Characterization and micromechanical modeling of the human cranial bone elastic properties

Abstract This paper is devoted to the experimental characterization and micromechanical modeling of the elastic behavior of the human cranial bone. Three points bending tests on the frontal, parietal and temporal bone specimens have been performed to determine their mechanical characteristics under quasi-static loading. It is shown that Young's modulus and the bending stiffness are significantly influenced by the bone morphology and orientation. The anisotropic bone elastic properties have been then estimated by means of the Mori–Tanaka homogenization scheme coupled to experimental measurements of structural anisotropy by microtomography techniques. The obtained micromechanical model has been implemented as an UMAT routine within the explicit dynamics code LS-DYNA© and applied successfully for the estimation of the mechanical properties of the human cranial frontal bone. The obtained numerical results show an overall good agreement when compared to the experimental data.

[1]  J. D. Eshelby.  The determination of the elastic field of an ellipsoidal inclusion, and related problems , 1957, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[2]  Jean Charles Gilbert,et al.  Numerical Optimization: Theoretical and Practical Aspects , 2003 .

[3]  F. Eckstein,et al.  Ct-based finite element models can be used to estimate experimentally measured failure loads in the proximal femur. , 2012, Bone.

[4]  Eric Markiewicz,et al.  Micromechanical Modeling of the Anisotropy of Elastic Biological Composites , 2009, Multiscale Model. Simul..

[5]  J. Mcelhaney,et al.  Mechanical properties on cranial bone. , 1970, Journal of biomechanics.

[6]  R. Hubbard,et al.  Flexure of layered cranial bone. , 1971, Journal of biomechanics.

[7]  K. Tanaka,et al.  Average stress in matrix and average elastic energy of materials with misfitting inclusions , 1973 .

[8]  S. Cowin,et al.  Dynamic permeability of the lacunar–canalicular system in human cortical bone , 2014, Biomechanics and modeling in mechanobiology.

[9]  J. D. Eshelby,et al.  The elastic field outside an ellipsoidal inclusion , 1959, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[10]  W. J. Whitehouse.  The quantitative morphology of anisotropic trabecular bone , 1974, Journal of microscopy.

[11]  J M Crolet,et al.  On the mechanical characterization of compact bone structure using the homogenization theory. , 1996, Journal of biomechanics.

[12]  P. Verschueren,et al.  The mechanical properties of cranial bone: the effect of loading rate and cranial sampling position. , 2009, Journal of biomechanics.

[13]  King H. Yang,et al.  Application of Optimization Methodology and Specimen-Specific Finite Element Models for Investigating Material Properties of Rat Skull , 2010, Annals of Biomedical Engineering.

[14]  Christian Hellmich,et al.  Mineral–collagen interactions in elasticity of bone ultrastructure – a continuum micromechanics approach , 2004 .

[15]  W. T. Dempster.  Correlation of types of cortical grain structure with architectural features of the human skull , 1967 .

[16]  R. Hill.  A self-consistent mechanics of composite materials , 1965 .

[17]  J. L. Wood,et al.  Dynamic response of human cranial bone. , 1971, Journal of biomechanics.

[18]  Caroline Deck,et al.  Finite-element models of the human head and their applications in forensic practice , 2008, International Journal of Legal Medicine.

[19]  Brittany Coats,et al.  Material properties of human infant skull and suture at high rates. , 2006, Journal of neurotrauma.

[20]  R. Mann,et al.  Characterization of microstructural anisotropy in orthotropic materials using a second rank tensor , 1984 .

[21]  Anne M.R. Agur,et al.  Grant's Atlas of Anatomy , 1943 .

[22]  Hakim Naceur,et al.  On the modeling and design of composite multilayered structures using solid-shell finite element model , 2013 .