Studies on Deformational Behavior of Cortical Bone using Small Punch Testing and Finite Element Simulation

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1 Proeeing of the Worl ongre on Engineering n omputer Siene 213 Vol II WES 213, Otoer, 213, Sn Frnio, USA Stuie on Deformtionl Behvior of ortil Bone uing Smll Punh eting n Finite Element Simultion N. K. Shrm, Swti Shrm, D. K. Sehgl, n R. K. Pney Atrt Bone nturl ompoite mteril h omplex hierrhil n heterogeneou truture. It i quite iffiult to nlyze the mehnil ehvior of ortil one ue to vriou ontrint oite with the peimen preprtion. hee ontrint my e overome uing mll ize peimen of ortil one. Smll punh teting, ue in the preent tuy, i very ueful tehnique to nlyze the eformtionl ehvior of mteril tht re iffiult to otin in uffiient ize for onventionl mehnil teting. he finite element moeling (FEM) of mll punh teting w rrie out uing ABAQUS oe. he mteril propertie of ortil one for FE imultion were oniere to e oth iotropi n trnverely iotropi in nture. hi wy totl ix inepenent FE moel were evelope n their reult were ompre with the orreponing experimentl one. A per the tuy, the FE reult of 1. mm thik peimen were oerve to e loer to the orreponing experimentl reult. However, for 1.5 mm thik peimen the FE moel reult were foun to e ignifintly evite from the experimentl reult. he heterogeneou n hierrhil truture of ortil one w oniere to e the min ue of thi evition. hi tuy how tht iotropi tenile propertie of ortil one re uffiient to preit the eformtionl ehvior of ortil uner mll punh teting. Inex erm Smll punh teting, ortil one, Finite element imultion, rnverely iotropi mteril B I. INRODUION ONE i well known heterogeneou n niotropi mteril. he niotropy in mehnil propertie of one h een regre eing ue y hrteriti ompoite truture of ontituent in one. he min ontituent of one re rigi hyroxiptite like minerl n plint ollgen firil [1-5]. he mehnil propertie of ortil one re iffiult to otin ue to vriou ontrin uh omplexity in one mteril, hpe n ize of one, vilility of the peimen from one iphyi, teting proeure et [6-1]. hee ontrint my e overome y employing mll ize Mnuript reeive July 23, 213. N. K. Shrm w with the Inin Intitute of ehnology Delhi, Huz Kh, New Delhi 1116, Ini. He i now with the Glol Univerity, Mirzpur Pole, Shrnpur, Uttr Preh , Ini (phone: ; e-mil: enkhrm@ yhoo.om). Swti Shrm i with the Inin Intitute of ehnology Delhi, Huz Kh, New Delhi 1116, Ini (phone: ; e-mil: wti.2517@gmil.om). D. K. Sehgl i with the Inin Intitute of ehnology Delhi, Huz Kh, New Delhi 1116, Ini (e-mil: profehgl@yhoo.om). R. K. Pney i with the Inin Intitute of ehnology Delhi, Huz Kh, New Delhi 1116, Ini (e-mil: rkpiit@yhoo.om). peimen for mehnil teting. he vntge of mll ize peimen inlue the poiility of mpling very mll volume of mteril within heterogeneou truture uh ortil one. hi my lo e ue for tuying iologil mteril tht re not ville in volume uffiient enough for onventionl mehnil teting. he mll peimen tet tehnique inlue wie rry of type n tehnique erie y Lu [11] n heon et l. [12]: tenile tet, miro hrne, mll punh (ll, her, n hemipheril he), en, frture, impt, n ftigue. In the preent invetigtion the mehnil ehvior of ortil one h een tuie uing mll peimen teting n finite element (FE) imultion. he lo-iplement ehvior of ortil one peimen w nlyze with the help of mll punh teting tehnique. he mll punh tet i verion of the ulge tet, the nme given y Bik et l. [13]. Mnhn et l. [14] n Hung