The Derivation of Elastic Fields of a Curvilinear Inclusion

The disturbed elastic fields of a curvilinear inclusion in an isotropic elastic plane are investigated analytically by a newly proposed technique. The boundary of the inclusion is characterized by arbitrary Laurent polynomials in the 2D Cartesian coordinate system, and constant eigenstrains are considered to occur in the inclusion. Based on the irreducible decomposition of an arbitrary tensor, the Eshelby tensor is attributed to two integrals on the curved boundary of the inclusion. The analytical solutions for the induced stress and displacement fields outside the inclusion domain are explicitly derived by utilizing the newly developed technique, including the salient features of the Faber polynomials. Examples show the efficiency of the technique in this paper.