Analysis of behind the armor ballistic trauma

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j o u r n a l o f t h e m e c h a n i c a l b e h a v i o r o f b i o m e d i c a l m a t e r i a l s 4 5 ( 2 0 1 5 ) 1 1 – 2 1

http://dx.doi.org/101751-6161/& 2015 El

nCorresponding autE-mail address:

Research Paper

Analysis of behind the armor ballistic trauma

Yaoke Wena,n, Cheng Xua, Shu Wangb, R.C. Batrac

aSchool of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, ChinabNo. 208 Research Institute of China Ordnance Industries, Beijing 102202, ChinacDepartment of Biomedical Engineering and Mechanics, Virginia Polytechnic Institute and State University, M/C 0219,Blacksburg, VA 24061, USA

a r t i c l e i n f o

Article history:

Received 2 September 2014

Received in revised form

6 January 2015

Accepted 12 January 2015

Available online 21 January 2015

Keywords:

Behind armor blunt trauma

Body armor

Ballistic gelatin

Ultrahigh molecular weight

polyethylene (UHMWPE) composite

.1016/j.jmbbm.2015.01.010sevier Ltd. All rights rese

hor. Tel.: þ86 25 [email protected] (Y.

a b s t r a c t

The impact response of body armor composed of a ceramic plate with an ultrahigh

molecular weight polyethylene (UHMWPE) fiber-reinforced composite and layers of

UHMWPE fibers shielding a block of ballistic gelatin has been experimentally and

numerically analyzed. It is a surrogate model for studying injuries to human torso caused

by a bullet striking body protection armor placed on a person. Photographs taken with a

high speed camera are used to determine deformations of the armor and the gelatin. The

maximum depth of the temporary cavity formed in the ballistic gelatin and the peak

pressure 40 mm behind the center of the gelatin front face contacting the armor are found

to be, respectively, �34 mm and �15 MPa. The Johnson–Holmquist material model has

been used to simulate deformations and failure of the ceramic. The UHMWPE fiber–

reinforced composite and the UHMWPE fiber layers are modeled as linear elastic

orthotropic materials. The gelatin is modeled as a strain-rate dependent hyperelastic

material. Values of material parameters are taken from the open literature. The computed

evolution of the temporary cavity formed in the gelatin is found to qualitatively agree with

that seen in experiments. Furthermore, the computed time histories of the average

pressure at four points in the gelatin agree with the corresponding experimentally

measured ones. The maximum pressure at a point and the depth of the temporary cavity

formed in the gelatin can be taken as measures of the severity of the bodily injury caused

by the impact; e.g. see the United States National Institute of Justice standard 0101.06-

Ballistic Resistance of Body Armor.

& 2015 Elsevier Ltd. All rights reserved.

rved.

; fax: þ86 25 84303132.Wen).

1. Introduction

Behind armor blunt trauma (BABT) may occur when personal

protective armor deforms dynamically to stop an incoming

projectile. The impact by a fragment simulating projectile (FGP)

causes local high rate loading of the thorax and subsequent

trauma to the thoracic cage and internal organs (Cannon, 2001;

Cannon and Tam, 2001). The relationships between injury

mechanisms and human torso response to BABT are not well

understood at present. For obvious reasons, effects of BABT on a

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Fig. 1 – Schematic sketch of the system used for studying theBABT (sketch not to scale).


human body cannot be experimentally studied and must bedetermined via proxies, the most common of which is ballisticgelatin because it's mechanical properties are believed to beclose to those of a human tissue (Payne et al., 2013). Thus theresponse of ballistic gelatin to impact loading provides a goodapproximation of that of a human tissue.

The “rigid body armor” consisting of a ceramic plate facingthe incoming projectile and a fiber–reinforced composite (FRC)backing is used to stop the projectile and protect a human torso.Generally, soft body armor is placed behind the FRC laminate toabsorb the residual energy of the bullet and the fragments. Afiber of choice for the FRC and the soft body armor is theultrahigh molecular weight polyethylene (UHMWPE) because ofits high specific strength and modulus. Different experimentalconfigurations including the punch-shear test can be used to findquasistatic tensile, compressive, inter-laminar shear and in-plane shear strengths of the UHMWPE FRC (Marissen et al.,2005; Umberger, 2010; Iannucci and Pope, 2011; Heru Utomo,2011; Wen et al., 2013). However, there are very few results (Kohet al., 2010; Chocron et al., 1997) available in the open literaturefor dynamic loading of the composite and the BABT.

