Three-dimensional dynamic Green’s functions in transversely isotropic bi-materials

By virtue of a complete representation using two displacement potentials, an analytical derivation of the elastodynamic Green’s functions for a linear elastic transversely isotropic bi-material full-space is presented. Three-dimensional point-load Green’s functions for stresses and displacements are given in complex-plane line-integral representations. The formulation includes a complete set of transformed stress–potential and displacement–potential relations, within the framework of Fourier expansions and Hankel integral transforms, that is useful in a variety of elastodynamic as well as elastostatic problems. For numerical computation of the integrals, a robust and effective methodology is laid out which gives the necessary account of the presence of singularities including branch points and pole on the path of integration. As illustrations, the present Green’s functions are analytically degenerated to the special cases such as half-space, surface and full-space Green’s functions. Some typical numerical examples are also given to show the general features of the bi-material Green’s functions.