Time-harmonic crack problems in functionally graded piezoelectric solids via BIEM

In-plane crack analysis of functionally graded piezoelectric solids under time-harmonic loading is performed by using a non-hypersingular traction based boundary integral equation method (BIEM). The material parameters are assumed to vary quadratically with both spatial variables. A frequency dependent fundamental solution, as well as its derivatives and asymptotic expressions, is derived in closed-form by using an appropriate algebraic transformation for the displacement vector and the Radon transform. Numerical results for the stress intensity factors (SIFs) are discussed for different examples. The accuracy of the presented method is checked by comparison with available results from the literature. Investigated are the effects of the inhomogeneity parameters, the frequency of the applied electromechanical load and the geometry of the crack scenario on the K-factors.