HEAD PROTECTION, THE APPLICATION OF MATHEMATICAL MODELLING KH Wilson and D J Ca, Stoes and Clothing Reseah and Development Establishment, Co/eheste, Essex, C2 7SS, UK Abstat - UK militay helmets onsist of a fibe einfoed polyme shell ombined with a high density foam line Suh a design povides the weae with potetion against jagmenting munitions and low speed impats This pape desibes the use of ompute models to simulate the esponse of militay helmets to impat onditions The models have been used to study the influene of helmet design paametes suh as; type and thikness of joam line, shell thikness and headlhelmet onjomity () Bitish Cown Copyight 1993/MOD Published with the pemission of the Contolle of He Majestys Stationay Offie Intodution Militay helmets ae designed fo a numbe of appliations In addition to a speified ballisti and impat pefomane, they must meet additional equiements of long-tem wea, omfot, stability and maximum oveage with an optimised weight Figue 1 lists some of the equiements fo uent in-sevie helmets Whilst these fatos ae not listed in any patiula ode, it should be noted that all situations demand impat potetion Heimets may be used in envionmental onditions anging fom the topis to the Ati ile Reliability of helmets is ensued by testing to investigate the effet on mehanial popeties ofthese extemes oftempeatue and humidity (Figue 2) Development of Compute Models The models wee developed unde an exta-mual eseah ontat in suh a manne as to minimise the mateials input data equied The authos of this pape do not pesume to take edit fo the wok aied out no to embak on a detailed explanation of the mathematis involved A bief desiption of the liteatue on whih they wee based and the models themselves is, howeve, petinent Relevant Liteatue The models wee developed afte the ompletion of a thoough liteatue eview Foams ae lassified by the way that they defom, that is, flexible o igid In addition they may at in an elasti, plasti o bittle manne Geneally, flexible foams ae elasti and igid foams fail by the plasti ollapse o bittle ushing ofthe ells The foam may ontain open o losed ells Foam mophology has been weil disussed in the liteatue (Patel and Finnie, 197, Chan and Nakamua, 1969, Dawson and Shotall, 1982 and Menges and Knipshild, 1975) Foam ells ae nuleated as spheial bubbles whih expand with ineasing pessue At a gas volume of 76% these bubbles impinge to fom iegula polyhedon ells density foams ontain angula ells, whilst high density foams ontain spheial ells Low The models utilised in this pape ae lagely based on the wok of Ashby whih has been published in numeous papes (Gibson et al, 198 and 1982, Gibson and Ashby, 1982-325 -
and Maiti et al, 1984) This wok is based on a dimensional analysis and has shown that the ation of the ell wall thikness to the length of ell detemines the foam mehanial popeties The dominant mehanism fo foam linea elasti defomation is the elasti bending of the thik ell walls In the plateau phase of defomation whih ditates enegy absoption: (i) elasti ell wall bukling leads to non-linea elasti behaviou (ii) plasti ollapse is due to the stess exeeding the polyme yield stess value (iii) bittle ushing ous when the sufae stess exeeds the failue stess Duing the densifiation poess, the modulus of the foam is equivalent to that of the base polyme when the voids have been ompessed (Rush, 1969) Ashby onfimed that this oued when the elative density was appoximately 33 The ompession of a losed ell foam leads to gas ompession esulting in a ontibution to the total foam stess and may assist in helmet line eovey (Rush, 197) The signifiane of pneumati damping in enegy absoption mehanisms is unlea and it is thought (Patel and Finnie, 197) that at high stain ates visoelastiity would dominate The visoelasti esponse of the foam is desibed using the wok of Rush (1969, 197a and 197b) fo ate independent esponse and that of Meineke and Shwabe (197 and 1971) and Meineke et al, 1971 fo ate dependent esponses Desiption of the Models The fist model, Genfoam, an be used to desibe the behaviou of a flat foam speimen unde both quasi-stati and dynami impat onditions The defomation poess was onsideed as a ombination of diffeent mehanisms These wee epesented analytially as a seies of paallel elements (Figue 3) Some of the mehanisms wee mutually exlusive