A Zener-Stroh crack along the interface of a rigid elliptical inhomogeneity in an anisotropic elastic matrix

We employ the Stroh sextic formalism for anisotropic elasticity and Muskhelishvili’s complex variable formulation for isotropic elasticity to derive a full-field closed-form solution to the two-dimensional problem of a non-planar Zener-Stroh crack lying along the interface of a rigid elliptical inhomogeneity embedded in an infinite anisotropic elastic matrix. The rigid inhomogeneity is treated as an isotropic elastic inhomogeneity with its shear modulus approaching infinity. A real-form expression for the rigid body rotation of the rigid elliptical inhomogeneity is obtained in terms of the two Barnett-Lothe tensors H and S for the matrix by imposing the condition that tractions are continuous across the entire elliptical interface.