Efficient interpolation algorithm of electro-elastic Green's function for boundary integral equation method and Eshelby inclusion problem

Abstract

This study proposes an efficient interpolation algorithm for electro-elastic Green's functions and its derivatives. The extended concept of the interior and exterior point Eshelby tensor and its application are also presented. The computation efficiency of Green's functions in the boundary integral equation method and Eshelby inhomogeneity problem are greatly improved by the efficient interpolation of Green's functions, where the relevant tables of Green's functions are preliminarily computed using spherical coordinates. The validity of the interpolated electro-elastic Green's functions is tested by comparing the results to those of the effective electro-elastic moduli deduced from the Mori–Tanaka theory, the boundary integral equation method, and the extended concept of interior and exterior Eshelby tensor.