Dynamic stress and electric field concentration in a functionally graded piezoelectric solid with a circular hole

This work addresses the evaluation of the stress and electric field concentrations around a circular hole in a functionally graded piezoelectric plane subjected to anti-plane elastic SH-wave and in-plane time-harmonic electric load. All material parameters vary exponentially along a line of arbitrary orientation in the plane of the piezoelectric material under consideration. The computational tool is a non-hypersingular traction based boundary integral equation method (BIEM). The kernel functions used in the BIEM are exact fundamental solutions that have been derived in previous work by the authors. Numerical solutions for the stress and electric field concentration factors (SCF and EFCF, respectively) around the perimeter of the hole are obtained. The simulation demonstrates the efficiency of the computational approach and its potential to reveal in an adequate way the dynamic stress and electric field distribution around the hole. Presented are results showing their dependence on various system parameters as e.g. the electro-mechanical coupling, the type of the dynamic load and its characteristics, the wave-hole and wave-material interaction and the magnitude and direction of the material inhomogeneity