Generalized continuum theories:Application to stress analysis in bone

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.