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2013 | 11 | 6 | 760-778
Tytuł artykułu

Analysis of two colliding fractionally damped spherical shells in modelling blunt human head impacts

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The collision of two elastic or viscoelastic spherical shells is investigated as a model for the dynamic response of a human head impacted by another head or by some spherical object. Determination of the impact force that is actually being transmitted to bone will require the model for the shock interaction of the impactor and human head. This model is indended to be used in simulating crash scenarios in frontal impacts, and provide an effective tool to estimate the severity of effect on the human head and to estimate brain injury risks. The model developed here suggests that after the moment of impact quasi-longitudinal and quasi-transverse shock waves are generated, which then propagate along the spherical shells. The solution behind the wave fronts is constructed with the help of the theory of discontinuities. It is assumed that the viscoelastic features of the shells are exhibited only in the contact domain, while the remaining parts retain their elastic properties. In this case, the contact spot is assumed to be a plane disk with constant radius, and the viscoelastic features of the shells are described by the fractional derivative standard linear solid model. In the case under consideration, the governing differential equations are solved analytically by the Laplace transform technique. It is shown that the fractional parameter of the fractional derivative model plays very important role, since its variation allows one to take into account the age-related changes in the mechanical properties of bone.
Wydawca

Czasopismo
Rocznik
Tom
11
Numer
6
Strony
760-778
Opis fizyczny
Daty
wydano
2013-06-01
online
2013-10-09
Twórcy
  • Voronezh State University of Architecture and Civil Engineering, 84, 20-letija Oktjabrja Str., 394006, Voronezh, Russia, yar@vgasu.vrn.ru
  • Voronezh State University of Architecture and Civil Engineering, 84, 20-letija Oktjabrja Str., 394006, Voronezh, Russia, mvs@vgasu.vrn.ru
Bibliografia
  • [1] M. Craig, C. Bir, D. Viano, S. Tashman, J. Biomech. 41, 2972 (2008) http://dx.doi.org/10.1016/j.jbiomech.2008.07.020[Crossref]
  • [2] W. Grimal, S. Naili, A. Watzky, J. Biomech. 38, 1247 (2005) http://dx.doi.org/10.1016/j.jbiomech.2004.06.010[Crossref]
  • [3] F.A. Bandak, R.E. Tannous, T. Toridis, Int. J. Solids Struct. 38, 1681 (2001) http://dx.doi.org/10.1016/S0020-7683(00)00129-3[Crossref]
  • [4] H. Kimpara et al., ASME J. Biomech. Eng. 128, 772 (2006) http://dx.doi.org/10.1115/1.2264394[Crossref]
  • [5] Z. Li et al., Annals Biomed. Eng. 34, 1452 (2006) http://dx.doi.org/10.1007/s10439-006-9145-1[Crossref]
  • [6] G.J. Dakin et al., ASME J. Biomech. Eng. 123, 218 (2001) http://dx.doi.org/10.1115/1.1372321[Crossref]
  • [7] D.W. van Lopik, M. Acar, Proc. Inst. Mech. Engs. Part K - J. Multi-Body Dyn. 221, 199 (2007) http://dx.doi.org/10.1243/09544100JAERO119[Crossref]
  • [8] S. Majumder, A. Roychowdhury, S. Pal, Int. J. Vehicle Safety 3, 117 (2008) http://dx.doi.org/10.1504/IJVS.2008.022213[Crossref]
  • [9] D.C. Viano, I.V. Lau, C. Asbury, A.I. King, P. Begeman, Accident Anal. Prevention 21, 553 (1989) http://dx.doi.org/10.1016/0001-4575(89)90070-5[Crossref]
  • [10] K. Kobayashi, Y. Tanabe, T. Hara, Trans. Japan Soc. Mech. Engs Part A 63, 2624 (1997) http://dx.doi.org/10.1299/kikaia.63.2624[Crossref]