Numerical simulations provide details of deformationsinduced by ballistic impact (Gower et al., 2008). Using materialparameters of Dyneema HB25 composite derived from their testdata, Ong et al. (2011) have numerically studied the response ofthe composite to ballistic loading. Grujicic et al. (2008, 2009) haveused the finite element method (FEM) to analyze deformations ofa representative volume element and deduce material para-meters of an UHMWPE FRC. Bürger et al. (2012) have developed astrain rate dependent constitutive relation for an UHMWPE FRCand implemented it in ABAQUS via a user defined subroutine,whereas the predicted energy absorbed during impact withoutconsidering delamination failure agreed well with the experi-mental value, the two values of the residual deformations werenot close to each other. In the numerical study of Krishnan et al.(2010) the computed damage induced in a ceramic armorimpacted by a M2AP bullet was found to agree well with thatobserved experimentally, however, the back face deformationswere under-predicted.

A limited set of experimental investigations have beenundertaken to provide insights into the BABT (Liu et al., 2012;Prat et al., 2012). van Bree and Fairlie (1999); van Bree andGotts (2000) have studied the propagation of a compressionwave in ballistic gelatin shielded by aluminum plates. Theyemployed a “Twin Peak” theory and modeled 20% ballisticgelatin as a compressible elastic–plastic material. Croninet al. (2001) used the Mooney-Rivlin material model for thegelatin to simulate the Twin Peak phenomenon in it, andsubsequently analyzed the dynamic response of a surrogatetorso covered by a Kevlar plate. Grimal et al. (2004) simplifiedthe problem by assuming the thorax material to be linearlyelastic, and approximated the impact load by a time-dependent pressure field of duration equal to that of the firstpressure wave observed behind a ceramic armor impacted bya high-velocity projectile. Roberts et al. (2005, 2007) havedeveloped a physical and a numerical model for a humansurrogate torso with the tissue considered as a viscoelasticmaterial. The study of the BABT is challenging due togeometric complexities and nonlinearities in the materialresponse.

In this paper, transient deformations of the system shownin Fig. 1 have been experimentally and computationallyanalyzed to shed some light on the BABT. Experimentalresults for impact loading of the armor covered ballisticgelatin impacted by a 7.62 mm bullet are first presented.Subsequently, numerical results obtained by using the FEMand the commercial software, LS-DYNA, are compared withthe corresponding experimental findings. Details of deforma-tions during tests are captured using the high-speed photo-graphy. The maximum depth and diameter of the temporarycavity formed in the gelatin are found to equal, respectively,�34 mm and 110 mm. The maximum pressure at a point40 mm away from the gelatin surface contacing the protec-tive armor equals �15 MPa. The computed time histories ofthe pressure and the cavity dimensions are found to be closeto the corresponding test values.

2. Experimental work

The rigid body armor studied here and schematically exhibitedin Fig. 1 consists of 7mm thick 99.5% Al2O3 ceramic tiles with11mm thick UHMWPE fiber–reinforced laminate backing. Thecombined thickness of the adhesive bonding the ceramic platewith the UHMWPE laminate and of the cover cloth equals 2mm,and neither one is included in the sketch of Fig. 1. The armorshielding the 30 cm�30 cm�30 cm block of gelatin (10% massfraction at 4 1C) resting on a table (e.g., see Fig. 2) was impactedby a 7.62mm diameter bullet whose geometry and materials aregiven in Section 3. The gelatin was prepared by following theprocedure proposed by Jussila (2004). The ceramic tiles eitherstop or slow down the bullet, and the UHMWPE soft body armorsheets placed behind the rigid armor absorb most, if not all, ofthe residual energy of the bullet and the fragments. Four

Fig. 2 – (a) Experimental set-up for studying BABT. (b) The pressure sensors embedded in the ballistic gelatin.

Fig. 3 – Locations of pressure sensors embedded in the gelatin block.

