BIEM via graded piezoelectric half-plane Green’s function for wave scattering by curvilinear cracks

Abstract

This work presents numerical solution for wave motion in a functionally graded piezoelectric half-plane that includes contributions of incident time-harmonic SH waves, waves reflected by the traction-free surface and scattered by multiple curvilinear cracks. A special type of material gradient is studied, where material properties vary exponentially with respect to the depth coordinate. A non-hypersingular traction Boundary Integral Equation Method based on analytically derived Green’s function of a graded half-plane is developed and verified. A series of numerical results show the influence of the material gradient characteristics, the properties of the applied dynamic load, the cracks geometry, the cracks interaction phenomenon and the coupled character of the electromechanical continuum on the wave motions and on the local mechanical and electrical stress concentration fields developing in the graded half-plane.