Three-dimensional Green's functions in anisotropic bimaterials

In this paper, three-dimensional Green's functions for anisotropic bimateri als are studied based on Stroh formalism and two-dimensional Fourier transf orms. Although the Green's functions can be expressed exactly in the Fourie r transform domain, it is difficult to obtain the explicit expressions of t he Green's functions in the physical domain due to the general anisotropy o f the material and a geometry plane involved. Utilizing Fourier inverse tra nsform in the polar coordinate and combining with Mindlin's superposition m ethod, the physical-domain bimaterial Green's functions are derived as a su m of a full-space Green's function and a complementary part. While the full -space Green's function is in an explicit form, the complementary part is e xpressed in terms of simple regular line-integrals over [0, 2 pi] that are suitable for standard numerical integration. Furthermore, the present bimat erial Green's functions can be reduced to the special cases such as half-sp ace, surface, interfacial, and full-space Green's functions. Numerical exam ples are given for both half-space and bimaterial cases with isotropic, tra nsversely isotropic, and anisotropic material properties to verify the appl icability of the technique. For the half-space case with isotropic or trans versely isotropic material properties, the Green's function solutions are i n excellent agreement with the existing analytical solutions. For anisotrop ic half-space and bimaterial cases, numerical results show the strong depen dence of the Green's functions on the material properties. (C) 2000 Elsevie r Science Ltd. All rights reserved.