  • [11] K. Murata, Y. Minakuchi, M. Nakamura, H. Yamada, K. Oshiba, Trans. Jap. Soc. Mech. Engs Part A 74, 1174 (2008) http://dx.doi.org/10.1299/kikaia.74.1174[Crossref]
  • [12] A.R. Kemper, C. McNally, S.M. Duma, Biomed. Sci. Instrum. 45, 395 (2009)
  • [13] W. Goldsmith, In: Y.C. Fung, N. Perrone, M. Anliker (Eds.), Biomechanics: Its Foundations and Objectives (Prentice-Hall, Englewood Cliffs, New Jersey, 1972)
  • [14] V.H. Kenner, W. Goldsmith, J. Biomech, 6, 1 (1973) http://dx.doi.org/10.1016/0021-9290(73)90032-8[Crossref]
  • [15] T.B. Khalil, D.C. Viano, J. Sound Vibr. 63, 351 (1979) http://dx.doi.org/10.1016/0022-460X(79)90679-5[Crossref]
  • [16] T.B. Khalil, D.C. Viano, J. Sound Vibr. 82, 95 (1982) http://dx.doi.org/10.1016/0022-460X(82)90545-4[Crossref]
  • [17] W.N. Hardy, T.B. Khalil, A.I. King, Int. J. Impact Eng. 15, 561 (1994) http://dx.doi.org/10.1016/0734-743X(94)80034-7[Crossref]
  • [18] Z. Zonga, H. P. Leeb, C. Lu, J. Biomech. 39, 284 (2006) http://dx.doi.org/10.1016/j.jbiomech.2004.11.015[Crossref]
  • [19] R. Willinger, H. S. Kang, B. Diaw, Annals Biomed. Eng. 27, 403 (2002) http://dx.doi.org/10.1114/1.165[Crossref]
  • [20] J.S. Ruan, T.B. Khalil, A.I. King, J. Biomed. Eng. 116, 44 (1994)
  • [21] X. Yue, L. Wang, F. Zhou, J. Univ. Science Techn. Beijing 15, 202 (2008) (in Chinese) http://dx.doi.org/10.1016/S1005-8850(08)60039-0[Crossref]
  • [22] P.G. Young, J. Sound Vibr. 267, 1107 (2003) http://dx.doi.org/10.1016/S0022-460X(03)00200-1[Crossref]
  • [23] E.A.C. Johnson, P.G. Young, J. Biomech. 38, 39 (2005) http://dx.doi.org/10.1016/j.jbiomech.2004.03.018[Crossref]
  • [24] S.W. Gong, H.P. Lee, C. Lu, IEEE Trans. Biomed. Eng. 54, 5 (2007) http://dx.doi.org/10.1109/TBME.2006.889158[Crossref]
  • [25] S.M. Baghaei, A.M. Sadegh, S.M. Rajaai, Proc. ASME Int. Mech. Engs Congr. Exp. 2, 679 (2009)
  • [26] S.M. Baghaei, A.M. Sadegh, S.M. Rajaai, IFMBE Proc. 24, 283 (2009) http://dx.doi.org/10.1007/978-3-642-01697-4_99[Crossref]
  • [27] P.G. Young, L. Beldie, B. Walker, R.T. Cotto, IFMBE Proc. 24, 293 (2009) http://dx.doi.org/10.1007/978-3-642-01697-4_102[Crossref]
  • [28] S.M. Baghaei, A.M. Sadegh, Int. J. Solids Struct. 48, 3257 (2011) http://dx.doi.org/10.1016/j.ijsolstr.2011.07.016[Crossref]
  • [29] J. Zhang, N. Yoganandan, F.A. Pintar, Annals of Advances in Automotive Medicine, 53rd Annual Scient. Conf., 249 (2009)
  • [30] Y. Chen, M. Ostoja-Starzewski, Acta Mech. 213, 155 (2010) http://dx.doi.org/10.1007/s00707-009-0274-0[Crossref]
  • [31] T.K. Chang, Y.A. Rossikhin, M.V. Shitikova, C.K. Chao, In: G.C. Sih, C.K. Chao (Eds.), Proc. of Meso 2010 - Multiscaling of Synthetic and Natural Systems with Self-Adaptive Capability, June 6–10, 2010, Taipei, Taiwan, (NTUST, Taipei, 2010)
  • [32] T.K. Chang, Y.A. Rossikhin, M.V. Shitikova, C.K. Chao, Theor. Appl. Fract. Mech. 56, 148 (2011) http://dx.doi.org/10.1016/j.tafmec.2011.11.003[Crossref]
  • [33] M. Heydari, S. Jani, Acta Bioeng. Biomech. 12, 47 (2010) [PubMed]
  • [34] Y.H. An, R.A. Draughn (Eds), Mechanical Testing of Bone and the Bone-Implant Interface (CRC Press, Boca Raton, 2000)
  • [35] N. Sakaki, In: Y.H. An, R.A. Draughn (Eds), Mechanical Testing of Bone and the Bone-Implant Interface (CRC Press, Boca Raton, 2000)
  • [36] J.D. Currey, J. Exper. Biol. 43, 279 (1965)
  • [37] G.W. Scott Blair, An Introduction to Biorheology (Elsevier, Amsterdam - Oxford - New York, 1974)
  • [38] X.H. Zhu, X. Dong, L. Liu, W.C. Xiu, Chinese J. Biomed. Eng. 12, 35 (1993) (in Chinese)
  • [39] J.G. Liu, M.Y. Xu, Chinese J. Biomed. Eng. 24, 12 (2005) (in Chinese)
