Blast-wave impact-mitigation capability of polyurea when used as helmet suspension-pad material

Materials and Design 31 (2010) 4050–4065

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Materials and Design

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Blast-wave impact-mitigation capability of polyurea when used as helmetsuspension-pad material

M. Grujicic *, W.C. Bell, B. Pandurangan, T. HeDepartment of Mechanical Engineering, Clemson University, Clemson, SC 29634, United States

a r t i c l e i n f o a b s t r a c t

Article history:Received 16 March 2010Accepted 1 May 2010Available online 7 May 2010

Keywords:Traumatic brain injuryHelmet designPolyureaComputational analysis

0261-3069/$ - see front matter � 2010 Elsevier Ltd. Adoi:10.1016/j.matdes.2010.05.002

* Corresponding author. Address: 241 EngineeringUniversity, Clemson, SC 29634-0921, United States. T864 656 4435.

E-mail address: [email protected] (M

Traumatic brain injury (TBI) is generally considered as a signature injury of the current military conflicts,with costly and life-altering long-term effects. Hence, there is an urgent need to combat this problem byboth gaining a better understanding of the mechanisms responsible for the blast-induced TBI and bydesigning/developing more effective head protection systems. In the present work, the blast-waveimpact-mitigation ability of polyurea when used as a helmet suspension-pad material is investigatedcomputationally. Towards that end, a combined Eulerian/Lagrangian fluid/solid transient non-lineardynamics computational analysis is carried out at two levels of blast peak overpressure: (a) one level cor-responding to the unprotected-lung- injury-threshold; and (b) the other level associated with the corre-sponding 50% lethal dose (LD50), i.e. with a 50% probability for lung-injury induced death. To assess theblast-wave impact-mitigation ability of polyurea, the temporal evolution of the axial stress and the par-ticle (axial) velocity at different locations within the intra-cranial cavity are analyzed. The results arecompared with their counterparts obtained in the case of a conventional foam suspension-pad material.This comparison showed that, the use of polyurea suspension pads is associated with a substantiallygreater reduction in the peak loading experienced by the brain relative to that observed in the case ofthe conventional foam. The observed differences in the blast-wave mitigation capability of the conven-tional foam and polyurea are next rationalized in terms of the differences in their microstructure andin their mechanical response when subjected to blast loading.

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1. Introduction

Traumatic brain injury (TBI) is generally considered as a signa-ture injury of the current military conflicts, with costly and life-altering long-term effects. Among the military service members,TBI is most often related to their exposure to blast and ballisticthreats (e.g. shrapnel, shell fragments, bullets, etc.). Essentially,as advanced body armor and head protection gear have greatly re-duced soldier fatalities from explosion and ballistic attacks, theproblem of TBI in the attack survivors has become more severe[1–3]. In particular, the problem of blast-induced TBI has becomevery critical since no external/internal physical injuries are typi-cally detected in the affected soldiers. Hence, to combat this prob-lem there is an urgent need to gain a better understanding of themechanisms responsible for the blast-induced TBI through theuse of various head protection systems and similar strategies.

A review of the literature carried out as part of the present workrevealed that there is a clear lack of understanding of blast-induced

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. Grujicic).

TBI [4,5]. Among the potential causes of the blast-induced TBI, theones most often cited include blast-pressure mechanical loads,head accelerations followed by impact, as well as exposure to elec-tromagnetic and thermal radiation [6]. Due to the fact that blastcan often propel the soldier and result in a head impact, earlyblast-induced TBI mitigation efforts were mainly focused on reduc-ing the acceleration of the head. However, shock tube experimentsinvolving restrained animal subjects confirmed that TBI may occureven in the cases when head impacts were absent [7]. Among themain mechanisms which may lead to blast-induced TBI are: (a) (0mode) bulk acceleration of the head [6]; (b) shock-wave ingressinto the intra-cranial cavity through skull orifices; (c) blast-in-duced compression of the thorax which causes a vascular surgeinto the brain [7]; and (d) blast-induced skull flexure can give riseto mechanical loads acting on the brain which (even at low blastpressures) may become comparable to those encountered ininjury-inducing impact situations.

Historically, the main head protection gear has been the helmet.Over the years, the design of military helmets has continuouslyevolved in order to respond to ever-increasing lethality anddiversity of threats, to take advantage of the new materials andfabrication/manufacturing technologies, and to meet continuouslygrowing demands for lower weight and improved comfort [8].

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For the most part, the so-called Advanced Combat Helmet(ACH) is the head protection gear currently being used by the USmilitary [8]. An ACH helmet (Fig. 1) consists of a 7.8 mm-thick out-er composite shell based on lower content phenolic resin rein-forced with higher-strength Kevlar 129 fibers, a modified edgecut for lower protection surface and a ‘‘suspension system” (a setof discrete foam pads strategically placed on the interior surfaceof the helmet and held in place by Velcro-based hook-and-loopfasteners).

In the present work, we focus on the ability of the ACH helmetdesign to provide the needed level of protection against TBIinducing blast loads. To protect their intellectual property andmaintain an advantage over their competitors the helmet manu-facturers have not revealed much detail regarding the materialselection, fabrication methods and designs of the suspensionpads. What is known for sure is that they are made of an elasto-meric foam-like material e.g. Vinyl Nitrile, their geometricaldimensions and their locations in the helmet. In the present work,the feasibility of utilizing polyurea (a thermoplastically-linkedelastomer) as a suspension-pad material will be investigated. Inrecent years, there have been various reports regarding the abilityof this material to disperse shock waves propagating through

Fig. 1. The Advanced Combat Helmet (ACH): (a) external side view, (b) su

and/or to efficiently dissipate the energy associated with suchwaves (e.g., [9–11]).

Polyureas are a class of elastomeric co-polymers which arephase-separated into nanometer size hard domains and a lowglass-transition temperature soft matrix. Hard domains act bothas inter-chain links and as nanometer-size reinforcements makingpolyurea a nano-scale composite material with a unique set ofmechanical properties.

Polyureas have been used commercially for more than a decade.The most common applications of polyureas include:

(a) Tough, abrasion-resistant, corrosion-resistant, durable andimpact-resistant (epoxy/rubber replacement) spray-on coat-ings/liners in various construction/structural applicationssuch as tunnels, etc.

(b) External and internal wall-sidings and foundation coatingsfor buildings aimed at minimizing the degree of structurefragmentation and, in turn, minimizing the extent of theassociated collateral damage in the case of a bomb blast.

(c) Gun-fire/ballistic resistant and explosion/blast mitigatingcoatings/liners or inter-layers in blast-resistant sandwichpanels for military vehicles and structures.

spension system side view and (c) suspension system bottom view.

4052 M. Grujicic et al. / Materials and Design 31 (2010) 4050–4065

The applications mentioned above capitalize on the exceptionalability of polyureas to alter/disperse shock waves and to absorb thekinetic energy associated with these waves [12] under high-rateloads [13]. This energy absorbing capacity of polyureas is oftenlinked to their ability to undergo a stress-/strain-induced phasetransition during which the rubbery state of the material is con-verted to the glassy state [11].

The main objective of the present work is to assess the ability ofpolyureas, when used as helmet suspension pads, to mitigate theeffects of blast loading and, in turn, to reduce the possibility forTBI. Traditionally, the development of advanced blast and ballisticprotection systems is carried out almost entirely using legacyknowledge and extensive fabrication/testing time-consuming/costly trial-and-error approaches. In recent years, this approachhas been increasingly being complemented by the appropriatecost- and time-efficient computer-aided engineering analyses. Thistrend has been accelerated by the recent developments in thenumerical modeling of transient non-linear dynamics phenomenasuch as those accompanying blast and ballistic loading conditions.In particular, recent advances have enabled the coupling betweenEulerian solvers (used to model gaseous detonation products andair) and Lagrangian solvers (used to represent solid componentsof the protection systems, as well as of the projectiles [14]). Inthe present manuscript, the coupled Eulerian–Lagrangian compu-tational procedure used in our prior work [14] to analyze theoccurrence of blast-induced TBI in the case of an unprotected hu-man head is extended to the case of the head protected by a helmetcontaining polyurea suspension pads.

