Green’s function of anisotropic elastic solids with piezoelectric or magneto-electro-elastic inclusions

Green’s function for a two-dimensional anisotropic elastic solid containing a rigid or elastic inclusion has been previously explored. According to the special feature of Stroh formalism for two-dimensional anisotropic elasticity, the same mathematical form of Green’s function can be extended to cases with piezoelectric and magneto-electro-elastic materials by expanding the related matrix dimension. In this paper, we show that some important constant terms are missing in the existing Green’s functions and the solutions should be corrected to ensure the displacement and traction continuity across the inclusion interface. Besides the necessary analytical check, a further verification is provided by applying the corrected Green’s functions to the problems of crack-inclusion interaction. We consider that the cracks exist in smart materials made by composites embedded with piezoelectric and/or magneto-electro-elastic sensors and actuators. Since the anisotropic elastic, piezoelectric and magneto-electro-elastic materials exist simultaneously, an adaptable adjustment technique is proposed. With this technique, the dislocation superposition method and boundary-based finite element methods developed previously for the problems with a single material type can now be extended to study the coupled-field interaction problems.