A three-scale identification of orthotropic properties of trabecular bone

Abstract

The bone is a hierarchically structured material with mechanical properties depending on its architecture at all scales. In human bodies, the bone consists of three types: Cortical bone, trabecular bone and marrow. It has been shown that the mechanical properties of the bone vary at different structural scales ( Rho et al. 1998 ). Therefore, in order to find the macroscopic properties of the bone, it is important to consider all of these scales. Many researchers have been investigated in this field, but the behaviour of the bone materials are modeled at different scales separately. Structurally, bone is considered like a composite material with a complex structure. For simplicity, many studies consider an isotropic linear elastic behaviour ( Sansalone et al. 2010; Hambli et al. 2010 ). In other research, several authors simulate bone as anisotropic behaviour ( Martinez-Reina et al. 2009; Doblare et al. 2002 ). To predict the orthotropic properties at different scales, Hamed et al. (2012) used homogenization approach. Elastic properties of trabecular bone are calculated at each structural level, from nanoscale to mesoscale. In the analysis, results from a lower level are used as inputs for a higher level. In the same way, Vaughan et al. (2012) proposed a three scale homogenisation scheme to estimate the effective properties of trabecular and cortical bone, based on finite element models. The objective of this study is to develop a multiscale approach that can incorporate multiscale variability in both bone composition and organization to predict the orthotropic behaviour.