Three-dimensional Green's functions in anisotropic piezoelectric bimaterials

In this paper, a recently proposed method by E. Pan and F.G. Yuan for the calculation of the elastic bimaterial Green's functions is extended to the analysis of three-dimensional Green's functions for anisotropic piezoelectric bimaterials. The method is based on the Stroh formalism and two-dimensional Fourier transforms in combination with Mindlin's superposition method. We first derive Green's functions in exact form in the Fourier transform domain. When inverting the Fourier transform, a polar coordinate transform is introduced so that the radial integral from 0 to +∞ can be carried out exactly. Therefore, the bimaterial Green's functions in the physical domain are derived as a sum of a full-space Green's function and a complementary part. While the full-space Green's function is in an explicit form, as derived recently by E. Pan and F. Tonon, the complementary part is expressed in terms of simple regular line integrals over [0, 2π] that are suitable for standard numerical integration. Furthermore, the present bimaterial Green's functions can be reduced to the special cases such as half-space, surface, interfacial, and full-space Green's functions. Uncoupled solutions for 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 with transversely isotropic and anisotropic material properties to verify the applicability of the technique. Certain interesting features associated with these Green's functions are observed and discussed, as related to the selected material properties.