Electroelastic Green's functions for transversely isotropic piezoelectric media and their application to the solution of inclusion and inhomogeneity problems

Abstract

Explicit formula are obtained for the coupled electroelastic Green's functions for a transversely isotropic piezoelectric medium. Four Green's functions are seen to exist which represent the coupled elastic and electric response to an applied unit point force or point electric charge. The resulting expressions are obtained by utilizing the contour integral representation of the Green's functions derived by Deeg [1]. The evaluation of the contour integrals then follows Willis' work [2] in anisotropic elasticity. When piezoelectric coupling is absent, the results reduce to those for uncoupled elasticity and electrostatics. The use of the electroelastic Green's functions in the analysis of piezoelectric inclusion and inhomogeneity problems is then illustrated. Finally, explicit expressions are obtained for a set of four tensors analogous to Eshelby's tensor for elastic inclusions. These expressions can be readily utilized in the solution of numerous problems in the micromechanics of piezoelectric solids such as defects, fracture mechanics, and composite materials.