Evaluation of the Eshelby solution for the ellipsoidal inclusion and heterogeneity

Abstract

We present a MATLAB code that evaluates the quasi-static elastic displacement strain and stress fields for the ellipsoidal inclusion and heterogeneity, the Eshelby solution. We first give an introduction to the underlaying inclusion problem. Then we describe the Eshelby solution for the elastic field inside and outside an ellipsoidal inclusion. We introduce the equivalency between the inclusion and inhomogeneity problems and elaborate the code's functionalities. Finally, we make the ellipsoidal inclusion undergo a series of geometrical transformations to emulate a spheroid inclusion, a 2D elliptical void, and a planar crack for which the surrounding elastic field is either known or accurately approximated. By comparing the Eshelby solution against those known solutions, we conclude that the code is valid. By these emulations, we show that the Eshelby solution can encompass many special problems in a unified form.