Elastostatic problems of crack lying along the interface of an elliptical inclusion embedded in elastic media

Abstract

The problems of an elliptical arc crack lying along the interface of an anisotropic inclusion are considered in this article. By means of the complex series expansion of the stress functions, the related coefficients in the stress functions are obtained using the continuity condition for the stresses at the imperfect interface and using equilibrium condition based on relationships of stresses and displacements at the imperfect interface between matrix and inclusion. The displacements and stresses at the interface in the matrix and in the inclusion can be calculated. The imperfection at the interface between matrix and inclusion is expressed by the Fourier series, which can be used to represent the crack lying along the interface and the perfect interface. The method presented in this article can be used to analyze the problems of crack, inclusion, and hole in the anisotropic materials due to separate or combined effect of eigenstrains and far-field tension.