A powerful series solution of some Eshelby’s problems of a single smooth inclusion

Abstract

Except for elliptical inclusions, the solution of the anisotropic Eshelby’s problem has been limited to polygonal inclusion for a long time. In this paper, the anisotropic Eshelby’s problem of a smooth inclusion characterized by Laurent polynomials and undergoing nonuniform eigenstrain in a magneto-electro-elastic (MEE) plane is investigated. Under the framework of Stroh formalism, the multiphysical perturbance can be described by a set of eigenfunctions, which are analytical functions expressed through the Cauchy integrations along the inclusion’s boundaries in the transformed complex planes. A powerful series solution is provided in order to solve the Cauchy integration without material parameter constrains. And the method can be used to solve a smooth inclusion undergoing nonuniform eigenstrain in an anisotropic bimaterial plane or an isotropic disk.