The Axisymmetric Contact Problem of a Transversely Isotropic Layer Subjected to a Tensile Stress Applied over a Circular Region

Abstract

We study an axisymmetric contact problem of a transversely isotropic layer subjected to a tensile stress applied over a circular hole of a rigid plate. The problem is equivalent to a mixed boundary-value problem of the theory of elasticity, and an exact solution is obtained through an infinite system of simultaneous equations. Convergence can be achieved using 8 terms of the series. Significant effects of the material anisotropy and the layer thickness on the stress fields are demonstrated with numerical results. The problem is applied to a biomechanical model of an articulating joint which assumes that an articular cartilage is a transversely isotropic layer and a subchondral bone is a rigid foundation. Numerical examples of the normal displacement in the circular hole for anisotropic cartilage material property are also presented.