2. Modeling and computational procedure

2.1. Transient non-linear dynamics analyses of blast-wave/solid-structure interaction

A typical transient non-linear dynamics problem such as theinteractions between an air-borne blast-wave with a human-headprotected by a helmet involves solving simultaneously thegoverning partial differential equations for the conservation ofmomentum, mass and energy along with the material constitutiveequations and the equations defining the initial and the boundaryconditions. The aforementioned equations are typically cast withina coupled Eulerian/Lagrangian formulation and solved numericallyusing a second-order accurate explicit scheme, i.e., due to the largemotions and deformations experienced by air, it is computationallyefficient to analyze the air-region using an Euler control-volumecomputational scheme (the computational grid is fixed in spaceand time while the material(s) move through it). On the otherhand, the helmet/head assembly which undergoes considerablyless motion and deformation is analyzed using a Lagrange scheme(the computational grid is tied to the material and moves and de-forms with it).

All the calculations carried out in this work were done usingABAQUS/Explicit, a general-purpose transient non-linear dynamicsanalysis software [15]. In our previous work [16], a detailed ac-count was provided of the basic features of ABAQUS/Explicit,emphasizing the ones which are most relevant for modeling theproblems involving blast-wave/solid-structure interactions. There-fore, only a very brief overview of this topic will be provided in theremainder of this section.

The interactions (including self-interactions) or bonding be-tween different components of the model are analyzed using theappropriate Lagrange-Lagrange and Euler–Lagrange contact/slidingand kinematic coupling options. For example, Lagrange–Lagrangeinteractions are analyzed in ABAQUS/Explicit using a ‘‘penalty”contact method within which the penetration of the surfaces into

each other is resisted by linear spring forces/contact-pressureswith values proportional to the depth of penetration. These forces,hence, tend to pull the surfaces into an equilibrium position withno penetration. Contact pressures between two Lagrangian bodiesare not transmitted unless the nodes on the ‘‘slave surface” of onebody contact the ‘‘master surface” of the other body. There is nolimit to the magnitude of the contact pressure that could be trans-mitted when the surfaces are in contact. Transmission of shearstresses across the contact interfaces is defined in terms of a staticand a kinematic friction coefficient and an upper-bound shearstress limit (a maximum value of shear stress which can be trans-mitted before the contacting surfaces begin to slide).

Interactions between an Eulerian region (such as the one con-taining air and a propagating blast wave) and a Lagrangian region(such as the one containing the helmet/head assembly) are treatedas a fluid/solid interaction problem. In these type of problems, theouter surfaces of the solid structures define some of the boundariesfor the Eulerian region (i.e. the Lagrangian region resides fully orpartially within the Eulerian region and provides no-flow boundaryconditions to the fluid in the direction normal to its surface) whilethe Eulerian region provides pressure-loading boundary conditionsto the Lagrangian region.

2.2. Geometrical and meshed models

The present investigation is a part of a larger research effort inwhich various means for blast mitigation are studied. Within thisresearch effort, work is underway to analyze the interactions be-tween a planar blast wave and the whole human head coveredwith the helmet. Examples of the brain, skull and helmet geomet-rical/meshed models are displayed in Fig. 2. The results of this ef-fort will be presented in one of our future communications. In thepresent work with the main objective of assessing the potential ofpolyurea as the helmet suspension-pad material in mitigating blastloading effects, a substantially simpler geometrical/meshed modelis analyzed, Fig. 3. The model used in the present work is represen-tative of an ACH ‘‘core-sample” consisting of a column of single ele-ments running in the direction normal to the helmet outer surface.The column, Fig. 3, is comprised of six segments each associatedwith a different component of the air/helmet/head assembly. Start-ing from air adjacent to the outer surface of the helmet moving in-ward, the six segments are arranged in the following order: (a) air;(b) Kevlar/Phenolic-resin composite helmet shell (7.8 mm); (c)polyurea suspension pad (14 mm); (d) the skull (6.5 mm); (e) theCerebro-spinal fluid (CSF) (2 mm) and (f) the Cerebrum (75 mm).Segment thicknesses (given within the parenthesis above) are cho-sen in such a way that they are consistent with the ACH helmet de-sign or the average thicknesses of the skull, the Cerebro-spinalfluid and the Cerebrum. Also, 1 mm initial gaps were assigned atthe composite-shell/suspension-pad and the suspension-pad/skullinterfaces in order to account for the fact that these interfaces areneither adhesively bonded nor in complete contact.

Due to the presence of both fluid (air) and solid (Kevlar/Pheno-lic-resin composite, polyurea, the skull, the Cerebro-spinal fluidand the Cerebrum) materials, the computational domain used con-tains both an Eulerian sub-domain (filled with air) and a Lagrang-ian sub-domain (filled with the solid materials).

2.2.1. Eulerian sub-domainThis sub-domain consists of a column of single non-distorting

right-angled hexahedron Eulerian elements/cells filled with air.Typically, the edge length was set to 1.0 mm. While the Eulerianmesh used is non-deformable, an adaptive meshing algorithmwas employed in order to capture the hydrodynamic fields in theregions adjacent to the blast-wave front with higher resolution.

SSkkuullll

CCeerreebbeelllluumm

PPiittuuiittaarryyGGllaanndd

CCeerreebbrroossppiinnaallFFlluuiidd

BBrraaiinnSStteemm

CCeerreebbrruumm

SSaaggiittttaallSSeeccttiioonn

((aa))

((bb)) ((cc)) SSkkuullll AACCHH HHeellmmeett

Fig. 2. (a) Sagittal section of the human head model and finite-element meshes of the skull and various brain sections used in our ongoing work; (b) and (c) the finite-elementmeshes for the skull and ACH Helmet.


This algorithm effectively attaches the mesh to the advancing blastwave.

2.2.2. Lagrangian sub-domainAs mentioned earlier, this sub-domain consists of five discrete

segments each filled with a different material. To account for thefact that some of the elements in the helmet/head assembly arenot mutually bonded (e.g., the suspension pads are typically onlyattached with Velcro to the helmet shell), different segments aremeshed independently and the adjacent segments are allowed toeither establish a contact or to be mutually bound (e.g., the Cere-bro-spinal fluid and the Cerebrum are assumed to be perfectlybonded). Each of the five segments is meshed using identicalright-angled hexahedral solid elements with a typical edge lengthof 0.01 mm. This mesh size was found to be a good compromise be-tween accuracy and computational efficiency. The use of finermeshes was found to produce somewhat different numerical val-ues of the stress/strain quantities of interest. However, they didnot alter the nature of the basic findings obtained in the presentwork.

As mentioned earlier, there are six different materials residingin the computational domain analyzed in the present work. A briefdescription of the constitutive models used to represent the behav-

ior of these materials under blast-loading conditions as well as themodel parameter identification are presented in the next section.

