Eshelby problem of polygonal inclusions in anisotropic piezoelectric bimaterials

Abstract

This paper studies the two–dimensional Eshelby problem in anisotropic piezoelectric bimaterials. Assuming that the inclusion is an arbitrarily shaped polygon with uniform eigenstrain and eigenelectric fields, we derive the exact closed–form solution by integrating analytically the line–source Green functions in the corresponding bimaterials. The required line–source Green functions are obtained in terms of the Stroh formalism and include six different interface models. Since the induced elastic and piezoelectric fields due to the eigenstrain and eigenelectric fields are given in the exact closed form in terms of simple elementary functions, those due to multiple inclusions can be superposed together. Benchmark numerical examples are also presented for the induced elastic and piezoelectric fields within a square inclusion due to a uniform hydrostatic eigenstrain with the bimaterials being made of typical quartz and ceramic.