et l. [15] were mong the erliet to tuy the mll punh tet tehnique for the etermintion of mehnil propertie of irrite mteril from mll irulr ik. hee tehnique lrgely involve loing upporte i or oupon with n inenter or punh, eforming it to filure, n nlyzing the reulting lo-iplement t. he finite element metho (FEM) i very vertile numeril tehnique for olving engineering prolem of pltiity, impt mehni, truturl nlyi n omputtionl mehni. he FE imultion of mll punh tet i lrge eformtion prolem n w rrie out uing the ommerilly ville ABAQUS oe. he min vntge of pplying FEM to lrge eformtion prolem i it vertility, i.e. it ility to imulte the progre of the eformtion proe n to otin omplete olution to the prolem inluing the eformtion hpe, nol iplement, nol veloity n itriution of tree n trin. In the preent tuy ix ifferent FE moel of mll punh tet were evelope n ompre with the experimentl reult. For ifferent FE moel one mteril w oniere to e iotropi well trnverely iotropi in nture. II. MAERIALS AND MEHOD Whole femorl ortil one of ovine hve een proure for the preent invetigtion. After removl of the oft tiue the one were oke in norml line n wrppe in norml line oke loth. hee one were further kept in plti g n tore t -2 efore proeing. he tenile propertie of ortil one in longituinl iretion (lo eing pplie long the long xi of one) n trnvere iretion (lo eing pplie perpeniulr to the long xi of one) were evlute uing WES 213

2 Proeeing of the Worl ongre on Engineering n omputer Siene 213 Vol II WES 213, Otoer, 213, Sn Frnio, USA trip type umell hpe peimen. he longituinl tenile peimen were prepre with guge length 25 mm, guge with 4 mm n totl length 8 mm, where, the trnvere tenile peimen were prepre with guge length 8 mm, guge with 4 mm n totl length 22 mm. Poion rtio in eh iretion w tete with the help of ixil extenometer of guge length 25 mm. he longituinl n trnvere ompreive propertie of ortil one were etermine uing ui peimen of eh ege equl to 5 mm. For mll punh teting on ortil one the mll peimen were prepre with retngulr ro-etion hving 2 mm with n two ifferent thiknee of 1 n 1.5 mm. he length of thee peimen w mintine equl to 1 mm. hee longituinl mll peimen of ortil one were prepre uh tht their length oinie with the long xi of the femur. he longituinl mll peimen of ortil one prepre for mll peimen teting re hown in Fig. 1. peimen uner qui-tti loing y peil ylinril tip hee rigi punh. ABAQUS tnr pkge i ue for omputtion n etile omputtionl reult re otine. For imultion the imenion of the retngulr peimen re eie oring to the inner qure (4 mm x 4 mm) ro-etion of the orehole of the peimen holer. he three imenionl FE moel of mll peimen tet in e of 1 mm n 1.5 mm thiknee of the mll ortil one peimen re hown in Fig. 3. hee moel were iretize with eon orer 2-noe rik (hexher) element. () () Fig. 1. Smll longituinl retngulr peimen of ortil one of ifferent thiknee (i.e. 1 mm, 1.5 mm) All ifferent peimen for experimentl teting were otine from the mile iphyi of the femorl one n were tore t room temperture in olution of 5% line n 5% ethnol t ll time until teting. Different experimentl tet were onute on MS 858 le op Mhine with very low trin rte (i.e. 1.8 mm/min for tenile n ompreive teting n.5 mm/min for mll peimen teting). he fixture for mll punh teting n it intlltion on MS 858 tle top mhine i hown in Fig. 2. () Fig. 2. Setup for mll punh teting, () fixture for mll punh teting n () intlltion of fixture on MS 858 tle top mhine he