2.3. Material models

The complete definition of a transient non-linear dynamicsproblem, (such as the interactions of blast waves with the helmet)entails the knowledge of the material models that define the rela-tionships between the flow variables (pressure, mass-density, en-ergy-density, temperature, etc.). These relations typically involvean equation of state, a strength model, and a failure model for eachconstituent material. These equations arise from the fact that, ingeneral, the total stress tensor can be decomposed into a sum ofa hydrostatic stress (pressure) tensor (which causes a change inthe volume/density of the material) and a deviatoric stress tensor(which is responsible for the shape change of the material). Anequation of state is then used to define the correspondingfunctional relationship between pressure, mass-density, and inter-nal-energy density/temperature, while a strength model is used todefine the appropriate relations between the deviatoric part of thestress tensor and various quantities characterizing the extent andrate of material deformation as well as the effect of material tem-perature. In addition, a material model generally includes a failure

Air

Kevlar/Phenolic Resin

Polyurea

Skull

Cerebro-spinal Fluid

Cerebrum

Fig. 3. Geometrical/meshed models used in the present work to analyze the interactions of an air-borne blast wave with the helmet/head assembly.


model, i.e. an equation describing the (hydrostatic or deviatoric)stress and/or strain condition(s) which, when attained, causes thematerial to fracture and lose its ability to support tensile normaland shear stresses. Due to the fact that blast levels considered inthe present work typically do not cause any detectable damageto the helmet, skull or the inter-cranial brain matter and due tothe fluid nature of air, failure of the materials encountered in thepresent problem was not considered. Likewise, since blast loadingscenarios considered in the present work are not generally accom-panied with significant thermal radiation or heat generation viaenergy dissipation, the effect of temperature on the materialbehavior was not considered.

As mentioned earlier, the present work investigates interactionsbetween an air-borne blast wave and (a core sample of) the hel-met/head assembly. Since these interactions typically result inthe formation of shock waves within the helmet/head assembly,special attention was paid to the ability of the material modelsused in the present work to enable formation of the shock waves.Specifically, as discussed in our prior work [14], formation of shockwaves demands that the associated pressure vs. specific volume(reciprocal of the density) relationship be non-linear and concaveupward (i.e., pressure increases at a higher and higher rate as thespecific volume decreases).

2.3.1. Air material modelAs mentioned earlier, the Eulerian domain was filled with air.

Air was modeled as an ideal gas and, consequently, its equationof state was defined by the ideal-gas gamma-law relation as [17]:

P ¼ ðc� 1Þ qq0

E ð1Þ

where P is the pressure, c the constant-pressure to constant-volumespecific heat ratio (=1.4 for a diatomic gas like air), q0 (=1.225 kg/m3) is the initial air mass density, and q is the current mass density.For Eq. (1) to yield the standard atmospheric pressure of 101.3 kPa,

the (initial) internal volumetric energy density E was set to 261.2 kJ/m3 which corresponds to the air mass specific heat of 717.6 J/kg Kand a reference temperature of 298 K. Since according to Eq. (1), Pscales linearly with q (i.e., with the reciprocal of the specific vol-ume), the present model enables shock formation.

Since air is a gaseous material, it has no ability to support shearstresses and no strength model was defined for this material.

2.3.2. Kevlar/Phenolic-resin composite material modelFollowing the work presented in Ref. [18], Kevlar/Phenolic-resin

composite material has been modeled using an orthotropic equa-tion of state and an orthotropic linear-elastic strength model.Within the orthotropic equation of state, pressure is defined as:

P ¼ �K1evol þ K2e2vol �

13ðC11 þ C21 þ C31Þed

11 �13ðC12 þ C22

þ C32Þed22 �

13ðC13 þ C23 þ C33Þed

33 ð2Þ

where K1 ¼ 19 ðC11 þ C22 þ C33 þ 2ðC12 þ C23 þ C31ÞÞ is the effective

bulk modulus, evol is the volumetric strain, K2, a non-linear correc-tion to the P vs. evol (=density) and the last three terms on the righthand side of Eq. (2) represent the contributions of the deviatoricstrains, ed

ij, to the pressure. It should be noted that these contribu-tions are absent in the case of an isotropic linear elastic material.It should be also noted that the presence of the K2e2

vol term in Eq.(2) introduces the material volumetric non-linearity which is re-quired for the formation of shock waves. As far as the strength mod-el is concerned, it is simply defined by a generalized Hooke’s lawwhich uses the elastic stiffness matrix to map the deviatoric straincomponents to the corresponding deviatoric stress components.The components of the elastic stiffness matrix, Cij, appearing inEq. (2) and in the equation for K1, are defined in terms of the corre-sponding engineering constants Eii, Gij and mij (i, j = 1, 2, 3) usingstandard relations. In Table 1, a summary is provided of the Kev-lar/Phenolic-resin composite material model parameters.

Table 1Equation of state and strength model parameters for the Kevlar/Phenolic-resincomposite shell.

Parameter Symbol Unit Value

Young’s modulus 11 E11 Pa 1.799e10Young’s modulus 22 E22 Pa 1.799e10Young’s modulus 33 E33 Pa 1.948e9Poisson’s ratio 12 m12 N/A 0.080Poisson’s ratio 23 m23 N/A 0.698Poisson’s ratio 31 m31 N/A 0.075Shear modulus 12 G12 Pa 1.860e9Shear modulus 23 G23 Pa 2.235e8Shear modulus 31 G31 Pa 2.235e8Bulk modulus K1 Pa 5.18e9Quadratic correction K2 Pa 5.0e10

Table 2Equation of state and strength model parameters for polyurea.


Reference Temperature Tref K 273Time shift parameter A – �10Time shift parameter B K 107.54Pressure shift coeff. CTP K/Pa 7.2e�9Constant-volume specific heat CV (MJm�3K�1) 1.97Bulk modulus slope m Pa/K �1.5e7Number of Prony series terms n – 4Reference bulk modulus Kref GPa 4.95Long-term shear modulus G1 MPa 22.4Prony series coeff. p1 – 0.8458Prony series coeff. p2 – 1.686Prony series coeff. p3 – 3.594Prony series coeff. p4 – 4.342Relaxation time q1 s 0.463Relaxation time q2 s 6.41e�5Relaxation time q3 s 1.16e�7Relaxation time q4 s 7.32e�10

Table 3Equation of state and strength model parameters for the skull material.


Density q kg/m3 1412Young’s modulus E GPa 6.50Poisson’s ratio m – 0.22Sound speed C0 m/s 1850Shock speed vs. particle-velocity slope s – 0.94


2.3.3. Polyurea material modelThe mechanical response of polyurea under blast-loading con-

ditions is represented using the material model reported in Ref.[19]. Within this model, the hydrostatic response of the materialis considered to be elastic while the deviatoric response of thematerial is assumed to be time-dependent and hence treated usinga geometrically-non-linear visco-elastic formulation.

Within the hydrostatic part of the model, pressure is defined as:

P ¼ �KðTÞ lnðJÞJ

; KðTÞ ¼ KðTref Þ þmðT � Tref Þ ð3Þ

where subscript ref is used to denote a quantity at the referencetemperature, K is the bulk modulus, T is the temperature, m amaterial parameter and J (=det(F)) with F being a quantity whichmaps the original/reference material configuration into the cur-rent/deformed material configuration. Since ln (J) represents thevolumetric strain, the effective bulk modulus KðTÞ

J increases withan increase in volumetric compression thus enabling formationof shock waves.