whilst othes had pesibed limits of appliability Mateials popeties equied as input data to the Genfoam model ae: (i) the Youngs modulus ofthe solid polyme (ii) the elative density ofthe foam, that is, the atio between the density of the foam and that of the solid polyme These wee obtained fom foam manufatues as onfidential infomation The behaviou of the omplete helmet ( shell plus line) und e impat was oiginally modelled using a finite element poess (Figue 4) This detailed epesentation was designed to investigate the stess-stain behaviou of the helmet omponents and both the defomed and igid body motions Pedition of the influene of design paametes on the impat esponse poved to be diffiult with the finite element model In patiula, mesh ollapse was obseved when the foam line was onstuted of a soft mateial The finite element model was, theefoe, used to validate a simple, moe flexible lumped paamete model The lumped paamete model (Genhel) inopoates the Genfoam model disussed peviously The following assumptions ae made in the Genhel model: (i) the head and helmet ae axisymmetial, that is, they ae defined by a single adius o uvatue (ii) the impato and the head ae stiffe than the helmet - 326 -
(iii) the foam has unifom thikness (iv) the line extends beyond the impat aea (v) the stain distibution in the line is independent ofthe amount of loading The omponents ofthe model ae shown in Figue 5 and inlude: (i) the impato mass (ii) the helmet shell mass (iii) a sping epesenting the ompession stiffness of the foam line (iv) a igid head fom Vaiations on Genhel allow fo the vetial impation of: (i) a helmet ontaining a headfom onto a flat sufae (ii) an impato dopping onto a esiliently mounted headfom to epesent the inteation of the helmet and skull lt is a goss simplifiation The only mateial popety equied as input data to the Genhel model is the Y oungs modulus of the helmet shell whih may be detemined using standad tehniques The Genfoam ompute pogamme stoes esults as stain, stain ate, total stess and enegy absobed (pe unit volume) at eah hosen time inement Paametes investigated by Genhel ae; duation and speed of impat, line type and thikness, and shell thikness, uvatue, Y oungs modulus and mass Results ae pesented as; foe, aeleation, displaement, defletion and veloity vesus time plots Validation of Models The Genfoam model was validated by ompaison of pedited impat esponses to those expeimentally detemined at SCRDE Figues 6a and 6b illustates suh a ompaison fo a 37J impat on two diffeent foam mateials Good ageement is obseved between the simulated and expeimental maximum deeleation and duation of esponse fo both mateials Suh data justifies the use of the Genfoam model to pedit foam esponse unde dynami loading onditions Foam Ais seen to exhibit both ineased deeleation and duation of esponse ompaed to F oam B and ould, theefoe, be ejeted fom a mateials seletion poedue Suh plots an, theefoe, be used fo the seening of possible andidate mateials fo use as helmet lines Genhel was validated by two ompaisons Fistly, a ompaison between the esponse to impat as pedited by the finite element model and Genhel This was onduted using a elatively stiff line to pevent the finite element gid fom ollapsing Seondly, the Genhel model was ompaed to expeimental data Figue 7 ompaes typial expeimental data fom a 122SJ impat on a ombat helmet to that pedited using the Genhel model The data is in the fom of an impato aeleation/time uve All majo featues of the expeimental uve ae seen to be epodued by the Genhel pedition Exellent ageement is obseved between the expeimental and pedited maximum aeleations and duation of esponse Confidene in both the Genfoam and Genhel models has, theefoe, been established - 327 -