Fig. 4 – Temporary cavity profiles in the gelatin for impact speed of 690 m/s.

j o u r n a l o f t h e m e c h a n i c a l b e h a v i o r o f b i o m e d i c a l m a t e r i a l s 4 5 ( 2 0 1 5 ) 1 1 – 2 1 13

pressure sensors embedded in the gelatin at locations shown inFig. 3 provided time histories of the pressure. “Floating” pressuresensors were not used because of the difficulty in placing themat the same exact locations during different experiments. Thesensors were embedded in the liquid gelatin before it solidified.

With brackets holding the sensors, the front surface of sensorscould be kept, within experimental errors, parallel to and 40mmaway from the front surface of the gelatin. Since the pressurewas measured for the time duration of 0.6ms after the bulletimpacted the armor, which is a very short time compared with

Fig. 6 – Time histories, at the four gages, of theexperimentally measured pressures for a 7.62 mm bulletimpacting at 692 m/s the gelatin block shielded bythe armor.


the time of the cavity formation, it is conjectured that thebracket had little or no effect on the measured pressure–timehistory because the cavity did not compress the bracket duringthis time interval. Test results with fixed and floating sensorshave not been compared since no tests with the latter wereconducted. Varas et al. (2011) have shown that gages marginallyaffect deformations of the gelatin and only introduce highfrequency oscillations in the gage readings. Transient deforma-tions of the gelatin were captured with a high-speed camera forthe three ballistic tests conducted at impact speeds of 697, 690and 692m/s.

The evolution of the temporary cavity in the gelatin isdisplayed in Fig. 4. A hemi-spherical cavity gradually formed,sprung back because of the recovery of elastic deformations,and essentially closed (or disappeared) at about 5 ms. Noresidual damage was visually seen in the gelatin suggestingthat its deformations were elastic. For the three impactspeeds time histories of the depths of the temporary cavitiesexhibited in Fig. 5 are close to each other. The mantle (or thelateral boundary) of the cavity could not be accuratelyidentified because it did not form a smooth surface. Thusthe cavity diameter values are not as accurate as those of thecavity depth, and are not close to each other as are values ofthe cavity depth. The cavity diameter for the impact speed of692 m/s is larger than that for the other two impact speedspossibly because the impact location for it was close to theborder of a ceramic tile. The cavity depth reaches its max-imum value of �34 mm at �2.5 ms, and the cavity diameterattains its maximum value of �105 mm at �3 ms after thebullet impacts the armor. The curves labeled ‘numerical’ inFig. 5 represent computed values for the 7.62 mm bulletstriking the armor covered ballistic gelatin at 692 m/s, anddifferences between the experimental and the numericalresults are discussed in Section 3.

For the impact speed of 692 m/s, time histories of thepressure at locations of the four gages exhibited in Fig. 6indicate that the peak pressures at the gage locations equal13.12, 14.47, 12.2 and 15.18 MPa, and there is a slight delay inthe times of these peak values in going from gage 4 to gage 1.The average value, 13.74 MPa, of the peak pressure differs

Fig.5 – Time histories of the cavity depth (left) and the cavity dia7.62 mm bullet impacting the armor shielding the ballistic gelat

from the four values by a maximum of 11.2%. Even with allnecessary precautions taken to ensure that distances of thefour gages from the anticipated line of impact and the frontimpacted face are the same, it may not be the case because ofthe difficulty in ensuring that the line of impact is perfectlynormal to the impact surface. Also the gelatin may not haveuniformly solidified around the gages. For the three impactspeeds, time histories of the pressure (not plotted here) ateach of the four pressure gages are close to each other withthe average of the peak pressures measured by the four gages

meter (right) determined from high-speed photographs for ain.


equaling 13.41, 15.88 and 13.74 MPa, respectively, for impactspeeds of 697, 690 and 692 m/s. Whereas the averaged peakpressures for impact speeds of 697 and 692 m/s are close toeach other that for the impact speed of 690 m/s differs fromthem by �18% which is within experimental errors consider-ing the number of variables involved, and the likelihood ofthe bullet not traveling along the axis symmetrically locatedwith respect to the four gages especially after traversingthrough the layered armor. At each gage location, the pres-sure sharply rises to the peak value in �0.06 ms, and subse-quently falls. The drop in the pressure at 0.1 ms to �2 MPa isfollowed by a series of high amplitude oscillations most likelydue to the interaction between the bullet and the armor. It isinteresting to note that a low amplitude (�1.2 MPa) longduration pressure pulse appears at �0.45 ms after impactwhich most likely is due to the impact between the deformedarmor and the gelatin. Thus there are two pressure waves:the first is a series of high-amplitude short duration pressurepulses due to the interaction between the bullet and thearmor, and the second is low amplitude long durationpressure pulse due to the interaction between the armorand the gelatin.

