Some New Three-Dimensional Green's Functions in Antisotropic Piezoelectric Bimaterials

Abstract

In this paper, we derive three-dimensional Green’s functions of point-force/pointcharge in anisotropic and piezoelectric bimaterials for six different interface models. Mechanically, the six interface models are either in perfect or smooth contact along the interface; electronically, they can be closed, open interface, or with continuous electrical potential and normal electrical displacement component along the interface. By introducing certain modified bimaterial Stroh matrices, along with the extended Stroh formalism and the Mindlin’s superposition method, the bimaterial Green’s functions for the six interface conditions are expressed in terms of a concise and mathematically similar uniform form. That is, the physical-domain bimaterial Green’s functions can all be expressed as a sum of a homogeneous full-space Green’s function in an explicit form and a complementary part in terms of simple line-integrals over [0, π] suitable for standard numerical integration. Furthermore, utilizing a direct connection between the 2D and 3D Stroh matrices observed in this paper, the corresponding 2D bimaterial Green’s functions are also derived, in exact-closed form, for the six interface conditions. Based on the bimaterial Green’s functions, the effects of different interface conditions on the mechanical and electrical fields are discussed. It is noted that only the complementary part of the solution contributes to the differences of the mechanical and electrical fields arising from different interface conditions. Also, numerical examples are presented for the Green’s functions in the bimaterials made of two half-spaces with two typical piezoelectric materials, quartz and ceramic. Certain new features are observed which could be of great interest to the design of piezoelectric composites and to the numerical modeling of strained quantum devices using the boundary element method.