Axisymmetric indentation problem of a transversely isotropic elastic medium with surface stresses

Abstract

The frictionless contact problem between an axisymmetric rigid indenter and a layered transversely isotropic medium with surface stresses is considered. The contact pressure is represented as a product of two series based on the solutions of the bulk material and the elastic surface. By using Hankel transforms, the coefficients in the product-series representation are determined by the normal displacement condition inside the contact area and the finite-pressure condition at the contact edge. Taking the spherical indentation as a specific example, the effectiveness of the solution procedure is verified for various contact scenarios. Comparing with the Green’s function method, this solution procedure is not only computationally efficient but also may give the contact pressure in its analytical form. For some specific problems, the effects of the material anisotropy and the layer thickness on the contact process with surface stresses are investigated.