The brackets used to hold the gages have little or no effect onthe pressure–time histories till 0.8ms after impact since thecavity did not compress the brackets till then. Thus the “fixed”and the “floating” sensors will very likely give identical values ofthe pressure. As mentioned above, floating sensors were notused because of the difficulty in ensuring that their locationswere the same in the three tests. Because of the noticeableexpansion of the cavity beyond 1ms after impact, the metalbracket may affect time history of the pressure since floatingsensors will move with the cavity while those mounted on abracket will not. Thus the floating sensors will give pressure at amaterial point of the gelatin and the fixed sensor at a location inspace with different gelatin material points pressing the sensoras time progresses.

3. Numerical simulations

Numerical simulations using verified computer codes andvalidated mathematical models provide details of deforma-tions that cannot be experimentally measured. For example,cracks formed in the interior of a structure may not be easilydetected during tests but can be identified during computa-tions. Here the FE commercial software, LS-DYNA, has beenused to simulate as closely as possible the impact conditions,specimen geometries, realistic values of material parametersand failure criteria.

Deformations of the adhesive and the cover cloth are notconsidered in the numerical solution of the problem mainlybecause of the excessive computational resources needed toanalyze deformations of very thin finite elements within thesematerials. Values of material parameters for the UHMWPEcomposite, listed in Table 1a and b are based on either literaturesearch (Ong et al., 2011; Grujicic et al., 2009) or our best estimates.These simplifying assumptions are necessary due to the lack ofvalues available in the literature and the lack of resources to testall materials for obtaining the actual mechanical properties esp-ecially of interfaces.

3.1. Material models

The Johnson–Holmquist (JH-2) material model (Johnson andHolmquist, 1994) was used to simulate deformations of theceramic tiles. This constitutive relation has three parts – arepresentation of the intact and fractured strength, a pres-sure–volume relation that can include bulking and a damagemodel that transitions the material strength from an intactstate to a fractured state. The strength and damage relationsare listed below for completeness.

The equivalent stress for a ceramic is given by

σn ¼ σn

i �Dðσn

i �σn

f Þ ð1Þ

where D, 0rDr1, is a scalar damage parameter and stressesin Eq. (1) are non-dimensionalized with respect to theequivalent stress at the Hugoniot elastic limit, σHEL. i.e,

σn ¼ σ=σHEL ð2ÞThe normalized intact and fracture strengths, σn

i and σn

f ,respectively, are given by

σn

i ¼AðPn þ TnÞNð1þ C ln _εnÞ ð3Þ

σn

f ¼ BðPnÞMð1þ C ln _εnÞ ð4Þ

where P is the actual hydrostatic pressure, T is the maximumtensile hydrostatic pressure the material can withstand,Pn ¼ P=PHEL, Tn ¼ T=PHELand PHEL is the hydrostatic pressureat the Hugoniot elastic limit. The non-dimensional effectivestrain rate is defined by _εn ¼ _ε=_ε0, where _ε is the actualeffective strain rate and _ε0 ¼ 1 s�1 the reference strain rate.

The damage parameter D is given by

D¼X

Δεp=εfp ð5Þ

where Δεp is the incremental effective plastic strain andεfp ¼D1ðPn þ TnÞD2 , and D1 and D2 are material constants.

Under dynamic loading, the equation-of-state (EoS) for abrittle material can be defined by the polynomial expression

P¼ K1μþ K2μ2 þ K3μ

3 þ ΔP ð6Þwhere μ¼ ρ=ρ0�1, ρ the current mass density and ρ0 the initialmass density. K1;K2 and K3, are constants and the pressureincrement ΔP is added when damage begins to accumulate (i.e.,D40). Values of material parameters for the 99.5% Al2O3 arelisted in Table 2.