To account for the aforementioned time-dependent character ofthe deviatoric material response, evaluation of the deviatoricstress, r0, at the current time t has to take into consideration theentire deformation history of a given material point from the onsetof loading at t = 0 to the current time. Based on the procedure out-lined in Ref. [19], r0 is defined as:

r0ðtÞ ¼ 2G1T

Tref

Z t

01þ

Xn

i¼1

pi exp�ðnðtÞ � nðsÞÞ

qi

� �D0ðsÞ

!ds ð4Þ

where G1 is the ‘long-term’ shear modulus (i.e., the value of theshear modulus after infinitely long relaxation time), n is the numberof terms in the Prony series exponential-type relaxation function, pi

and qi are respectively the strength and the relaxation time of eachProny series term, n is the so-called reduced time and D0 is the devi-atoric part of the rate of deformation tensor, D ðD0ij = Dij � 1/3 � Diidij,i, j = 1, 2, 3, dij is the Kronecker delta second order tensor and sum-mation is implied over the repeated indices). The reduced time con-cept is used to take into account the effect of temperature andpressure on the relaxation kinetics and is defined as:

nðtÞ ¼Z t

0

dt

10AðT�CTP P�Tref Þ=ðBþT�CTP P�Tref Þð5Þ

where A, B and CTP are material constants. Thus, the effect of tem-perature, T, and pressure, P, over a time period t on the material re-sponse is assumed to be identical to the material response at thereference temperature and pressure over a time period n(t). The rateof deformation tensor, D, is related to the deformation gradient, F,as:

D ¼ symð _FF�1Þ ð6Þ

where ‘sym’, the raised dot and superscript ‘�1’, are used to denoterespectively the symmetric part, the time derivative, and the in-verse of a second order tensor.

A summary of all material model parameters for polyurea isprovided in Table 2.

2.3.4. Skull-material modelSkull is composed of bone material which is characterized by

relatively high levels of hydrostatic and deviatoric rigidity/stiff-ness. The hydrostatic part of the skull-material model is repre-sented using the Mie–Gruneisen equation of state of the form:

P ¼q0C2

0ð1�q0q Þ

½1� sð1� q0q Þ�

2 ð7Þ

where q0 is the initial/reference density and coefficient C0 (thesound speed) and s relates the shock speed Us and the resulting par-ticle velocity, Up, as:

Us ¼ C0 þ s � UP ð8Þ

Eq. (7) also referred to as a shock-Hugoniot equation of state, isoften used to introduce material volumetric non-linearities and,thus, to promote the formation of shocks in solid materials. Thevalues for the equation of state parameters q0, C0, and s for theskull material are listed in Table 3 [20].

Due to the high shear rigidity of skull material and resultingsmall shear strains, the deviatoric response of this material is de-fined as linear elastic. Consequently, this response is quantifiedby a single material parameter, the shear modulus l defined interms of the corresponding Young’s modulus E and the Poisson’sratio m, as l = E/[2(1 + m)]. The E andm values for the skull materialare listed in Table 3.

2.3.5. Cerebro-spinal fluid and cerebrum material modelsIt is well-recognized that due to the interplay between a num-

ber of phenomena such as non-linear visco-elasticity, anisotropy,


extreme rate dependency/sensitivity, etc., the behavior of brain-tissue materials like the ones constituting the Cerebro-spinal fluidand Cerebrum is highly complex. In addition, the consistency andconstituent response of soft biological tissues is generally associ-ated with considerable variability. Consequently, and followingthe analyses carried out in our prior work [14], simpler materialmodels which rely on relatively few parameters that can be deter-mined with a greater statistical confidence were selected for use inthe present work. Specifically, the materials constituting the Cere-bro-spinal fluid and Cerebrum are assumed to be isotropic (direc-tion-invariant) and homogeneous (spatially uniform) and tobehave as elastic (time-invariant, materially-non-linear) materialswith respect to their hydrostatic/volumetric response and as visco-elastic or visco-hyper-elastic (time-dependent, geometrically/materially-non-linear) with respect to their deviatoric/shearresponse.

In accordance with these observations/assumptions, the hydro-static portion of the soft-tissue material model is defined using aninitial value of the bulk modulus and one or more parametersdefining the type and extent of non-linearity between the pressure,density, and internal energy.

Specifically, following Moore et al. [21], the non-linear hydro-static/volumetric (pressure, P, vs. density, q) elastic response ofbrain-tissue materials is modeled using a Tait-type equation ofstate of the form:

P ¼ Bqq0

� �C0þ1

� 1

" #ð9Þ

where B and C0 are material-specific parameters. The Tait equationof state is commonly used to model the behavior of fluids underhigh pressures (including the formation of shocks) and, due tochemical similarity between brain tissue and water and the atten-dant blast-induced high pressures, was deemed an appropriatechoice. Due to aforementioned similarity between water and thebrain tissue, C0 was set to its value of 6.15 in water while B wasdetermined from the condition:

K ¼ B � ðC0 þ 1Þ ð10Þ

where K is the (initial) bulk modulus. A summary of the Tait equa-tion of state parameters q0, B, and C0 for the Cerebro-spinal fluidand Cerebrum materials is displayed in Table 4.

As far as the deviatoric/strength part of the material model isconcerned, it was initially considered to be visco-elastic and to in-clude a time-dependent shear modulus (diminishing from an ini-tial larger value to a smaller long-term value) and one or moreparameters accounting for the type and extent of geometrical/material non-linearities. It was soon recognized that the shear-modulus relaxation times for the two intra-cranial materials inquestion are on the order of tens or hundreds of millisecondsand are, thus, several orders of magnitude longer than the charac-teristic blast-wave/human-head interaction times. Under theseconditions, it was deemed justified to assume that time-dependentshear-deformation effects play a secondary role in the response ofthe Cerebro-spinal fluid and Cerebrum materials to the blast.Therefore, the deviatoric portion of the material response was as-sumed as time-invariant. However, a provision had to be made

Table 4Equation of state and strength model parameters for the CSF and cerebrum materials.

Structure Density, q(kg/m3)

Bulk modulus,K (GPa)

Tait EOSparameters

Shear modulus,l (kpa)

BMPa C0

Cerebrum 1040 2.19 306.3 6.15 22.53CSF 1040 2.19 306.3 6.15 22.00

for the potential effect of large-deformation induced geometricaland material non-linearities and, consequently, the deviatoric por-tion of the material model was defined using a hyper-elastic for-mulation. Following the analysis carried out in our prior work, aNeo-Hookean hyper-elastic model was selected which definesthe deviatoric stress as:

r0 ¼ J�1F l � logffiffiffiCp� �dev

� �FT ð11Þ

where F and J were defined previously, l is the shear modulus andC = FTF (is the right Cauchy-Green deformation tensor, and super-script T is used to denote a transpose). For simplicity,

ffiffiffiCp

term is re-placed with its first-order and second-order linearized forms [22]. Asummary of the Neo-Hookean hyper-elastic model parameters isprovided in Table 4.

2.3.6. Ethylene-Vinyl-Acetate foam material modelAs mentioned earlier, the main objective of the present work is

to assess the blast-wave impact-mitigation potential of polyureawhen used as suspension-pad material and compare it to the samepotential of the currently used suspension-pad material. Unfortu-nately, the nature of the suspension-pad foam material currentlyused in the ACH helmet has not been reported in the public do-main. What is known for sure is that the material is an elastomericfoam. Hence, it was decided to choose an elastomeric foam whichis widely used in energy-absorbing and impact-mitigating applica-tions. Considering the fact that Ethylene-Vinyl-Acetate (EVA) is anelastomeric foam which is very widely used in these applications,this material was selected as the helmet suspension-pad referencematerial.

In accordance with the analysis presented in Ref. [23], EVA foammaterial was modeled as a hyper-elastic highly-compressible non-linear material whose behavior is described by the following strainenergy function:

U ¼XN

i¼1

2li

a2i

kai1 þ kai

2 þ kai3 � 3þ 1

biðJelÞ�aibi � 1� ��

ð12Þ

where N represents the number of terms in the summation, li, ai,and bi are material-dependent parameters, ki (i = 1, 2, 3) are theprincipal stretches (i.e., Eigen values of the deformation gradient,F) while Jel = det(F). In the EVA model used in Ref. [23], N was setto 2.0. A summary of the EVA hyperfoam model parameters is givenin Table 5. The expressions for the stress components can be ob-tained using the standard procedure which involves differentiationof the strain energy function defined by Eq. (12) with respect to thecomponents of the Green Lagrange strain, E = 0.5 � (C–I), where C isthe right Cauchy-Green deformation tensor while I is the second or-der identity tensor. The resulting second Piola-kirkhhof stress isnext converted into the (true) Cauchy stress using standard rela-tions. This procedure showed that the material model at hand intro-duces the type of material volumetric non-linearity which isrequired for the formation of shocks.

