On the Displacement of a Two-Dimensional Eshelby Inclusion of Elliptic Cylindrical Shape

Abstract

In a companion paper,ff2 we have obtained the closed-form solutions to the stress and strain fields of a two-dimensional Eshelby inclusion. The current work is concerned with the complementary formulation of the displacement. All the formulae are derived in explicit closed-form, based on the degenerate case of a three-dimensional (3D) ellipsoidal inclusion. A benchmark example is provided to validate the present analytical solutions. In conjunction with our previous study, a complete elasticity solution to the classical elliptic cylindrical inclusion is hence documented in Cartesian coordinates for the convenience of engineering applications.