Micromechanical Modeling of the Anisotropy of Elastic Biological Composites

Abstract

In this paper, a Mori–Tanaka micromechanical modeling of effective elastic properties of trabecular bone is coupled with experimental measurements of morphology obtained from X-ray microtomography. The principle of modeling is based on the Eshelby and Hill polarization tensors of isolated ellipsoidal inclusions embedded in an infinite matrix. The problem is entirely geometrized and is treated in terms of averages of Walpole's components of the fourth-order tensors describing the problem. The structural anisotropy of trabecular bone was determined in three-dimensional space by means of the mean intercept length method and expressed by a fabric tensor, which is a second rank tensor describing the orientation distribution of inclusions volume fractions and degree of anisotropy of trabecular bone. Modeling results showed the high effects of the aspect ratio and orientation distribution of pores on the effective elastic properties of trabecular bone.