Green's function in plane anisotropic bimaterials with imperfect interface

Abstract

The fundamental solutions or Green's functions for 2D or 3D anisotropic media with imperfect interface remain a challenging problem. In this paper, a general method is presented for the rigorous solution for the 2D Green's function in an anisotropic elastic bimaterial subject to a line force or a line dislocation. Most significant is the fact that the bonding along the bimaterial interface is considered to be homogeneous imperfect. Specifically, the tractions are continuous but the displacements are discontinuous and proportional, in terms of interface stiffness parameters, to their respective traction components. Using complex variable techniques, the basic boundary-value problem for two analytic vector functions is reduced to a coupled linear first-order differential equation for a single analytic vector function defined in the lower half space. The coupled linear differential equation for the single analytic vector function can be subsequently decoupled into three independent linear first-order differential equations for three newly defined analytic functions. Closed-form solutions for the 2D Green's function are derived in terms of the exponential integral. Unlike previous works which involve some sort of inverse transform method to obtain the physical quantities from the transform domain, the key feature of the present method is that the physical quantities can be readily calculated without the need to perform any inverse transform operations.