestress plateau and densication regions are not clear. Tisis believed to be due to the destruction o oam cells andthe permanent damage. Te yield stress, Youngs Modulusand total absorbed energy by the oam material are listed inable.

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0.6

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0.3

0.2

0.1

0

0.60.50.40.30.20.10 0.7 0.8 0.9

Stress(M

Pa)

Strain (mm/mm)

Experiment

Literature

F : Comparison between literature data and experimental

data.

Guide tube

Gu

ide

tub

e

Fo

am

F : Set-up or drop test experiment.

o validate the results o the experiment, the stress straincurve at a strain rate o .s1 was compared to thestress strain curves ound in the literature []. As observedin Figure, there is a slight difference in the two curves. Tisis because o the small difference in the strain rate and thedensity o the material. Te specimen in the literature had

slightly higher density and the strain rate was a little larger.

.. Gravity-Driven Drop est. A specimen o EPS crushableoam having a square base with the side length o mmand the height o mm was secured to the ground. A mm long cylinder (. kg)witha diameter o mm anda semi-spherical head was dropped on the specimen througha cylinder tube guide. Te altitude o the long rod drop was meters and the projectile accelerated due to gravity andreached the velocity o . m/s beore hitting the specimen.Te set up o theexperiment is shown in Figure . A localizeddamage was observed on the projected area o the projectileand the surrounding surace area o the specimen was not

Hole

FoamP

roject

ile

F : Localized damage on the specimen.

Pro

ject

ile

Com

pressedmater

ial

F : Depth o penetration o projectile into EPS oam speci-men.

affected as seen in Figure. Tis damage was conned to astraight cylindrical hole in the oam specimen. Due to thesmall elastic recovery o the specimen, the projectile bouncedup slightly afer reaching the maximum depth o penetration.Te damage in the specimen was highlighted as shown inFigure . able summarizes the results o the drop testexperiment.

3. Numerical Simulation

.. Compression est Simulation. Te simulation o the quasistatic compression test was successully perormed using LS-Dyna. LS-Dyna provides many material models or differenttypes o oams []. However, based on previous work byOzturk and Anlas [], the best candidate or modeling EPScrushable oam is MA CRUSHABLE FOAM. Tis materialmodel required the input o ve parameters: density omaterial, modulus o elasticity, Poissons ratio, stress straincurve, tensile stress cutoff, and damping coefficient. Terst our parameters were ound experimentally. However,tensile cutoff and viscous damping coefficient were obtained

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: Maximum depth o penetration o the projectile.

DOP (mm)

Specimen

Specimen

Specimen

Specimen Average

rom the literature []. Te parameters or the materialmodel are listed in able . Te model was nely meshedto obtain accurate results. Te lower nodes o the modelwere xed while the upper nodes were given a prescribedmotion at mm/min. Te results o the simulation arelisted in Figure. A comparison between the simulation andthe experimental results show very small difference and thus

veries the material model developed or compression.

.. Drop est Simulation. Te material model developed orthe compression test simulation must be improved beore itcould be used in the drop test simulation. Te main reason isthat in the long rod impact the compression orce is localizedin a small area on thesurace o the oam thus creating a com-bination o compression and shear. Te material ailure wassimulated with the aid o MA ADD EROSION based onthe plastic strain and tensile stress []. Without introducingailure in the material model, thecrushable oam deormationdue to the localized orce shows problematic urrowing []and an unrealistic dent shape as shown in Figure . Tebrittle ailure mode cannot be obtained without using anappropriate ailure criterion.

Te existing model was improved to avoid the negativevolume error which occurs due the large deormation inthe oam. o prevent this error, the stress strain curve wasextended exponentially at large strains []. Te extendedcurve is shown in Figure. Also, one point integration solidelement was used with hourglass control type []. o avoidmesh tangling in highcompression areas, interior contact wasutilized with the activation thickness actor o .. Contactinterior type was activated to control a combined mode ocompression and shear in LS-DYNA [].

Allowing the oam elements to ail and erode causesanother problem. Some elements on the surace o oamwill erode and the projectile will come into contact with

some o the elements within the oam. Tus, suraceto surace contacts are not recommended. o overcomethis problem, AUOMAICE NODE O SURFACE con-tact was used and a set o all the oam nodes was dened thatwere used in the contact command. However, this methodcarries a computational penalty.

By deault, LS-DYNA removes the mass o the erodedelements to increase the stability o the calculation. However,the mass o the eroded elements must be considered as thereduction o mass might cause incorrect results. In CON-ROL CONAC card, the value o ENMASS is changed tounity so that the mass o the eroding nodes is retained andcontinue to be active in contact [].

5000

4500

4000

3500

3000

2500

2000

1500

1000

500

0

0 5 10 15 20 25 30 35 40 45

Force

(N)

Displacement (mm)

ExperimentSimulation

F : Comparison between the experimental and simulationresults o the static compression test at mm/min.

4. Discussion

.. Quasi Static Compression est. Te compression testwas conducted to obtain the material properties o EPScrushable oams as well as to develop a preliminary materialmodel. Te most important required properties or modelingthe material are the density, stress strain curve, the elastic

modulus, and Poissons ratio. Tese properties were oundexperimentally. Te elastic modulus and stress strain curvewere ound to be dependent on the strain rate. As the strainrate increases, the elastic modulus increases and the stressstrain curve becomes stiffer. As or Poissons ratio, it wasound to be independent o the strain rate and was alwaysequivalent to zero [].

