Deformation of a Thin Bonded Transversely Isotropic Elastic Layer

Abstract

In this chapter we study frictionless contact problems for a thin transversely isotropic elastic layer bonded to a rigid substrate and indented by a smooth absolutely rigid punch under the assumption that the layer thickness is relatively small compared to the characteristic size of the contact area. We apply a perturbation technique to obtain asymptotic solutions of different degrees of accuracy and formulate simple mathematical models (called asymptotic models) to describe the deformational behavior of a bonded compressible elastic layer in the thin-layer approximation. In particular, the effects of unilateral contact interaction (with a priori unknown contact area) and the tangential displacements at the contact interface (taken into account in formulating the contact condition) are considered. It is shown that the case of an incompressible layer requires special consideration.