Solution of the plane problem for anisotropic media containing an elliptic inhomogeneity with dislocation-like interface

A general form solution of the plane problem for anisotropic media containing an elliptic inhomogeneity with a dislocation-like interface is presented. It is based on the complex series expansion of the stress functions. A general procedure for the determination of coefficients in the series using a continuity condition for the stresses at the imperfect interface and a discontinuity condition for a jump in the normal or tangential displacements at the interface is illustrated. The jump in the displacement components is described by the dislocation-like model based on the assumption that discontinuity of displacement across the interface is linearly proportional to the elastic displacement at the interface in the inhomogeneity. The model can reasonably characterize the imperfect interface from perfect bonding to complete debonding due to separate or combined effect of eigenstrains and far-field tension. Convergence of the results is obtained by truncating a finite number of terms in the series. The present solution is verified with available analytical results for the case of a perfect interface. In this paper, the pattern for the stresses in the heterogeneous anisotropic materials is shown. The effect of imperfect parameters on the distributions of stresses is also discussed. The method and procedure proposed in the paper are useful in analyzing the strength and failure of anisotropic materials containing an inhomogeneity with imperfect interface.