The UHMWPE fiber–reinforced composite and the UHMWPEfiber layers aremodeled as linear elastic orthotropicmaterials withstrength based failure criteria. The values of elastic constants forthe UHMWPE composite, listed in Table 1a and b, are taken fromGrujicic et al. (2009), and those of strengths are best estimates asdescribed below. Grujicic et al. and Ong et al. have modeled theUHMWPE fiber–reinforced composite as an orthotropic elastic–plastic material with the linear elastic response represented byHooke's law and the plastic deformations by Hill's yield surface.They found values of material parameters including those for theequation of state (i.e., a relation between the pressure and thedensity change during plastic deformations) since only deviatoricstresses are given by the flow rule. Because of our neglectingplastic deformations of the laminate and the UHMWPE fibers, wedo not need the equation of state. This assumption considerablysimplifies the analysis and significantly reduces the computationaltime needed to analyze the problem. Without comparing results

Table 1a – Mechanical properties of the UHMWPE laminate.

Elastic modulus (GPa) Shear modulus (GPa) Poisson's ratio (� )

E1 93 G12 4.6 ν12 0.006E2 93 G23 5 ν13 0.06E3 11.5 G13 5 ν23 0.06Tensile strengths (GPa) Compressive strengths (GPa) Shear strengths (MPa)XT 3 XC 2 S12 500YT 3 YC 2 S13 500ZT 3 ZC 2 S23 500

Table 1b – Mechanical properties of the UHMWPE sheets.

Elastic modulus (GPa) Shear modulus (GPa) Poisson's ratio (� )

E1 93 G23 5 ν12 0.006E2 93 G13 5Tensile strengths (GPa) Compressive strengths (GPa) Shear strengths (MPa)XT 3 XC 2 SC 500YT 3 YC 2

Table 2 – Values of material parameters for the 99.5% Al2O3 ceramic (Cronin et al., 2003; Ong et al., 2011).

ρ (g/cm3) G(GPa)

A B C M N T(GPa)

HEL(GPa)

PHEL

(GPa)D1 D2 K1

(GPa)K2

(GPa)K3

(GPa)

3.89 133 0.949 0.5 0.0135 0.6 0.6 0.262 8 1.46 0.02 1 193 212 185

Fig. 7 – Quasi-static compression tests for UHMWPE laminate.


with and without the consideration of plastic deformations, onecannot quantify the error introduced by this assumption whichwill strongly depend upon the failure criteria.

In order to determine the strength of the UHMWPE laminate,uniaxial compression tests along the thickness direction wereconducted. From a typical engineering axial stress vs. the engi-neering axial strain curve exhibited in Fig. 7, the through-thicknesscompressive strength was found to be �650MPa. From results ofthe quasi-static punch–shear tests on the UHMWPE compositelaminate we deduced the shear strength equal to �160MPa.However, a comparison of the numerically computed responseof the UHMWPE laminate using a linear elastic material and the

experimental results for the impact of a series of a 4.8mmdiameter steel sphere on the 11mm thick UHMWPE laminate inthe velocity range of 400–900m/s revealed that Zc¼2 GPa, and theshear strength¼500MPa provided a good agreement between thetwo values of the penetration depth. Since the penetration depthcan depend upon other parameters, these values of the compres-sive and the shear strengths can be considered as good estimatesrather than the actual strength values.

Even though the mechanical response of a ballistic gelatinis rate-dependent, the data for rate dependence available inthe open literature has considerable scatter. A hyperelasticconstitutive relation with tabulated values of data from the

Fig. 8 – For the 10% ballistic gelatin, engineering axial stress-engineering axial strain curves at different strain rates(Cronin et al., 2006; Cronin, 2011).

Fig. 9 – The 7.62 mm bullet geometry and its discretizationinto the FE mesh.

ohnso

n–C

ookrelation

)forth

ebu

llet

com

pon

ents.

G(G

Pa)

T(K

)Tm

(K)

A(M

Pa)

B(M

Pa)

cn

mD1

7729

317

9379

251

00.01

40.28

1.03

27

293

600

1417

.60.03

50.68

51.68

377

293

1793

792

510

0.01

40.28

1.03

2


experimental axial stress – axial strain curves exhibited inFig. 8 was used to model the 10% ballistic gelatin (Du Bois,2003; Hallquist, 2013; Cronin et al., 2006; Cronin, 2011).

