On the unified approach to anisotropic and isotropic elasticity for singularity, interface and crack in dissimilar media

Abstract Proposed in this paper is the equivalence between anisotropic and isotropic elasticity for two-dimensional deformation under certain conditions. That is, the isotropic elasticity can be reconstructed in the same framework of the anisotropic elasticity, when the interface between dissimilar media lies along a straight line. Therefore, many known solutions for an anisotropic bimaterial are valid for a bimaterial, of which one or both of the constituent materials are isotropic. The usefulness of the equivalence is that the solutions for singularities and cracks in an anisotropic/isotropic bimaterial can easily be obtained without solving the boundary value problems directly. The interaction solutions of singularities, interfaces, and cracks in infinite anisotropic bimaterial are summarized, to be used for the cases of isotropic/isotropic and anisotropic/isotropic bimaterials. Conservation integrals also have the similar analogy between anisotropic and isotropic elasticity so that J integral and J-based mutual integral M are expressed in the same complex forms for anisotropic and isotropic materials, when both end points of the integration paths are on the straight interface. The use of J and M integrals together with the present equivalence are exemplified to obtain energy release rate, stress intensity factors, and T-stresses of interfacial cracks lying in the interface of anisotropic/anisotropic, isotropic/isotropic, or anisotropic/isotropic solids.

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