Efficient boundary element analysis of cracks in 2D piezoelectric structures

This study deals with the computation of intensity factors for cracks in two-dimensional piezoelectric solids under static electromechanical loading. A direct collocation boundary element code with subdomain technique is developed, whereby the fundamental solutions are computed by a fast numerical algorithm applying Fourier series. Linear boundary conditions can be prescribed in a very general form in different coordinate systems. The discretization of the boundary contours is performed by quadratic isoparametric elements. Directly at the crack tips discontinuous quarter-point elements are used to model the typical behavior of the near tip solution with high accuracy, especially the 1/r-singularity of stresses and electric displacements. In order to demonstrate and to verify the accuracy of the method, the electromechanical Griffith crack is analysed under mixed mode loading (I + IV and II + IV) situations. Furthermore the analysis of a crack in a bi-material composite of PZT/Epoxy resin is presented as a practical example and the analysis of a kinked crack as a non-straight crack example.