In order to verify that the code correctly uses the inputengineering axial stress vs. the engineering axial strain data,we analyzed homogeneous uniaxial deformations of a blockof the gelatin. The numerically computed stress-strain curvesat different strain rates were found to be close to thecorresponding experimental ones, but are not reported here.

The 7.62 mm bullet geometry is exhibited in Fig. 9. TheJohnson–Cook constitutive relation was employed to simu-late thermo-mechanical deformations of the bullet materialswith values of material parameters listed in Table 3. In theJohnson–Cook failure/damage model, only the parameter D1

was assigned a non-zero value implying that a material pointwas assumed to fail when the effective plastic strain thereequaled D1.

Tab

le3–Values

ofm

aterials

(J

ρ(g/cm

3)

Jack

et7.92

Lead

filler

11.34

Stee

lco

re7.83

3.2. Contact conditions at interfaces

The nodes at the boundary of a contact surface between thearmor and the gelatin are constrained to translate togetheralong the impact direction. It will approximately simulate thestrapping of the armor to the gelatin block. The possibledelamination between adjacent plies of the composite lami-nate and of the UWMWPE fiber layers has been simulated byusing the interface strength-based cohesive zone model(CZM) given below. That is delamination ensues at a point


when��σn

��NFLS

0@

1A

2

þ

��σS��

SFLS

0@

1A

2

Z1 ð7Þ

Here σn and σS are the current normal and shear stresses,respectively, and NFLS and SFLS the interlaminar normal andshear strengths. In the CZM, when the relative displacementeither in the normal or in the tangential direction reaches acritical value, CCRIT, complete separation/sliding occurs there.Values assigned to parameters are: NFLS¼SFLS¼60MPa,CCRIT¼0.001mm.

3.3. Failure criteria

A ceramic point is assumed to have failed when the damageparameter, D, defined by Eq. (5) is equals to 1. A material pointof the composite laminate and the UWMWPE fiber layers isassumed to fail along the principal direction 1 if stressesthere satisfy the condition

ðσ11XT

Þ2 þ ðσ12S12

Þ2 þ ðσ13S13

Þ2Z1 ð8Þ

Here σ11, σ12 and σ13 are the axial, the in-plane shear and theout-of-plane shear stresses, and XT, S12 and S13 the correspond-ing strengths (Menna et al., 2011). For failure due to the axialcompressive stress on the material principal plane 1, XT inEq. (8) is replaced by the axial strength, XC , in compression.Once a failure criterion is satisfied in one material principaldirection, material parameters only in that direction aredegraded. The UHMWPE sheets were assumed not to failbecause no failure of fibers was observed during theexperiments.

Based on test data for the 10% ballistic gelatin, Cronin (2011)proposed the failure criterion listed below in which h¼ 0:2corresponds to the initiation of damage in the gelatin, C¼ 5:7 to100% damage of failure of the gelatin, and I1 equals the firstinvariant of either the right or the left Cauchy-Green strain tensor.

D¼012 1þ cos πðf �CÞ

hC

h i

1

ðI1 �3Þr ð1�hÞCð1�hÞCofoC

ðI1�3ÞZC

8><>:

ð9Þ

3.4. Element deletion

A failed element is deleted from the analysis domain result-ing in a void or a crack whose surfaces are taken to betraction free. For an orthotropic material, an element isdeleted only when the failure criteria are met in the thicknessand the in-plane directions.

3.5. Material models used in LSDYNA

The material models, MAT_JOHNSON_COOK, MAT_JOHNSON_HOLMQUIST_CERAMICS, MAT_COMPOSITE_FAILURE_SOLID_MO-DEL, MAT_COMPOSITE_FAILURE_SHELL_MODEL, MAT_SIMPLI-FIED_RUBBER/FOAM_WITH_FAILURE listed, respectively, asmaterials 15, 110, 59, 181 in LS-DYNA were used to simulatethe bullet materials, the ceramic, the UHMWPE laminate, theunidirectional UHMWPE fiber sheets, and the ballistic gelatin.