Mehanism of Loading Duing Impat Initially, Genhel was used to onside one geomety of helmet shell and two diffeent foam mateials This eseah laified the mehanisms assoiated with impats of 122SJ onto (militay) helmets and demonstated that loal bending and igid body motion oued This late featue led to ompession of the line, whilst the inteation of impato and shell podued the haateisti shape of the measued impats Genhel allows fo the pedition of the foes in the helmet and line and the aeleation, displaement and veloity of the impato and helmet Figues 8-11 illustate these fatos and may be used to desibe the sequene of events duing impat When the impato hits the shell, displaement of the helmet ous esulting in impato deeleation (time peiod 5ms-1ms) The light weight helmet aeleates apidly and its veloity fist equals and then exeeds that of the impato The fist peak in the foe/time uve ous at the point of equal veloity (l25ms) The helmet own begins to flatten and this downwad movement is esisted by ompession foes geneated in the foam line This esults in etadation of the helmet The impato is now tavelling at an equal veloity ompaed to the helmet and this oesponds to the fist tough in the foe/time uve (23ms) Loal shell defomation is aused by the ineased veloity of the impato and the elasti eovey of the foam line, whih pushes the shell upwads This late mehanism auses the impato to deeleate The seond peak in the foe/time uve ous when the impato and shell expeiene equal veloity (4ms) The impato and helmet ae now moving away fom the headfom lf the helmet emains in ontat with the headfom and moe elasti foam eovey ous, a thid peak may be obseved The ebound speed of the impato is geate than that of the helmet due to the elaxation of esidual shell bending Influene of Design Paametes Fom the above disussion it is seen that the Genhel model povides a onvenient means fo examining both design paametes and mateials utilised fo militay helmets Paametes of patiula inteest ae: (i) line mateial (ii) line thikness (iii) headfom adius (iv) shell thikness Eah of these fatos is disussed fo the uent ombat helmet undegoing a impat of 5kg at 7m/s, that is 122SJ Line mateial Thee diffeent foam mateials wee hosen fo assessment These wee designated: X - high density polyethylene - 328 -
Y - polypopylene Z - low density polyethylene The foe/time uves pedited by Genfoam ae pesented in Figue 12 Mateial Xis seen to tansmit the minimum peak foe to the headfom The emaining mateials ae all seen to exhibit lage impat peak foes due to the densifiation of the foams The duation of the foes tansmitted by foams Y and Z ae simila to half the natual fequeny of the peiod of vibation of the human skull and ae undesiable In addition, the duation of the omplete esponse is longe than obseved with foam X F oam Z is seen to exhibit the wost impat potetion of the thee foams examined and the impat esults in foam ollapse Foam X appeas to be the most suitable fo use as a (militay) helmet line Line thikness Figue 13 illustates the effet of eduing the thikness of a line manufatued of mateial X by appoximately 3% signifiantly, seveal peaks ae obseved Whilst the aveage foe ating on the headfom is not seen to vay natual fequeny of the skull and ae undesiable The duation of these peaks is simila to half the At a time peiod of appoximately 6ms, shap peaks ae obseved due to the fomation of lage stains and foam densifiation elatively thik line is theefoe equied fo adequate impat potetion in a typial militay helmet A Head adius Alteing the headfom adius may be used to assess the influene of loseness of helmet fit Figue 14 illustates the effet of a 122SJ impat onto a helmet mounted on a 8mm and a 85mm headfom The ineased adius of 85mm has led to an ineased peak foe and edued defletion ompaed to the 8mm headfom The lage ontat aea would, howeve, ompensate fo the ineased foe and the foam line will expeiene a edued level of stess This would suggest a edution in ontat pessue on the headfom and lead to the onlusion that onfomal ontat does offe an advantage in impat potetion Shell thikness The Genhel simulated esponse to an impat fo ombat helmets of aveage thikness Smm, 7mm and 9mm ae pesented in Figue 15 Minimum vaiation in peak foe expeiened by the helmet is obseved on deeasing the helmet thikness fom 9mm to 7mm Howeve, a edution of appoximately 18 75% in the peak foe is obseved when the shell thikness is edued fom 7mm to Smm Whilst the edution in the maximum foe is desiable, onflition with ballisti potetion equiements may ou Conlusions 1 lt has been demonstated that the flat foam model, Genfoam, simulates impat behaviou to expeimental data The pedited deeleations and duation of esponse show good oelation 2 The lumped paamete model, Genhel, has been used to suessfully pedit the esponse to impat of a ombat helmet All featues ofthe impats wee epodued The model was used to pedit the vaiation of foe, aeleation, displaement and veloity /time esponse ofthe helmet and the impato - 329 -