  • [40] J.G. Liu, M.Y. Xu, Mech. Time-Dependent Mat. 10, 263 (2006) http://dx.doi.org/10.1007/s11043-007-9022-9[Crossref]
  • [41] N. Sebaa, Z.E.A. Fellah, W. Lauriks, C. Depollier, Signal Processing 86, 2668 (2006) http://dx.doi.org/10.1016/j.sigpro.2006.02.015[Crossref]
  • [42] Yu.A. Rossikhin, M.V. Shitikova, Appl. Mech. Reviews 50, 15 (1997) http://dx.doi.org/10.1115/1.3101682[Crossref]
  • [43] Yu.A. Rossikhin, M.V. Shitikova, Appl. Mech. Reviews 63, 010801-1 (2010)
  • [44] T.F. Nonnenmacher, R. Metzler, In: R. Hilfer (Ed.), Applications of Fractional Calculus in Physics (World Scientific, Singapore-New Jersey-London-Hong Kong, 2000)
  • [45] R.L. Magin, Critical Reviews Biomed. Eng. 32, 1 (2004) http://dx.doi.org/10.1615/CritRevBiomedEng.v32.10[Crossref]
  • [46] D. Baleanu, K. Diethelm, E. Scalas, J.J. Trujillo, Fractional Calculus. Models and Numerical Methods (World Scientific, New Jersey-London-Singapore-Beijing-Shanghai-Hong Kong-Taipei-Chennai, 2012)
  • [47] D. Baleanu, J.A.T. Machado, A. Luo, Fractional Dynamics and Control (Springer, Berlin-Heidelberg, 2012) http://dx.doi.org/10.1007/978-1-4614-0457-6[Crossref]
  • [48] V.D. Djordjevic, J. Jaric, B. Fabry, J. Fredberg, D. Stamenovic, Annals Biomed. Eng. 31, 692 (2003) http://dx.doi.org/10.1114/1.1574026[Crossref]
  • [49] T.C. Doehring, A.D. Freed, E.O. Carew, I. Vesely, J. Biomech. Eng. 127, 700 (2005) http://dx.doi.org/10.1115/1.1933900[Crossref]
  • [50] D. Craiem, R.L. Armentano, Biorheology 44, 251 (2007) [PubMed]
  • [51] L.M. Petrovic, D.T. Spasic, T.M. Atanackovic, Dentin Materials 21, 125 (2005) http://dx.doi.org/10.1016/j.dental.2004.01.004[Crossref]
  • [52] A.D. Freed, K. Diethelm, Biomech. Mod. Mechanobiol. 5, 203 (2006) http://dx.doi.org/10.1007/s10237-005-0011-0[Crossref]
  • [53] A.D. Freed, K. Diethelm, Fractional Calculus Appl. Anal. 10, 219 (2007)
  • [54] M. Zhang et al., Ultrasound Med. Biology 34, 1033 (2008) http://dx.doi.org/10.1016/j.ultrasmedbio.2007.11.024[Crossref]
  • [55] S. Hodis, M. Zamir, J. Biomech. 42, 1010 (2009) http://dx.doi.org/10.1016/j.jbiomech.2009.02.010[Crossref]
  • [56] D. Craiem, R.L. Magin, Phys. Biology 7, 013001 (2010) http://dx.doi.org/10.1088/1478-3975/7/1/013001[Crossref]
  • [57] F.C. Merala, T.J. Roystona, R. Magin, Commun. Nonlinear Sci. Num. Simul. 15, 939 (2010) http://dx.doi.org/10.1016/j.cnsns.2009.05.004[Crossref]
  • [58] X.H. Zhu, J. Chen, D. Shi, G. Wu, Natural Science J. Jilin Univ. Techn. 4, 111 (1987) (in Chinese)
  • [59] Yu.A. Rossikhin, M.V. Shitikova, J. Sound Vibr. 330, 1985 (2011) http://dx.doi.org/10.1016/j.jsv.2010.11.010[Crossref]
  • [60] Yu.A. Rossikhin, M.V. Shitikova, Acta Mech. 189, 87 (2007) http://dx.doi.org/10.1007/s00707-006-0412-x[Crossref]
  • [61] Yu.A. Rossikhin, M.V. Shitikova, In: Proc. ASME 2012 International Mechanical Engineering Congress & Exposition IMECE2012, Nov. 9–15, 2012, Houston, Texas, USA (ASME Publisher, 2012)
  • [62] Yu.A. Rossikhin, M.V. Shitikova, Shock Vibr. Digest 39, 273 (2007) http://dx.doi.org/10.1177/0583102407080410[Crossref]
  • [63] T.Y. Thomas, Plastic Flow and Fracture in Solids (Academic Press, New York, 1961)
  • [64] X. Wang, R.W. Osborn, J.C. Wolf, S. Puram, Agerelated changes in the mechanical properties of interstitial bone tissues, In: Proc. 50th Annual Meeting of the Orthopaedic Research Society, March 7–10, 2004, San Francisco, Paper No. 0037
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_2478_s11534-013-0194-4
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