Interface circular inclusion under mixed conditions of interaction with a piecewise homogeneous transversally isotropic space

Abstract

We reduce the problem of a circular absolutely rigid inclusion of arbitrary shape that is under conditions of complete adhesion to one transversally isotropic half-space and under conditions of smooth contact with another transversally isotropic half-space to a system of two-dimensional singular integral equations. We obtain solutions of this system in an explicit form, which enables us to determine the stress field and the field of displacements in the vicinity of the inclusion under arbitrary load. Dependences of translational and circular displacements of the inclusion on the resultant loads, principal moments, and elastic properties of the half-spaces are determined. We investigate the asymptotics of stresses in the vicinity of the inclusion and determine the directions of the largest and smallest stress concentration.