Eshelby’s inclusion and dislocation problems for an isotropic circular domain bonded to an anisotropic medium

Abstract

This paper mainly investigates a two-dimensional Eshelby’s problem of an inclusion of arbitrary shape embedded within an isotropic elastic circular domain which is perfectly bonded to the surrounding infinite anisotropic elastic medium. The Muskhelishvili’s complex variable formulation in isotropic elasticity and the Stroh formalism in anisotropic elasticity are employed to derive a very simple and explicit analytical solution. The coefficients in the derived six analytic functions within the isotropic circular domain only contain the Barnett-Lothe tensors for the surrounding anisotropic medium and the shear modulus and Poisson’s ratio for the isotropic circular domain. Several examples are discussed in detail to demonstrate and validate the obtained analytical solution. By using a similar method, we also investigate a line dislocation located in an isotropic circular cylinder which is perfectly bonded to the surrounding anisotropic medium and derive the image force acting on the line dislocation.