Concentrated sources on the interface of diffusive bimaterial media: The steady-state deformation

Abstract

While the fundamental solutions of concentrated forces and dislocations in purely elastic media are available for various applications, solutions in the corresponding diffusive materials have seldom been derived due to the involved complexity. In this paper, in terms of the cylindrical system of vector functions and under the assumption of steady-state deformation, we derive analytically the elastic and diffusive fields induced by the concentrated forces and dislocations which are located on the interface of a transversely isotropic and diffusive bimaterial space. Solution of the concentrated diffusive source has been also derived. These solutions can further be reduced to the corresponding isotropic bimaterial case and the transversely isotropic full-space case. Based on the newly derived solutions, field quantities induced by different concentrated dislocation sources are presented numerically to demonstrate the effect of the diffusive coefficients, material heterogeneity, and dislocation types on the induced fields.