Preliminary Study on Mechanical Bone Remodeling Permitting Residual Stress

Remodeling is a critical feature of living tissue such as bone. From the mechanical viewpoint, remodeling is recognized as a regulation process of stress due to tissue growth and atrophy. The volumetric change of the bone tissue causes a nonuniform natural state. Because of the statical indeterminacy, residual stress may remain in the tissue even when all external forces are removed. Permitting the existence of the residual stress, a rate-type model is proposed for mechanical bone remodeling by means of volumetric growth/atrophy of the tissue. The rate of remodeling is expressed as a function of the local stress and its derivatives, seeking the equistress state. This does not refer to any goal stress specified a priori. The basic features of the proposed model are examined using a simple model of the diaphysial bone. A case study is conducted for a simplified tibia-fibula system, and it is demonstrated that the proposed model has the capability to describe the bone remodeling process qualitatively.