Table 5Linear visco-elastic model parameters for ethylene–vinyl-acetate (EVA).


Shear modulus l1 MPa 8.874Shear modulus l2 MPa �7.827Exponent a1 – 2.028Exponent a2 – 1.345Exponent b1 – 0.32Exponent b2 – 0.32


2.4. Problem formulation

As mentioned earlier the problem analyzed in the present workdeals with the interaction of an air-borne blast-wave with thehelmet/head assembly. The computational domain contains anair-filled Eulerian sub-domain, Fig. 3. The initial pressure in thissub-domain is set to the atmospheric level and no-flow boundaryconditions are applied to the four lateral faces of the sub-domain.On the front face of this sub-domain, a time-dependent pressureimpulse (see discussion below) is prescribed. As a result, a blast-wave enters this sub-domain and propagates towards the air/helmet contact surface. Upon reflection of the blast-wave from thiscontact surface, the reflected wave propagates in the oppositedirection and ultimately exits the Eulerian sub-domain.

The five Lagrangian segments are all assumed to be initially sta-tionary and stress-free. Since the Lagrangian sub-domain used rep-resents a square-base core sample (cut-out) through the helmet/head assembly in a direction normal to the helmet outer surface,zero displacement/velocity boundary conditions are applied alongall the four lateral faces of this domain. The back face of the Cere-bro-spinal fluid and the front face of the Cerebrum are kinemati-cally coupled using a ‘tie’ option. The adjacent faces of the otherLagrangian segments on the other hand are allowed to interactvia the previously discussed penalty-contact algorithm. The backface of the cerebrum was either fixed in the column-axis directionor set free. The choice of the last boundary condition was found notto affect the main conclusions resulting from the present work.

As mentioned earlier, loading conditions used in the presentstudy are associated with an impact of a propagating air-borneblast-wave with a solid structure.

Following Moore et al. [21], two air-blast wave cases were con-sidered: (a) the case associated with a peak overpressure of 5.2 atmcorresponds to a blast-induced lung-injury threshold and is equiv-alent to a free-air explosion of 0.0698 kg of TNT at a standoff dis-tance of 0.6 m; and (b) an air-blast wave characterized by an18.6 atm peak overpressure which corresponds to the 50% lethaldose (LD50) for lung-injury related death and is equivalent to afree-air explosion of 0.324 kg of TNT at a standoff distance of0.6 m. Since finite-element analyses involving air-blast loadingare not that common, a brief summary of this type of loading isprovided in next section.

2.5. Blast-wave loading

Detonation of an explosive charge in air results in the formationof rapidly expanding gaseous reaction products which compressthe surrounding air and move it outward with a high velocity thatinitially approaches the detonation velocity of the explosive (ca.7200 m/s). The rapidly expanding detonation products create ashock wave, i.e. a wave which is associated with discontinuitiesin the hydrodynamic quantities (pressure, density, temperatureand velocity) [24]. The relationship between air states upstreamand downstream relative to the shock wave are defined by themass, momentum and energy conservation equations (the so-called jump equations) [24]. The shock wave traveling throughthe air is composed of highly compressed air particles which arecapable of exerting high pressure to any surface they impingeupon. A shock wave is associated with a discontinuous change inthe shock-front pressure from the ambient pressure Pa (ahead ofthe shock-wave front) to Ps (behind it). The (Ps � Pa) pressure‘‘jump” is commonly referred to as the ‘‘blast overpressure”.

A fixed location in space first experiences blast overpressure asthe shock-wave front passes over it. Then, the pressure decaysexponentially with time as the shock-wave front moves away. Thisis followed by a negative-pressure (suction) phase. Typically, dura-tion of a shock-wave pressure pulse at a fixed point is quite short

with the characteristic time being on the order of a few tens orhundreds of microseconds. The free-air pressure vs. time relationat a fixed point is typically described using the Friendlander equa-tion of the form:

PðtÞ ¼ ðPs � PaÞ 1� t � ta

td

� �e�ðt�taÞ=h þ Pa ð13Þ

where ta is arrival time, td duration of the positive phase and h atime-decay constant [25]. A schematic of the air-borne blast-waveas described by the Friendlander equation is shown in Fig. 4.

The load intensity of air-blast on a target surface depends on thetype and mass of the explosive and the standoff distance, r, be-tween the explosive charge and the target surface. The free-airpeak pressure, P, of the blast wave for a given explosive-chargemass, m, and a standoff distance, r, is generally defined as:

P ¼ Kemr3

h ið14Þ

where Ke is an explosive-material dependent coefficient [26].When the air-borne shock wave strikes a target surface, it is re-

flected (i.e., the air molecules are forced to move in the oppositedirection) and due to conservation of the linear momentum, theoverpressure within the (compressive) shock-wave generatedwithin the solid structure is amplified relative to that of the inci-dent blast-wave. The magnification, which can be highly non-lin-ear, depends on the strength of the incident blast wave and theangle of incidence. For weak shock waves, the aforementionedreflection typically results in doubled shock-wave intensity. Forstrong shock waves, on the other hand, reflection-based shockintensity amplifying coefficients of 8 have been reported for thecase of ideal gas and as high as 20 for the case of real gases inwhich the effects of air-molecule dissociation and ionization areconsidered [24].

In addition to the peak pressure, specific impulse is anotherquantity which characterizes the extent of shock loading experi-enced by the target structure. The specific impulse loading, I, expe-rienced by the target structure can be calculated as the timeintegral of the shock-induced pressure during the positive phase:

I ¼Z taþtd

ta

Pampdt ð15Þ

where Pamp is the incident pressure multiplied by the wave-reflec-tion pressure-amplification coefficient.

The pressure vs. time relations associated with free-air detona-tion of 0.0698 kg and 0.324 kg were obtained using ConWep, ablast simulation code developed by the US Army Corps of Engi-neers [25].

3. Results and discussion

In this section, the main results obtained in the present workare presented and discussed. Since the present work involvedblast-impact simulations at two different peak pressures, the re-sults obtained for these two pressure levels are first presentedand discussed. This is followed by an additional analysis and dis-cussion aimed at explaining the observed differences in theblast-mitigation potential of the two suspension-pad materials(i.e., EVA and polyurea).

3.1. 5.2 atm peak-pressure blast impact

The temporal evolution of axial stress at the centroids of threebrain elements located respectively at distances of 2 mm,39.5 mm and 77 mm from the skull/CSF interface for the cases ofEVA and polyurea suspension pads are displayed respectively in

Time, ms

Pres

sure

,atm

0 0.5 1 1.5 2 2.5 3

1

2

3

4

5

6

ta+tdta

Ps

Pa

+

-

Peak Pressure

Time of Arrival

Positive Phase

NegativePhase

Fig. 4. A typical free-air pressure vs. time relation at a fixed point as defined by the biphasic Friendlander equation.


Fig. 5a and b. The corresponding results but for the particle velocityare displayed respectively in Fig. 6a and b.

