Devolution of Inhomogeneities in Bone Structure—Predictions of Adaptive Elasticity Theory

Abstract

In this paper we consider an initially inhomogeneous adaptive elastic body subjected to a steady homogeneous stress state. The adaptive elastic body, which is a model for living bone tissue, is inhomogeneous in both its anisotropic elastic properties and its density. The principal result of the paper is the determination of the devolution of the initially inhomogeneous body to a homogeneous body under the influence of the steady homogeneous stress state. A cylindrical body that is inhomogeneous along the axis of the cylinder, but homogeneous in each transverse plane of the cylinder, is used as an example. This cylindrical body is loaded by a steady uniform stress directed along the cylindrical axis. The temporal devolution of an inhomogeneity in the initial shape of a sine wave is illustrated. As time progresses the amplitude of the sine wave decreases, rapidly at first and then more slowly. As time becomes very large the sine wave becomes a straight line signifying that the cylinder has become homogeneous.