IMAGE SINGULARITIES OF GREEN'S FUNCTIONS FOR ANISOTROPIC ELASTIC HALF-SPACES AND BIMATERIALS
Thomas C. T. Ting · The Quarterly Journal of Mechanics and Applied Mathematics · 1992
Using Stroh's formalism, simple explicit expressions of Green's functions for anisotropic elastic half-spaces and bimaterials subject to line forces and line dislocations are presented. One of the novel features is that, knowing the Green's function for an infinite space, Green's functions for half-spaces and bimaterials can be written down immediately with very little derivation. The other novel feature is the physical interpretations of Green's functions. The Green's function for a half-space consists of ten Green's functions for the infinite space. One of the ten Green's functions has its singularities located in the half-space where they are prescribed. The other nine represent image singularities which are located outside the half-space not occupied by the material. The locations of the nine image singularities as well as the nature of the singularities are presented explicitly. For bimaterials which consist of two anisotropic half-spaces bonded together, there are nine image singularities each for the two materials. Again the locations and the natures of the singularities are presented explicitly. We also suggest graphical solutions for finding the locations of these singularities. Since the Green's function for an infinite space has a real-form solution, this implies that Green's functions for half-spaces and bimaterials can have real-form solutions. The image singularities for degenerate materials for which isotropic materials are a special case are discussed briefly. An anomaly is that the image singularities for degenerate materials are not simply line forces and line dislocations. Although the Green's functions obtained here are for line forces and line dislocations, the results can be applied to Green's functions for other types of singularities such as concentrated couples. In particular, the locations of image singularities presented here are independent of the types of singularities concerned.