A brief examination of the results displayed in Figs. 5a and band 6a and b reveals that:

(a) Both peak axial stresses and peak axial velocities take onslightly (10–15%) higher values in the case of EVA than inthe case of polyurea suspension pads, i.e. the maximum com-pressive axial stress in the EVA case is around�19 MPa whileits polyurea counterpart is around �17 MPa. Likewise, themaximum particle (axial) velocity in the EVA case is around13 m/s while the corresponding velocity in the polyurea caseis around 11 m/s.

(b) Somewhat more pronounced (15–30%) differences betweenthe two suspension-pad cases are observed in the corre-sponding upstream axial-stress/particle velocity states awayfrom the shock-wave front;

(c) A major difference is observed in the shock-wave arrivaltime into the brain portion of the model in the cases ofEVA and polyurea suspension-pad materials. That is, theshock-wave enters the ‘‘intra-cranial cavity” at a post-blasttime of ca. 210 ls in the EVA case. The same event is associ-ated with a significantly shorter arrival time of ca. 22 ls inthe case of polyurea; and

(d) In the case of EVA, as seen in Fig. 5a, the brain is loaded inthree distinct stages: (i) with a relatively weak shock associ-ated with an axial stress-level of ca. �1 MPa; (ii) with a rel-atively strong second shock associated with �5 MPa axialstress which enters the intra-cranial cavity at ca. 210 ls;and (iii) with an even stronger shock associated with�19 MPa axial stress and entering the intra-cranial cavityat ca. 285 ls. In sharp contrast, in the polyurea case, onlyone sustained shock-wave enters the intra-cranial cavitybut this wave is characterized by a series of periodic axial-stress/particle velocity spikes. Since these spikes appearbefore the shockwave ever reaches the free end of the cere-

brum (the moment of shock arrival to the cerebrum free endis manifested by an abrupt increase in the particle velocity inbrain element three, Fig. 6b), it is evident that these spikesare not related to the initial shock reflection from the freeend of the cerebrum segment. A close examination of theshock-propagation histories within the helmet/head assem-bly revealed that these spikes originate at the air/composite-shell interface. However, in the EVA case, they are dampedout by the accompanying volumetric compression and,hence, never enter the intra-cranial cavity.

As clearly demonstrated in our prior work [14], high peak axialstresses and particle velocities associated with the shock-wavepropagation within the brain are conducive to the developmentof TBI. Hence, based on the results presented in Figs. 5a and band 6a and b, it is expected that polyurea will possess comparableor somewhat improved blast-mitigation capacity in comparison toEVA.

3.2. 18.6 atm peak-pressure blast impact

To establish the effect of blast peak-pressure on both the stres-ses/velocities experienced by the brain and on the relative perfor-mance of EVA and polyurea as blast-mitigating suspension-padmaterials, the corresponding results pertaining to the temporalevolution of the axial stress and particle velocity for the case of18.6 atm peak-pressure blast impact are displayed in Fig. 7a andb and Fig. 8a and b, respectively. A brief examination of the resultsdisplayed in these two figures shows that:

(a) Both peak axial stresses and peak particle velocities take onsubstantially higher values in the case of EVA than in thecase of polyurea suspension pads i.e., the maximum com-pressive axial stress in the EVA case is around �800 MPawhile its polyurea counterpart is around �250 MPa. Like-wise, the maximum particle velocity in the EVA case is

Fig. 5. Temporal evolution of axial stress associated with a blast-impact peakpressure of 5.2 atm at three locations within the brain for the case of: (a) EVA, and(b) polyurea suspension-pad material.

Fig. 6. Temporal evolution of particle (axial) velocity associated with a blast-impactpeak pressure of 5.2 atm at three locations within the brain for the case of: (a) EVA,and (b) polyurea suspension-pad material.


around 360 m/s while the corresponding velocity in thepolyurea case is only around 145 m/s.

(b) The upstream axial-stress/particle velocity states furtheraway from the shock-wave front are, however, quite compa-rable in the two cases.

(c) The shock-wave arrival times are again substantially shorterin the case of polyurea case than in the EVA case.

(d) Peak axial stresses and peak particle velocities experiencedby the brain are significantly increased, while the shock-wave arrival times are significantly decreased in the18.6 atm peak-pressure case relative to their counterpartsobserved in the case of 5.2 atm blast peak-pressure. Thisfinding is fully justified since a stronger air-borne blast waveis expected to create a stronger shock in the targetedmaterial.

(e) In the case of EVA, the aforementioned three-stage loading isnot particularly apparent and in addition, there is an abruptdecompression of the upstream cerebrum material.

(f) The previously observed series of spikes is not well-defined/present any longer in the case of polyurea.

The results presented in this section as well as the previous sec-tion clearly established that polyurea displays a superior blast-mit-igation potential relative to that observed in EVA. In the nextsection, an attempt is made to explain this finding.

3.3. Shock-wave evolution within the helmet

To help explain the aforementioned findings regarding the tem-poral evolution of the particle velocity at different locations in thebrain, evolution of the (compressive) shock and decompression(tensile) waves within different segments of the ACH helmet isanalyzed in this section. The corresponding results for the axialstress are not displayed since they were quite analogous to the par-ticle velocity and, hence, did not provide any additional insight intothe problem at hand.

To help explain differences in the blast-impact-mitigation capa-bility of EVA and polyurea, the variation of the shock impedance (aproduct of the material reference density and the shock speed, rateof shock-wave advancement through a medium) of all the atten-dant materials with the shock-wave strength (as quantified by

Fig. 7. Temporal evolution of axial stress associated with a blast-impact peakpressure of 18.6 atm at three locations within the brain for the case of: (a) EVA, and(b) polyurea suspension-pad material.

Fig. 8. Temporal evolution of particle (axial) velocity associated with a blast-impactpeak pressure of 18.6 atm at three locations within the brain for the case of: (a) EVA,and (b) polyurea suspension-pad material.


the upstream particle velocity) was determined using the sametype of transient non-linear dynamics computational analysis asthat described in Section 2.4. The results of this computationalanalysis are displayed in Fig. 9. It should be noted that since EVAundergoes extensive compression when subjected to shock load-ing, Fig. 9 contains shock-impedance curves for both EVA foamand (fully compressed) EVA bulk material. The results displayedin this figure show that EVA foam has a substantially lower shockimpedance. This finding has a profound effect on the way the initialshock-wave generated at the air/composite-shell interface is prop-agated inward towards the intra-cranial cavity. For planar shockstraveling in the host material, as is the present case, the interactionof the shock with an interface separating the host and the adjoin-ing material results in the formation of a (transmitted) shock in theadjoining material (the strength of which depends on the host-material/adjoining-material shock-impedance mismatch). At thesame time, a reflected wave is generated within the host materialwhich is either of a (compressive) shock-character (when the hostmaterial possesses a lower shock impedance) or of a (tensile)decompression-character (when the host material possesses ahigher shock impedance) [27]. Furthermore, when the two materi-als are not in direct contact and one of them is propelled and col-

lides with the other, strengths of the two resulting shocks are alsoa strong function of the attendant shock-impedance mismatch[27].

Evolution of the shock waves within the ACH helmet equippedwith EVA and polyurea suspension pads in the case of 5.2 atmpeak-pressure blast-wave are displayed in Figs. 10a–d and 11a–d,respectively. The corresponding shock-wave evolution results forthe case of 18.6 peak-pressure blast-wave are displayed in Figs.12a–d and 13a–d. It should be noted that the post-blast-impacttimes associated with the corresponding parts of Figs. 10–13 (e.g.Fig. 10b and 11b) are not all identical. However, these times corre-spond to the identical shock-evolution events. Specifically, part (a)in Figs. 10–13 correspond to a moment when the shock wave hasadvanced roughly half-way into the composite shell; part (b) cor-responds to an instant shortly after the aforementioned shock-wave has collided with the composite shell/suspension-padmaterial interface; part (c) corresponds to a moment when theshock-wave has advanced almost the entire length of the suspen-sion-pad material and part (d) corresponds to a moment shortlyafter the shock-wave described in part (c) has collided with thesuspension-pad/skull material interface.

