Analytic Formulation of Anti-Plane Elastic Field for an Elliptical Inhomogeneity with Polynomial Eigenstrains in Anisotropic Materials

Abstract

This article presents a unified analytical solution for the anti-plane elastic field in an elliptical inhomogeneity with polynomial eigenstrains in anisotropic materials possessing an elastic plane of symmetry. The elastic field takes the form of a quadratic polynomial, with coefficients determined analytically based on the principle of minimum potential energy. Expressions for the elastic energy are given by means of complex representation and conformal transformation. The resulting solution is verified for the shear stress at the interface between the elliptical inhomogeneity and matrix. Numerical examples are given to illustrate the distributions of shear stress and strains at the interface.

Keywords:

• elliptic homogeneity
• polynomial eigenstrains
• complex function method
• anisotropic materials
• anti-plane deformation