Generalized Continuum Theories: Application to Stress Analysis in Bone*

Abstract

Bone is a heterogeneous material with microstructural features. Continuum models of bone on the basis of classical elasticity ignore microstructure-related scale effects on the macroscopic mechanical properties. Consequently, these models do not provide a complete description of the mechanical behavior when the microstructural size of bone approaches the macroscopic length scale. Such effects are most pronounced near bone–implant interfaces and in areas of high strain gradients. This issue is investigated here by studying generalized continuum mechanics theories which account for the influence of microstructure-related scale effects on the macroscopic properties of bone. Furthermore, a two-dimensional finite element on the basis of the micropolar continuum theory is summarized. As a simple illustrative example, a bone–prosthesis configuration is analyzed. Results show that the stress concentrations in bone near the bone–prosthesis interface are substantially smaller with micropolar theory compared to classical theory of elasticity.