SW

SW

DW

SW

SW

SW

(a)

(b)

(c)

(d)

Fig. 10. Spatial distribution of the particle (axial) velocity associated with a blast-impact peak pressure of 5.2 atm within the helmet composite shell, EVA suspensionpad and skull at four different times: (a) 9.6 ls, (b) 15 ls, (c) 176 ls and (d) 187 ls.

Fig. 9. Variation of the shock impedance with shock strength (as quantified by theupstream particle velocity) for the materials constituting the helmet/headassembly.


The results displayed in Figs. 10–13 are utilized in two ways: (a)First, they are analyzed in order to understand shock-wave propa-gation through the ACH helmet and the skull; and (b) secondly, torelate differences in the shock-wave propagation through the ACHhelmet equipped with EVA and polyurea suspension pads to theobserved differences in the intensity, waveform and the arrivaltime of the shock waves within the intra-cranial cavity.

For brevity, only the results displayed in Figs. 12 and 13 are dis-cussed in detail. However, the results displayed in Figs. 10–13 areall used in order to explain differences in the shock-impact-mitiga-tion capabilities of EVA and polyurea.

Examination of the results displayed in Fig. 12a–d reveals that:

(a) Initially, an inward propagating shock-wave (SW) is gener-ated within the composite shell, Fig. 12a.

(b) Upon impingement of this shock-wave with the composite-shell/suspension-pad material interface, an outward travel-ing decompression wave (DW) (i.e., a tensile wave travelingtoward the air/composite-shell interface) is formed withinthe composite shell which nearly doubles the upstream(behind the wave) particle velocities. At the same time, aninward traveling shock-wave is created within the EVA sus-pension-pad material, Fig. 12b. In addition, a portion of theEVA segment adjacent to the composite-shell/suspension-pad interface experiences a high-level of (volumetric) com-pression. This effectively partitions the EVA segment intotwo regions, one containing highly compressed-EVA mate-rial and the other containing the EVA foam. Since the shockspeed is substantially higher in the compressed-EVA than inthe EVA foam, a shock-wave approaching the compressed-EVA/EVA-foam interface drives this interface at a velocityhigher than the EVA-foam shock speed. This is an exampleof the so-called ‘‘Snowplowing Effect” [27].

(c) As the shock wave continues to propagate towards the sus-pension-pad/skull interface, the upstream particle and thecompressed-EVA/EVA-foam interface velocities continue toincrease, Fig. 12c. This finding is the result of the fact thatthe aforementioned decompression wave reflects (repeat-edly) as a shock-wave at the composite-shell/air interfaceand subsequently exerts additional (repeated) loading tothe suspension-pad material.

(d) Upon the arrival of the compressed-EVA/EVA-foam interfaceat the suspension-pad/skull interface, two shock waves (onetraveling inward and the other traveling outward) are gener-ated, Fig. 12d. This is a result of the fact that compressed-EVA acts effectively as a ‘‘flyer-plate” and loads the skullballistically (i.e., by impact). As will be seen later, this behav-ior is drastically different than that observed in the polyureasuspension-pad case.

The findings reported above are next compared and contrastedwith the polyurea results displayed in Fig. 13a–d. Examination ofthe results displayed in these figures reveals that:

(a) As in the EVA case, an initial inward propagating shock-waveis generated within the composite shell, Fig. 13a.

(b) As in the EVA case, upon impingement of this shock-wavewith the composite-shell/suspension-pad material interface,an outward traveling decompression wave is formed withinthe composite shell, Fig. 13b. However, the decompressionwave is substantially weaker in this case since the shockimpedance of polyurea is only slightly lower than that ofthe composite shell. As a result, only a minor increase inthe upstream particle velocities is associated with the

SW

SW

DW

SW

SW

SW SW

SW

(a)

(b)

(c)

(d)

Fig. 11. Spatial distribution of the particle (axial) velocity associated with a blast-impact peak pressure of 5.2 atm within the helmet composite shell, polyureasuspension pad and skull at four different times: (a) 9.6 ls, (b) 13.4ls l, (c) 18.4 lsand (d) 20.1 ls.

SW

SW

DW

SW

SW

SW

(a)

(b)

(c)

(d)

Fig. 12. Spatial distribution of the particle (axial) velocity associated with a blast-impact peak pressure of 18.6 atm within the helmet composite shell, EVAsuspension pad and skull at four different times: (a) 6 ls, (b) 9 ls, (c) 29.9 ls and(d) 43.2 ls.


decompression wave. As in the EVA case, an inward travelingshock-wave is created within the polyurea suspension-pad material. However, due to nearly incompressible natureof polyurea, this wave is associated with very littlecompression.

(c) Analogous to the EVA case, as the polyurea-borne shockwave continues to propagate towards the suspension-pad/skull interface, the upstream particle velocities continue toincrease, Fig. 13c. However, this increase is quite small incomparison to that observed in the EVA case. This findingis the result of the fact that the shock-wave speeds arecomparable in the composite-shell and the polyurea suspen-sion-pad. Consequently, repeated loading of the polyureasuspension-pad by the shock-wave reflected from the com-posite-shell/air interface (observed in the EVA case) doesnot take place (over the time period examined).

(d) As in the EVA case, upon the collision of the polyurea-borneshock-wave with the suspension-pad/skull interface, twoshock waves (one traveling inward and the other travelingoutward) are generated, Fig. 13d. However, this finding isnot a result of the ballistic loading mentioned in the EVA

case but rather associated with the fact that polyurea pos-sesses a lower-level of shock impedance than the skull,Fig. 9.

To further highlight the differences between EVA and polyureaas shock impact-mitigating materials, the following two data-reduction analyses were carried out for the high blast peak-pres-sure case:

(a) The initial air-borne blast-wave pressure vs. time functionwas integrated up to the moment of shock-wave generationwithin the skull. The results obtained showed that the com-puted specific impulse is nearly three times higher in thecase of EVA than in the polyurea case. This finding is relatedto the fact that the skull shock-wave generation time in theEVA case is controlled by the arrival of the relativelyslow-moving compressed-EVA/EVA-foam interface to thesuspension-pad/skull interface rather than by the arrival ofa shock-wave at this interface (as in the case of polyurea).Consequently, the skull shock-wave generation time isapproximately 3.5 times longer in the EVA than in the poly-urea case.

SW

SW DW

SW SW

SW SW

SW

(a)

(b)

(c)

(d)

Fig. 13. Spatial distribution of the particle (axial) velocity associated with a blast-impact peak pressure of 18.6 atm within the helmet composite shell, polyureasuspension pad and skull at four different times: (a) 6 ls, (b) 9.6 ls, (c) 10.3 ls and(d) 13.2 ls.


(b) The shock-wave related impulse within the first brainelement is integrated up to a time of 75 ls. This time is sub-stantially longer than the corresponding shock-wave arrivaltimes at this element for the EVA and polyurea cases. Theresults obtained showed comparable computed specificimpulses in the two cases. This finding is consistent withthe linear momentum conservation principle. In addition,this finding shows that since the shock-wave arrival timesare substantially longer (and thus the difference betweenthe upper integration limit of 75 ls and the shock arrivaltime is substantially shorter) in the case of EVA, the peakloads experienced by the brain are substantially higher inthe EVA case.