retngulr hpe mll peimen geometry i lerly not xiymmetri, o three imenionl finite element moel i require. In thi tuy, three imenionl finite element moel h een propoe for imulting mll punh tet with retngulr hpe mll (fixe em) () Fig. 3. hree imenionl FE moel of mll punh tet in e of () 1 mm n () 1.5 mm thiknee of the mll peimen he ize of the ylinril hee punh i oniere 1.82 mm imeter, 2. mm with n 4 mm height. he ylinril hee tip rigi punh i moelle with rigi oy option uing rigi element from ABAQUS lirry. wo oppoite ie ege of the mll peimen re oniere fixe y ounry onition option ENASER (motion ontrine in ll iretion). op urfe of retngulr peimen i efine SLAVE urfe for intertion. he ylinril tip urfe of rigi punh i efine MASER urfe for intertion. A loe urfe intertion of SLAVE n MASER urfe i efine y ontt lgorithm. he qui-tti loing imultion i imulte with mplitue option n mll inrementl tep re ue t referene noe of ylinril tip punh. For FE imultion, ortil one mteril w oniere to e oth iotropi n trnverely iotropi in nture. he mll peimen in her punh teting i uner pure ening itution, therefore, the upper urfe of the peimen i uner ompreion where the lower urfe i uner tenion. hi neeitte the prtitioning of the mll peimen one mteril my ehve in ifferent mnner WES 213

3 Proeeing of the Worl ongre on Engineering n omputer Siene 213 Vol II WES 213, Otoer, 213, Sn Frnio, USA uner tenile n ompreive loing. herefore the ehviour of ortil one peimen uner mll punh teting w nlyze uing ix inepenent FE moel. hee moel were tegorie oring to the peifie mteril propertie ; FI (hving fully tenile mehnil propertie oniering one mteril to e trnverely iotropi), I (hving ifferent ehviour uner tenion n ompreion with trnverely iotropi mteril propertie), FI (hving fully ompreive mehnil propertie oniering one mteril to e trnverely iotropi), FI (hving fully tenile mehnil propertie oniering one mteril to e iotropi in nture), I (hving ifferent ehviour uner tenion n ompreion with iotropi mteril propertie) n FI (hving fully ompreive mehnil propertie oniering one mteril to e iotropi in nture). he niotropi yieling riterion in e of trnverely iotropi mteril propertie w peifie uing Hill potentil funtion [16]. III. RESULS AND DISUSSION he tenile n ompreive propertie of ortil one otine from ifferent experimentl proeure re lite in le 1. he nottion ue for ifferent mehnil propertie for tenile n ompreive loing n in longituinl n trnvere iretion re given elow; E i = Elti moulu of ortil one in GP σ yi = Yiel tre of ortil one in MP σ ui = Ultimte trength of ortil one in MP ε ui = Frture trin of ortil one where i = 1, 2 for repetively longituinl n trnvere iretion of loing n =, for repetively the ompreive n tenile loing ABLE I PROPERIES OF ORIAL BONE ALONG DIFFEREN MAERIAL ORIENAIONS AND LOADING ONDIIONS Propertie Vlue n = 4 E ±.8 E ±.6 E ± 1.9 E ± 1.7 σ y ± 3.4 σ y ± 3.7 σ y ± 5.4 σ y ± 4.4 σ u ± 3.4 σ u ± 2.6 σ u ± 4.2 σ u ± 3.9 ε u ±.23 ε u ±.26 ε u1.228 ±.43 ε u2.145 ±.49 n = numer of peimen tete n the vlue reporte here re the verge vlue. he ifferent tete peimen of ortil one in e of ompreion, tenion n mll punh teting re hown in Fig. 4. () () Fig. 4. Different tete peimen of ortil one uner () ompreion () tenion n () mll punh teting he experimentl lo-iplement igrm otine from mll punh tet hve een ompre with ifferent lo-iplement igrm otine from the FE moel in e of oth 1 mm n 1.5 mm thiknee of the mll peimen. he omprion of experimentl loiplement