Hypersingular BEM for dynamic fracture in 2-D piezoelectric solids

Fracture behavior of piezoelectric solids under time-harmonic loading is numerically analyzed in this paper. A 2-D boundary element method (BEM) based on both displacement and traction boundary integral equations is presented. The time-harmonic Green’s functions for the infinite plane are split into singular plus regular terms, the singular ones coinciding with the static Green’s functions. In this manner the singular and hypersingular integrals arising in the formulation may be treated by the same simple regularization procedure proposed by the authors for static piezoelectricity. Quarter-point elements are used for the direct evaluation of stress and electric displacement intensity factors from nodal values. Several numerical examples for the scattering of waves by different crack configurations including branched and curved cracks and crack interaction problems are given to demonstrate the performance of the proposed method.