A Unified Two-Phase Potential Method for Elastic Bi-material: Planar Interfaces

This paper gives a unified approach to analyze two-dimensional elastic deformations of a composite body consisting of two dissimilar anisotropic or isotropic materials perfectly bonded along a planar interface. The Eshelby et al. formalism of anisotropic elasticity is linked with that of Kolosov-Muskhelishvili for isotropic elasticity by means of two complex matrix functions describing completely the arising elastic fields. These functions, whose elements are holomorphic functions, are defined as the two-phase potentials of the bimaterial. The present work is concerned with bi-materials whose constituent materials occupy the whole space and are connected by a planar interface. The elastic fields arising in such a bimaterial are given by universal relationships in terms of the two-phase potentials. Then, the general results obtained are implemented to study two interesting bimaterial problems: the problem of a uniformly stressed bimaterial with a perfect interfacial bonding, and the interface crack problem of a bimaterial with a general loading. For both problems, all combinations of the elastic properties of the constituent materials are considered. For the first problem, the constraints, which must be imposed between the components of the applied uniform stress fields, are established, so that they are admissible as elastic fields of the bimaterial. For the interface crack problem, the solution is obtained for a general loading applied in the body. Detailed results are given for the case of a remote uniform stress field applied to the bimaterial constituents.