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Construction of the electroelastic Green's function of the hexagonal infinite medium and its application to inclusion problems

The absence of explicit Green's functions for piezoelectric media has hindered progress in the modeling of material properties of piezoelectric materials for a long time. Due to the importance of piezoelectrics in smart structures, the construction of explicit Green's functions for such materials is highly desirable. We introduce here a method of integral transformation to construct the electroelastic Green's function for a piezoelectric hexagonal infinitely extended medium in explicit compact form. This Green's function gives the elastic displacements and electric potentials caused by a unit point force and a unit point charge, respectively. This explicit form of the Green's function is convenient for many applications due to its natural representation in a tensor basis of hexagonal symmetry. For vanishing piezoelectric coupling the derived Green's function coincides with two well known results: Kroner's expression for the elastic Green's functional tensor is reproduced and the electric part then coincides with the electric potential caused by a unit point charge. For spheroidal inclusions having the same electroelastic characteristics and orientation as the hexagonal matrix the constructed Green's function is used to obtain the electroelastic analogue of Eshelby tensor in explicitly form.