Construction of the Electroelastic Green's Function of the Hexagonal Infinite Medium and its Application to Inclusion Problems

摘要

The absence of explicit Green's functions for piezoelectric media has hindered progress in the modelling of mateiral properties of piezoelectric materials for a long time. Due to the improtance 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 (4 x 4) Green's function for a piezoelectric hexagonal (transversely isotropic) infinitely extended medium in explicit compact form.~7 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 applciations due to its natural representation is a tensor basis of hexagonal symmetry. for vanishing piezoelectric coupling the derived Green's function coincides with two well known results: Kroener's expression for the (3 x 3) elastic green's function tensor~3 is reproduced and the electric part then coincides with hte electric potnetial (solution of Poison equation0 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 explicit form.