Treated is an arbitrarily shaped anti-plane shear crack in a finite inhomogeneous piezoelectric domain under time-harmonic loading. Within a unified scheme different types of inhomogeneity are considered for which the material parameters may vary in two directions. The problem is solved by using a numerically efficient non-hypersingular traction based boundary equation method (BIEM). The fundamental solutions for the different inhomogeneity types are derived in closed form. This is done by an appropriate functional transformation of the displacement vector in order to obtain a wave equation with constant coefficients and subsequently by application of the Radon transform. Numerical results for the stress intensity factors (SIF) are discussed for several examples. They show the effect of the material inhomogeneity and the efficiency of the method.

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