A Comparison between the experimental and simulationresults shows the capability o the model to reproduce thestress strain curve with acceptable accuracy as shown inFigure . Tereore, the suggested material parameters arecapable o accurately predicting the load and deormation oEPS crushable oams.

However, it should be noted that even though the mate-rial model showed good accuracy in the compression testsimulation, it is still a preliminary model and needs to beimproved i it were to be used or large deormation andailure simulations o EPS oam.

Failure due to shear or tension must be introduced inthe material model. Although crushable oams are not usedunder tension or shear loading, localized impact or thegeometry o the crushable oam might result in a combinedmode o shear, tension and compression [].

.. Drop est. Te drop test experiment serves as an addi-tional verication o the suggested material parameters. Te

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: Input card or MA CRUSHABLE FOAM.

Parameter Description Value Units

MID Material ID number

RO Density . Kg/m

Youngs Modulus . GPa

PR Poissons ratio LCID Load curve ID or nominal stress versus strain

SC ensile stress cut-off 0.1 (10)3 GPa

DAMP Rate sensitivity via damping coefficient .

F : Deormation o EPS oam without introducing ailure criterion.

rst problem encountered in the simulation was the negativevolume problem due to instability. Te existing model canwithstand compression until only around percent o itsoriginal length. Tis is because the stress strain curve usedin the model was obtained rom the compression test inwhich the compression limit was percent. However, in thedrop test experiment, due to the high kinetic energy o theprojectile, the crushable oam elements might be compressedmore than percent o their original length. It may occurthat the strain in the simulation exceeds the last point o thestress-strain curve. I this happens, LS-DYNA extends thecurve linearly with last slope o the curve. Tis might lead torelatively small stress values and the negative volume problemmight occur.

Te negative volume error problem was prevented byadopting two approaches. First, the stress strain curve wasexponentially extended at large strains as shown i Figure .Tis can be a very effective approach. Another importantparameter which greatly helps in preventing the negative

volume error is by introducing the contact interior in LS-DYNA. Tis type o contact was especially designed to be

used or simulating sof materials. Te contact interior type was activated, which was designed to control combinedmodes o compression and shear.

In the experiment, the brittle ailure was observed inthe material due to shear loads. o simulate this modeo ailure, ADD EROSION was utilized which allows theintroduction o ailure criteria in the material model asMA CRUSHABLE FOAM does not allow material erosion.Te ailure criteria dened was the maximum tensile stressand maximum plastic strain. Te values o these criteriawere ound by visual investigation and comparison betweenexperiment and the simulation. Te points at which thematerial starts to crack and ail in the experiment were

identied, and the respective ailure criteria values wereintroduced into simulation by trial and error method.

Comparing the projectile depth o penetration in theexperiment and simulation validates the developed materialparameters. As shown in Figure, the depth o penetrationprole obtained in the simulation shows that the projectilereaches the maximum depth o penetration o mmat milliseconds. Tis value o the maximum depth openetrationmatches the experimental average valueas shownin able . Also, the graph shows that the depth o penetrationslightly decreases afer reaching the maximum depth openetration then increases back to the maximum. Tis isinterpreted as the long rod projectile bouncing back slightlyafer reaching the maximum depth o penetration, whichwas actually observed in the experiment. Furthermore, visualcomparison between the physical testing and numericalsimulations shows the similarity in the ailure mode o thecrushable oams. As depicted in Figure, the damage on theoam was localized on the projected area o projectile and theailure occurs due the shear strain.

5. Conclusions

Compression tests on EPS crushable oams were carried outat different strainrates. Te effect o strainrate on the materialproperties was established. It was ound that at higher strainrates the material is able to withstand higher loads andabsorbs more energy. Moreover, elastic modulus and yieldstrength increments were ound to be proportional to thestrain rate increase.

Compression test simulations were successully per-ormed and the results were validated by the experimentalwork. Te material model was capable to reproduce the stressstrain curve with acceptable accuracy.

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0

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Stress

(MPa

)

Stain (%)

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0.25

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0.35

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0.45

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0 20 40 60 80 100

Stress

(MPa

)

Strain (%)

F : Original (lef) and extended (right) stress-strain curve.

0

0 20 40 60 80 100

Dep

tho

fpenetra

ion

(mm

)

Time (ms)

200

180

160

140

120

100

80

60

40

20

F : Missile depth o penetration (simulation results).

Drop tests using long rod projectile impact against EPScrushable oam were conducted. Te depth o penetrationwas recorded and the average value was calculated. Teailure mode and the deormation in the specimen wereinvestigated. Numerical simulations were perormed usingthe enhanced material parameters along with an appropriateailure criterion that were able to reproduce the ailuremodes observed during the experiments. Maximum depth o

Pro

ject

ile

M

aximumshearingstra

in

Com

pressedmater

ial

F : Foam ailure process in numerical analysis.

penetration obtained in LS-DYNA simulations agreed closelywith experimental work.

Conflict of Interests

Te authors declare that there is no conict o interestsregarding the publication o this paper.

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