urve with thoe otine from FE trnverely iotropi moel re hown in Fig. 5 n Fig. 6 repetively for 1 mm n 1.5 mm thiknee of the peimen, where, the orreponing omprion with thoe otine from FE iotropi moel re hown in Fig. 7 n Fig. 8 repetively for 1 mm n 1.5 mm thiknee Diplement (mm) Fig. 5. omprion etween experimentl n trnverely iotropi finite element lo-iplement igrm for 1. mm thik mll peimen (where = experimentl urve, = FI, = I n = FI) Diplement (mm) Fig. 6. omprion etween experimentl n trnverely iotropi finite element lo-iplement igrm for 1.5 mm thik mll peimen (where = experimentl urve, = FI, = I n = FI) () WES 213

4 Proeeing of the Worl ongre on Engineering n omputer Siene 213 Vol II WES 213, Otoer, 213, Sn Frnio, USA Diplement (mm) Fig. 7. omprion etween experimentl n iotropi finite element lo-iplement igrm for 1. mm thik mll peimen (where = experimentl urve, = FI, = I n = FI) Diplement (mm) Fig. 8. omprion etween experimentl n iotropi finite element lo-iplement igrm for 1.5 mm thik mll peimen (where = experimentl urve, = FI, = I n = FI) he experimentl n FE reult of mll punh tet re reporte in le II for ifferent thiknee of the mll peimen. ABLE II EXPERIMENAL AND FINIE ELEMEN RESULS OF SMALL PUNH ES Metho Exp reult FI I FI FI I FI Speimen thikne (mm) Filure lo (N) A per the unpire t-tet nlyi, for 1. mm thik longituinl peimen, the filure lo otine from experimentl urve w not foun to e ignifintly Stiffne (kn/mm) Lo t rek wy (N) ifferent from finite element reult of I, FI, FI, I, n FI, however, it w ignifintly ifferent (p <.5) from FI moel reult. On the other hn, the tiffne vlue of experimentl urve were foun to e ignifintly ifferent (p <.1) from ll finite element reult. he experimentl lo t rekwy point (lo point orreponing to.2 % offet point) w not oerve to e ignifintly ifferent from finite element reult of I, FI, n FI while it w oerve to e ignifintly ifferent (p <.1 FI n p <.5 for FI n I) for FI, FI n I ompre to experimentl reult. For 1.5 mm thik peimen, the experimentl filure lo w foun to e ignifintly ifferent (p <.1 for FI, I n FI, p <.1 for FI, p <.5 for FI n p <.1 for I) from ll finite element reult. he tiffne of experimentl urve w foun to e ignifintly ifferent (p <.1) from ll finite element urve. Similrly, the lo t rekwy point of experimentl urve w lo oerve to e ignifintly ifferent (p <.1 for FI, FI, I n p <.1 for I n FI, p <.1 for FI) from ll finite element urve. A per the ove iuion, the experimentl n finite element reult were foun to e ignifintly ifferent in e of 1.5 mm thik mll peimen, where, for 1. mm thik mll peimen the orreponing experimentl n FE moel reult were not ignifintly ifferent. hi how tht thikne of the ortil one peimen ply n importnt role uring eformtion of one. he hierrhil ompoite like truture of ortil one my e the min reon of thi eformtionl ehviour. Further, one i oniere to e highly heterogeneou mteril ue to vrition in it ompoitionl prmeter uh enity, poroity, minerliztion et., however, for FE imultion the mteril w oniere to e homogenou. he mimth etween experimentl n FE moel reult of 1.5 mm thik peimen how tht peimen thikne inree the mteril eome more heterogeneou in nture. herefore, for mll peimen teting the FE moel of one peimen hving le thn 1.5 mm thikne n preit loer reult to the experimentl one. It i lo evient from thi tuy tht the lo-iplement urve otine from iotropi fully tenile FE moe (FI) i loer to the experimentl urve. hi how tht tenile propertie re