Elastic Green's function for a composite solid with a planar interface

The elastic plane-strain Green's function is calculated for a general anisotropic composite solid with a plane interface and a line load parallel to the composite interface. The interface may be between two different solids or between different orientations of the same solid such as a grain boundary. The equations of elastic equilibrium are solved by the Fourier transform method. Analytical expressions are obtained for the Green's function in real as well as Fourier space. These expressions should be useful for calculations of elastic properties of a composite solid containing defects. Two sum rules are also derived for matrices which constitute the Green's function and the stress tensor. These sum rules can serve as numerical checks in detailed computer simulation calculations.