Based on all the findings reported and discussed in the presentsection, the following picture emerges regarding the differences inEVA and polyurea as suspension-pad shock mitigating materials.Polyurea, being a bulk and nearly incompressible material withshock impedances comparable to those found in the remainderof the helmet/head assembly, is not prone to accumulation of thelinear momentum before this momentum is transferred to thebrain. In other words, the momentum which is preserved and can-

not be dissipated is transmitted continuously to the intra-cranialcavity while ensuring more uniform loading of the brain.

In sharp contrast to polyurea, EVA is a highly compressible foammaterial which under weak-shock-loading conditions, possessesvery low shock impedance in comparison to the materials foundin the remainder of the helmet/head assembly. However, undersufficiently strong shock-loading conditions EVA undergoes exten-sive (volumetric) compression and the resulting material, depend-ing on the extent of compression, can possess substantially higherlevels of shock impedance. The two blast peak-pressure levels usedin the present work can be considered as producing shockwaves ofa moderate and relatively high strength, respectively. Consideringthe fact that EVA behaves differently under moderate and strongshock-loading conditions, the two blast peak-pressure EVA casesare considered separately.

In the case of the lower blast peak-pressure which is associatedwith a shock of moderate strength, the extent of EVA compressionand the corresponding particle velocities are also moderate,Fig. 10a–d. Since these particle velocities are lower than the asso-ciated EVA-foam shock speed, the EVA-borne shockwaves outrunthe advancing compressed-EVA/EVA-foam interface and continueto travel towards the suspension-pad/skull interface at a speedhigher than the compressed-EVA/EVA-foam interface. Theseshock-waves are responsible for the first-stage loading of the brainas discussed in conjunction with Figs. 5a and 6a. When the advanc-ing compressed-EVA/EVA-foam interface ultimately reaches thesuspension-pad/skull interface, two shockwaves are created. Theinward traveling shock-wave is responsible for the second stageof brain loading while the outward traveling shock-wave uponreflection from the suspension-pad/composite-shell interface leadsto the third-stage of brain loading. Since the foregoing explanationsuggests that shock transmission under the lower blast peak-pres-sure in the EVA is a fairly continuous process and, thus, resemblesthe shock transmission process in polyurea, it is not surprising thatthe blast-impact mitigation performance of the two materials wasalso similar (as evidenced by comparing Figs. 5 and 6).

In the case of the higher blast peak-pressure which is associ-ated with a shock of high strength, the extent and the rate ofEVA compression are quite high, Fig. 12a–d. Since the associatedparticle velocities are now greater than the corresponding EVA-foam shock speed, no transmission of the shockwaves into theEVA-foam takes place. In other words, the skull becomes awareof the blast load only when the compressed-EVA/EVA-foam inter-face reaches the suspension-pad/skull interface. By this time, con-siderable momentum accumulation within the shell/suspensionpad assembly has taken place. Hence the initial loading experi-enced by the skull, and in turn by the brain, will be significantlyhigher under higher blast peak-pressure in the EVA case, makingblast-impact mitigation potential of this material inferior to thatof polyurea.

4. Conclusions

Based on the results obtained in the present work, the followingmain summary remarks and conclusions can be drawn:

1. A simple ‘‘core-sample” model of the helmet/head assembly isused to investigate computationally the potential of polyurea(a segmented, thermo-plastically cross-linked elastomer) as ablast-impact mitigating helmet suspension-pad material andcompare it with the performance of conventional Ethylene-Vinyl-Acetate (EVA) foam. This entailed the identification andparameterization of a number of atmospheric, helmet and bio-logical (skull/brain) materials, as well as modeling of the fluid/solid and solid/solid interactions.

Pres

sure

No Artificial Viscosity

With Artificial Viscosity

Upstream

Downstream (a)


2. The results obtained show that, at moderate blast peak-pres-sures, the brain experiences comparable loading histories inthe two suspension-pad material cases. In sharp contrast, at rel-atively high blast peak-pressures, polyurea was found to sub-stantially lower the peak loading experienced by the brain.Since high peak stresses and high peak velocities associatedwith shock-wave propagation within the brain are typicallylinked with traumatic brain injury (TBI), it appears thatpolyurea is a preferred choice in helmet suspension-padapplications.

3. Similarities and differences between EVA and polyurea at differ-ent blast peak-pressure levels are rationalized in terms of theirmicrostructure and mechanical response to shock loading. Spe-cifically, high compressibility of EVA, which is highly beneficialfor energy absorption under quasi-static loading conditions, canbe a liability in shock-mitigating helmet applications.

Distance

Pres

sure

No Artificial Viscosity

With Artificial Viscosity

Downstream (b)

Acknowledgements

The material presented in this paper is based on work sup-ported by the Office of Naval Research (ONR) research contractentitled ‘‘Elastomeric Polymer-By-Design to Protect the WarfighterAgainst Traumatic Brain Injury by Diverting the Blast Induced ShockWaves from the Head”, Contract Number 4036-CU-ONR-1125 asfunded through the Pennsylvania State University. The authorsare indebted to Dr. Roshdy Barsoum of ONR for continuing supportand interest in the present work and to professors J. Runt, J. Tarter,G. Settles, G. Dillon and M. Hargether for stimulating discussionsand friendship.

Distance

Upstream

Fig. A1. The artificial-viscosity algorithm’s effect on resolving the shock-wavefront: (a) a finer computational mesh, and (b) a coarser computational mesh.

Appendix A. Artificial viscosity

In assessing the potential of polyurea as a helmet suspension-pad material, the computational analysis carried out in the presentwork is concerned with the short-term transient response of thehelmet/head assembly to blast loading. Since this type of responseis dominated by the propagation, reflection, transmission andinteraction of the shock waves within different sections of the hel-met/head assembly, accurate representation of the shock waves isvery critical. In attaining this goal, the so-called ‘‘artificial-viscosity”algorithm was utilized. Since this algorithm, if not used properly,may compromise the quality of the overall computational results,a brief overview of its physics and utility is given in this section.

One of the most common problems associated with numericalmodeling of strong shocks is the formation of non-physical pres-sure oscillations behind the shock. An example of the upstreampressure oscillations in the case of a one-dimensional shock-wavepropagation is displayed in Fig. A1a. The effect of the mesh size onthe shock-wave representation can be seen by comparing the re-sults displayed in Fig. A1 and b. It is seen that the use of a coarsermesh, Fig. A1b, compromises the accuracy of the shock-wave frontrepresentation (i.e., the shock-wave front is unrealistically spreadout) while the upstream pressure level and the extent of its oscil-lations are essentially unchanged. While there may be a number ofpossible reasons for the occurrence of pressure oscillations, thestandard remedy is the introduction of the so-called ‘‘artificial vis-cosity” terms into the momentum and energy conservation equa-tions. It should be noted that while the term ‘‘artificial viscosity”is used, the corresponding mathematical algorithm is aimed atincluding the effect of a real physical phenomenon (i.e., the dissi-pation of the kinetic energy into heat, the extent of which scaleswith the shock strength).

Essentially, the artificial-viscosity algorithm replaces pressure,P, in the momentum and energy conservation equations with a

P + Q term. The artificial-viscosity pressure, Q, is defined as a sumof two terms, one scaling linearly and the other quadratically withthe volumetric strain rate, _evol, as:

Q ¼ aqc0Le _evol þ bqL2e_e2vol ð16Þ

where a (typical value = 0.06) and b (typical value = 1.2) are artifi-cial-viscosity parameters, q is the material density, c0 the speed ofsound in the material, and Le is the element characteristic length.

The effect of the application of the artificial-viscosity algorithmon the shock-wave profile for two mesh sizes is displayed inFig. A1a and b. It is seen that significantly reduced pressure oscil-lations are obtained at the expense of a slightly less sharp shockfront.

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Blast-wave impact-mitigation capability of polyurea when used as helmet suspension-pad material