Elastic Green’s function for a bimaterial composite solid containing a free surface normal to the interface

Abstract

Elastic plane strain Green’s function is calculated for an anisotropic bimaterial composite solid containing a free surface normal to the interface. An exact integral representation is obtained for the Green’s function, which is evaluated numerically. The integral is also evaluated analytically, which gives a series representation for the Green’s function. The singularities in the stress field associated with the presence of the free surface are identified and discussed. These singularities can be of the type r^-δ, ln(r) as well as higher powers of ln(r), where δ is between 0 and 1 and r is the radial distance from the intersection of the free surface and the interface. The stress field may also contain an oscillatory factor of the type exp[ιg ln (r)] where g depends upon the material parameters of the two solids. For illustration, the formalism is applied to a cubic solid containing a Σ-5 grain boundary.