10 - Integrated Remodeling to Fatigue Damage Model of Bone

Abstract

Bone is a living tissue that continually undergoes damage under normal everyday mechanical loadings. It maintains its structural integrity by a continuous process of damage detection and repair, and by adaptation to changes in the mechanical environment. These adaptive changes are regulated by the so-called process of bone remodeling. The aim of the current chapter is to develop an integrated remodelingto-fracture model to simulate the bone remodeling process considering the anisotropy of trabecular bone. For this purpose, models for density of continuum solid bodies are developed in the framework of the thermodynamics of irreversible processes, considering bone elasticity with damage properties, in which the damage stimuli is incorporated. The asymptotic homogenization technique is involved to derive the effective anisotropic continuum mechanical properties of the trabecular bone from an initially discrete structure representative of femur bone microstructure, consisting of a piling up of hexagonal planar cells. As a consequence, relationships are established between the apparent density of bone and its effective anisotropic properties, that is the elastic and shear moduli and Poisson’s ratio. Damage is directly incorporated into the effective density, the evolution of which is computed versus time. This formalism is involved to simulate bone remodeling for 2D geometries in the context of damaged anisotropic bone elasticity, showing the influence of the external mechanical stimuli on the evolution of the density of bone.