The tie-break contact module with failure option 6 was adoptedto simulate failure between adjacent plies (Kotzakolios et al.,2011; Hallquist, 2013). The eroding contact algorithm CONTAC-T_ERODING_SURFACE_TO_SURFACE module was used to simu-late the smooth (frictionless) interaction between the bullet andthe armor. The CONTACT_AUTOMATIC_SINGLE_SURFACE wasadopted to simulate smooth contact between adjacent layers ofthe UHMWPE fiber. The non-interpenetration of one materialinto the other across a contact surface was ensured by usingdefault values of parameters in the penalty algorithm of LS-DYNA. Debonding between the ceramic and the UHMWPElaminate was simulated via a tie-break contact algorithm. Wheneither the normal or the shear stress between the ceramic andthe laminate reached 60MPa, the tie contact was releasedimplying that material points on the two sides of the contactsurface independently deformed.

3.6. Numerical results

Assuming that the bullet strikes at the centroid of theimpacted face of the composite structure at normal incidenceand always travels along the line of impact, deformations ofonly one-quarter of the structure and the bullet were ana-lyzed because of the symmetry in the rigid body armor's, softbody's, gelatin's geometries, locations of pressure gages, andinitial and boundary conditions. The element size in theimpacted region is quite small and it increases graduallywith an increase in the distance from the impacted region, e.g., see Fig. 10. After computing results for different FEmeshes, the FE mesh having uniform elements of size0.19 mm�0.19 mm�0.35 mm in the contact region was usedto compute results presented below.

The 11 mm thick UHMWPE FRC laminate consists of morethan 100 unidirectional 01 and 901 alternating plies. If eachply is modeled as a separate layer even with only oneelement through its thickness and the element aspect ratiokept less than 4, the FE mesh will have too many elements tomake the analysis computationally prohibitive. FollowingKrishnan et al.'s (2010) work the laminate was divided into16 layers of the equal thicknesses, and modeled using 8-nodebrick elements. Each one of the 46 layers of the UHMWPEfibers was separately modeled using 4-node shell elements.

The computed cavity profile in the gelatin at differenttimes is exhibited in Fig. 11. The comparison of these resultswith the corresponding experimental cavity shapes depictedin Fig. 4 suggests that the computed cavity depth is smallerbut the cavity diameter is larger than that found experimen-tally. By comparing computed results with the test findingsexhibited in Fig. 5 we conclude that the computed rate ofincrease of the cavity depth is less than the experimentalone. The maximum computed cavity depth, �28 mm, occursat �3.5 ms whereas in tests the maximum cavity depth of�34 mm occurs at�2.5 ms. The computed cavity diameter of100, 120 and 130 mm at 1, 1.5 and 2 ms, respectively, differsfrom the experimental one by 39%, 41% and 37%, respectively.Reasons for these large differences between the two sets ofresults include: (1) material properties of the UHMWPEcomposite are very likely strain rate sensitive and dependupon the curing cycle used but here we have assumed themto be rate independent, (2) either the assumed failure criteria

Fig. 10 – Schematic sketch of the problem studied, and discretization of the ceramic layer and the UHMWPE FRC into finiteelement meshes of 8-node brick elements. The UHMWPE fiber layers and the gelatin are not shown in the figure but areincluded in the analysis of the problem.

Fig. 11 – Evolution of the computed temporary cavity in the ballistic gelatin for 7.62 mm bullet striking armor covered ballisticgelatin at initial velocity of 692 m/s.


or values of parameters in them may be incorrect for thecomposite studied here, (3) the 11 mm thick UHMWPE lami-nate composed of 100 alternating unidirectional 01 and 901plies has been divided into only 16 layers, (4) interfaceconditions between adjacent plies or materials are not simu-lated correctly, (5) the dependence of numerical results uponthe FE mesh used, and (6) neglecting deformations of theadhesive and the cloth. Considering the number of materialparameters and other variables involved, the agreementbetween the computed and the experimental values of thecavity diameter and the cavity depth is reasonable. Never-theless, one can use the computational model to discern therelative importance of different material and geometric vari-ables on the maximum pressure at a point and the depth ofthe temporary cavity that are used as measures of theseverity of the trauma by the United States National Instituteof Justice. In a future work, one should conduct a sensitivity

study similar to that done by Antoine and Batra (2015) for thelow velocity impact of a transparent armor and delineateparameters to which the maximum pressure at a point andthe cavity depth are most sensitive, and then focus on findingmore accurate values of these parameters.