ominting in e of mll punh teting n one mteril ehve lmot iotropi in nture. IV. ONLUSION he eformtionl ehvior of ortil one w nlyze uing mll punh teting. he mll punh teting w onute on mll ortil one peimen of two ifferent thiknee (1. mm n 1.5 mm). he finite element imultion of mll punh tet w rrie out uing ABAQUS oftwre to ompre the lo-iplement ehvior of ortil one. he eformtionl ehvior of ortil one uner mll punh teting w moele uing trnverely iotropi well iotropi mteril propertie of one. Vriou e hve een inorporte in FE imultion of ortil one fter prtitione the mll retngulr peimen from the mile. enile n ompreive propertie otine from full ize tet hve WES 213

5 Proeeing of the Worl ongre on Engineering n omputer Siene 213 Vol II WES 213, Otoer, 213, Sn Frnio, USA een fe to the oftwre to perform the FE imultion. he FE reult of 1. mm thik peimen were foun to e in etter greement with the orreponing experimentl reult. he evition in FE n experimentl loiplement urve for 1.5 mm thik peimen w oniere to e ue to hierrhil n heterogeneou nture of ortil one. From thi invetigtion it w oerve tht iotropi tenile propertie re uffiient to etter imulte the mll punh teting of ortil one. REFERENES [1] N. Ski, N. Mtuhim,. Ikw, H. Ymmur, n A. Fuku, Orienttion of one minerl n it role in the niotropi mehnil propertie of one-trnverely niotropy, Journl of Biomehni, vol. 22, pp , [2] S. Weiner, n H. D. Wgner, he mteril one: truturemehnil funtion reltion, Ann Rev Mter Si, vol. 28, pp , [3] R. A. Roinon, n S. R. Elliot, he wter ontent of one: I. he m of wter inorgni rytl, orgni mtrix, n O2 pe omponent in unit volume of og one, Journl of Bone Joint Surgery, vol. 39 A, pp , [4] R. B. Mrtin, Poroity n peifi urfe of one. R ritil Review, [5] E. Luhinetti, ompoite moel of one propertie, in Bone Mehni Hnook, 2n e. h. 3, Bo Rton, E. FL: R Pre, 21, pp [6] J. MElhney, J. Fogle, E. Byr, n G. Wever, Effet of emlming on the mehnil propertie of eef one, J Appl Phyiol, vol. 19, pp , [7] R. W. Mlen, J. A. MGeough, M. B. Brker,. M. ourtrown, Age relte-hnge in the tenile propertie of ortil one: he reltive importne of hnge in poroity, minerliztion n mirotruture, J Bone Joint Surg Am, vol. 75A, pp , [8] F. G. Evn n M. Leow, Regionl ifferene in ome of the phyil propertie of the humn femur, J Appl Phyiol, vol. 3, pp , [9] D.. Reilly, A. H. Burtein, n V. H. Frnkel, he elti moulu for one, Journl of Biomehni, vol. 7, pp , [1] N. K. Shrm, D. K. Sehgl, n R. K. Pney, Stuie on lotionl vrition of her propertie in ortil one with Ioipeu her tet, Applie Mehni n Mteril, vol , pp , 212. [11] G. E. Lu, Review of mll peimen tet tehnique for irrition teting, Metllurgil rntion A, vol. 21A, pp , 199. [12] J. S. heon n I. S. Kim, Initil eformtion uring mll punh teting, Journl of eting n Evlution, vol. 24, pp , [13] J. M. Bik, J. Kme, n O. Buk, Smll punh tet evlution of inter-grnulr emrittlement of n lloy teel, Sript Metllurgi, vol. 17, pp , [14] M. P. Mnhn, A. S. Argon, n O. K. Hrling, he evelopment of miniturize ik en tet for the etermintion of pot irrition mehnil propertie, Journl of Nuter Mteril, vol , pp , [15] F. M. Hung, M. L. Hnilton, n G. L. Wire, Ben teting for miniture ik, Nuler ehnology, vol. 57, pp. 234, [16] N. K. Shrm, D. K. Sehgl, R. K. Pney n R. Pl, Finite element imultion of ortil one uner ifferent loing n niotropi yieling itution, Proeeing of Worl ongre on Engineering n omputer Siene 212, Sn Frnio, USA, vol. II, pp , 212. WES 213