Antiplane interaction of an anisotropic elliptic inclusion with an arbitrarily oriented crack

The antiplane interaction problem for an anisotropic elastic inclusion embedded in an anisotropic elastic matrix with an arbitrarily oriented crack, located either in the matrix or in the inclusion, is considered in this paper. The proposed analysis is based upon the use of conformal mapping, analytical continuation and Laurent series expansion of the corresponding complex potentials. By applying the existing solutions for dislocation functions, the integral equations for a line crack are formulated and the mode-III stress intensity factors are obtained numerically. Several numerical examples are given to demonstrate the effects of geometrical parameters and material property combinations on the strength of the antiplane stress singularity.