Side views of distributions in the gelatin block of thepressure at different times are displayed in Fig. 12. It isintersting to note that the pressure profile is nearly hemi-spherical at 0.1 and 0.2 ms, and becomes conical at 0.5 ms.The computed peak pressures at points A, B and C (see Fig. 3for locations of these points) equal 163.6, 34.5 and 11.2 MPa,respectively. The peak pressure decreased by a factor of about15 during the passage of the pressure wave from point A onthe front face of the gelatin to point C situated 40 mm awayfrom it.

The time histories exhibited in Fig. 13 of the computed andthe experimentally measured pressure suggest that the two

Fig. 12 – Side view of the computed pressure in the gelatin block.

Fig. 13 – Time histories of the computed and theexperimental pressures at a point in the gelatin situated40 mm away from its front face and on the line coincidingwith the axis of the bullet.


sets of results qualitatively agree with each other. Theexperimentally measured average peak pressure at point Cis �10% more than the computed one (12.2 MPa vs. 11.2 MPa),and their times of occurrence are a little different. However,subsequent to the occurrence of the peak pressure thecomputed results are noisier than the experimental ones. Itsuggests that the strain-rate dependent hyperelastic modelfor the gelatin used in computations does not accuratelyrepresent the material response of the gelatin. Whereasvalues of material parameters are determined using test datafor uniaxial deformations, deformations of the gelatin are 3-dimensional. It has been shown by Varghese and Batra (2009)that for a polycarbonate modeled as a thermo-elasto-visco-plastic material, values of material parameters found usingthe test data for uniaxial deformations do not accuratelyrepresent the response of the PC in simple shearing deforma-tions. The low amplitude long duration pressure pulse due tothe interaction between the armor and the gelatin seen inexperiments is absent in the computations possibly due tonot accurately simulating the interaction between theUHMWPE layers and the gelatin.

Ideally one should compute results with successively ref-ined FE meshes till the computed solution has converged.However, it has not been attempted because of the number ofsubstructures involved. Authors are aware of the fact that thecomputed results depend upon the FE mesh, the contactconditions at the interfaces, the element deletion criteria,initial and boundary conditions, and values of materialparameters. The present work provides reasonably good

values of behind the armor trauma caused by the impact ofa fast moving bullet. The challenge is to relate dimensions ofthe temporary cavity formed in the gelatin to the damagecaused to the human body which requires collaborationbetween engineers and medical doctors.

4. Conclusions

The impact response of a gelatin block protected by armorcomprised of a cermaic plate with ultrahigh molecular weightpolyethylene fiber (UHMWPE) reinforced laminate and alter-nate layers of 01 and 901 UHMWPE fibers has been experi-mentally and numerically studied to provide details of behindthe armor ballistic trauma. Values of material parametersappearing in the constitutive relations and in the failurecriteria for each component have been taken from the openliterature. Results computed using the commercial software,LS-DYNA, are found to be in reasonable agreement with thetest findings. For a 7.62 mm bullet traveling at 692 m/s andimpacting at normal incidence the shielded gelatin block, it isfound that the computed maximum depth and diameter ofthe temporary cavity formed in the armor shielded gelatinequal �28 and �130 mm, respectively. The experimentalvalues of the maximum cavity depth and the diameter equal,respectively, �34 and �105 mm. The computed and theexperimentally measured pressure–time histories qualita-tively agree with each other. The experimentally measuredaverage peak pressure at a point 4 cm away from the gelatinface contacting the armor is �10% more than the computedone. However, the computed time histories exhibit consider-able more noise than the experimental ones, and do not havethe secondary low amplitude long duration pulse seen intests. Nevertheless, the presented computational model canbe used to ascertain the relative importance of variousmaterial and geometric parameters and find values of themaximum pressure in the gelatin that occur at the gelatin/armor interface and may not be easily found experimentallydue to difficulties in placing sensors on the interface.

r e f e r e n c e s

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Analysis of behind the armor ballistic trauma