On a hierarchy of effective models for the biomechanics of human compact bone tissue

Abstract

We derive a hierarchy of effective models that can be used to model the biomechanics of human compact bone taking into account scale-size effects observed experimentally. The classification of the effective models depends on the hierarchy of four characteristic lengths: The size of the heterogeneities, two intrinsic lengths of the constituents, and the overall characteristic length of the domain. Depending on the different scale interactions between the size of the heterogeneities, the two intrinsic lengths of the constituents, and the characteristic length of the domain we obtain either an effective Cauchy continuum or an effective Cosserat continuum. The passage to the limit relies on suitable use of the periodic unfolding operator. Moreover, we perform numerical simulations to validate our results.

Analysis of micropolar elastic multi-laminated composite and its application to bioceramic materials for bone reconstruction

“…For example, finite element techniques have been implemented to determine the effective properties of micropolar multi-layered composites in studies discussed in [26][27][28]. Multi-scale homogenization approaches have been carried out to analyze micropolar heterogeneous structures in studies discussed in [29][30][31][32], among others. Despite the realized works in these fields, more analyses are required on this topic.…”