Abstract
This chapter introduces Eshelby's equivalent inclusion method (EIM) for an ellipsoidal inhomogeneity in an infinite domain and generalizes it for polyhedral inhomogeneities. It provides the exact solution for a single ellipsoidal particle in an infinite domain but generates an approximate one for the case of multiple particles. They can be extended to their 2D counterparts, elliptical and polygonal inhomogeneities, respectively. Particularly, for polyhedral particles, the analytical solution with polynomial eigenstrains is not effective considering the singularity effects in the neighborhood of the vertices. Particle discretization is introduced to obtain higher accuracy. To show the boundary effect, the Green's function for a semi-infinite domain is used in the EIM to study the local field for particles at different distances to the surface.
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