Closed-form Green's functions for transversely isotropic bi-solids with a slipping interface

Abstract

Green's functions are obtained in exact closed-forms for the elastic fields in bi-material elastic solids with slipping interface and differing transversely isotropic properties induced by concentrated point and ring force vectors. For the concentrated point force vector, the Green functions are expressed in terms of elementary harmonic functions. For the concentrated ring force vector, the Green functions are expressed in terms of the complete elliptic integral. Numerical results are presented to illustrate the effect of anisotropic bi-material properties on the transmission of normal contact stress and the discontinuity of lateral displacements at the slipping interface. The closed-form Green's functions are systematically presented in matrix forms which can be easily implemented in numerical schemes such as boundary element methods to solve elastic problems in computational mechanics.