Three-dimensional Green's functions in anisotropic piezoelectric bimaterials

In this paper, a recently proposed method by E. Pan and F.G. Yuan (Int. J. Solids Struct., 2000) for the calculation of the elastic bimaterial Green's functions is extended to the analysis of three-dimensional Green's functio ns for anisotropic piezoelectric bimaterials. The method is based on the St roh formalism and two-dimensional Fourier transforms in combination with Mi ndlin's superposition method. We first derive Green's functions in exact fo rm in the Fourier transform domain. When inverting the Fourier transform, a polar coordinate transform is introduced so that the radial integral from 0 to +infinity can be carried out exactly. Therefore, the bimaterial Green' s functions in the physical domain are derived as a sum of a full-space Gre en's function and a complementary part. While the full-space Green's functi on is in an explicit form, as derived recently by E, Pan and F. Tonon (Int. J. Solids Struct., 37 (2000): 943-958), the complementary part is expresse d in terms of simple regular line integrals over [0, 2 pi] that are suitabl e for standard numerical integration. Furthermore, the present bimaterial G reen's functions can be reduced to the special cases such as half-space, su rface, interfacial, and full-space Green's functions, Uncoupled solutions f or the purely elastic and purely electric case can also be simply obtained by setting the piezoelectric coefficients equal to zero. Numerical examples for Green's functions are given for both half-space and bimaterial cases w ith transversely isotropic and anisotropic material properties to verify th e applicability of the technique. Certain interesting features associated w ith these Green's functions are observed and discussed, as related to the s elected material properties. (C) 2000 Elsevier Science Ltd. All rights rese rved.