3 Genfoam has been suessfully used to suvey available foam mateials The mateial whih displayed the equied haateistis of minimum peak foe tansmitted was a high density polyethylene foam 4 Genhel was used to identify the influene of design paametes Pedition suggested that good impat potetion equies lose fitting shells, elatively thik lines and a edued shell thikness Howeve, this late fato may onflit with ballisti potetion equiements Refeenes Gibson LJ, Shaje GS, Robetson CI and Ashby MF The mehanis of ellula mateials Cambidge Univesity Engineeing Depatment CUED/C/MATS/TR68 198 Gibson LJ and Ashby MF The mehanis of thee-dimensional e/lula mateials Po Roy So A 382 1982 p43 Gibson LJ, Ashby MF, Shaje GS and Robetson CI The mehanis of twodimensional ellula mateials Poe Roy Soe A 382 1982 p25 Maiti SK, Gibson LJ and Ashby MF Defomation and enegy absobing diagams fo e/lula solids Ata Met 32 1984 p 1963 Patel MR and Finnie 1 Stutual featues and mehanial popeties of igid ellula plastis J Mats 5 197 p99 Chan R and Nakamua M Mehanial popeties of plasti foams J Cell Plas 5 1969 pll2 Dawson JR and Shotall JB The miostutue of igid polyuethane foams J Mat Sei 17 1982 p22 Menges G and Knipshild F Estimation of mehanial popeties fo igid polyuethane foams Polym Eng & Sei 8 1975 p623 Rush KC Load ompession behaviou of flexiblefoams J Appl Polym Sei 13 1969 p2297 Rush KC Load ompession behaviou of bittle foams J Appl Polym SCi 14 l 97a p1263 Rush KC Enegy absobing haateistis of foamed polymes J Appl Polym Sei 14 197b p1433 Meineke EA and Shwabe DM Enegy absoption in polymei foams I: pedition of impat behaviou jom Jnston data fo foams with ate independent modulus J Appl Polym Sei 14 197 p2239 Shwabe DM and Meineke EA Enegy absoption in polymei foams II: pedition of impat behaviou jom lnston data fo f oams with ate de pendent modulus J Appl Polym Sei 15 1971 p2381 Meineke EA, Shwabe DM and Chiang RR Impat analysis fo ellula polymei mateials J Elastoplastis 3 1971 p 19-33 -
w w Linea Elasti Plasti t Buklin 1-3C - -3 l:c - 2C - 2C CM] +2C, wet +2:C, wet + 1 s, dy 5 at +25C +1, dv Conditions (+2C) +44C - +44 C +SOC +so Fiat Fiat Fiat Fiat Fiat Bittle, 1Densifi ation1 1Visoeiasti1 stain, stain ate 2own Rea + font Sown Sown + font Sown Positions ommuniations 1 BOMB DISPOSAL Impato TANK CREW FIGURE 3 ELEMENTS I N THE GENFOAM MODEL 1 22 3 1 22 (J) Non-linea elasti IBomb disposal ank ew 1 22 1 63 Paahutists ENERGY PARACHUTIST FIGURE 2 IN-SERVICE HELMETS RIOT Fie esistant IComfotable Combat H ELM ET COMBAT FIGURE 1 REQUIREM ENTS FOR MILITARY H ELMETS
FIGURE 4 FINITE ELEMENT MODEL l Impat spoed FIGURE 5 LUMPED PARAMETER MODEL Impato -- t Impat speed Cown bending - stiffuess Foam hne - 332 -
F IGliRE <-\ CO:\ l faiuson OF lrel>icted AND EXPEIUi\IENTAL DECl:: LERATION Füll FOAM /\! 2 15 1 1 [ l k --- FIGllRE 6ß 1 Timt ms CO:\IPARISON OF PREDICTED AND EXPERll\ IENTA L DECELERATIOl\ FOR F/\1\1 ß 2 15 j \,,// Ptdiltd 1 /,,,, o Tisnem1 FIGURE 7 1 22SJ SIJ\IUL/\TED IMPACT ON COMBAT HELMET J OO E 2 : 1 :- 1 2 Gnhtl 1 3 E1ptimn11I 1 5-333 - Timt ms
FIGURE 8 SIMULATED lmpact SHELL AND LINER 16 14 F 12 1 8 e N - - : :! 6 4 2 () 75 15 v 45 375 3 225 525 6 675 : Heimet sheu Heimet line FIGURE 9 SIMULATED IMPACT HELMET AND IMPACTOR 1 A 5 I OL m q -5 : -1-15 75 15 225 3 375 45 525 6 675 - lmpato FIGURE Heimet + line 1 SIMULATED IMPACT HELMET AND JMPACTOR oo D ( -2-4 s p 1 a -6-8 -1-12 -14 m m -16-18 -2 75 15 225 3 375 45 525 6 675 75 825 9 975 - lmpato 334 - ( Heimet + line
FIGURE 1 1 SIMULA TED IMPACT l l ELMET AiiD I IPACTOR 2 e,, 1-2 -4 - m 6, -8-1 75 15 225 3 375 45 525 6 ln pato 675 75 825 9 975 Heimet + line FIGURE 12 SIMULATED IMPACT COMPARISO: OF FOAMS 45 4 F 35 25 3 2 15 N 1 5 75 15 225 o 3 Foam X 375 45 525 Foam Y 6 675 75 \ 825 Foam Z FIGURE 13 SIMULA TED I MPACT EFFECT OF LINER THICKNESS 2 18 16 F t!\ 14 12 1 8 6 4 2 75 15 225 3 375 45 D Standad - 335 - -$- Redued 525 6 675
FIGURE 1 4 SIMULATED IMPACT HOMM HEAD RADlllS 14 12 F 1 11 e!\ -- 6 4 2-15 \ DeOtion m 85MM HEAD RADillS 16 14 12 F 1 8 e f; 6 4 2-1 DeOetlon m FIGURE 15 S IMULATED I MPACT EFFECT OF SHELL THICKNESS, FOAM X 14 12 F ( 1 8 * 6 * 4 \ \ 2 75 15 225 3 375 45 525 6 675 75 o X, 7mmshell - X, Smm shll - 336 -, X,9mm shell