Crack analyses in three-dimensional piezoelectric structures by the BEM

The aim of this paper is the modeling of cracks in three-dimensional piezoelectric structures by means of boundary elements. A single region, direct collocation boundary element code has been implemented, where the anisotropic, piezoelectric fundamental solutions for the coupled electromechanical field problem are calculated applying the Radon transform. For the discretization of the boundary, continuous as well as discontinuous boundary elements with quadratic shape functions are used. The crack itself is modeled by special crack front elements accounting for the r12-behavior of the displacements and electric potentials and the r-12-singularity of the tractions and electric displacements around the crack front. Once the piezoelectric field problem has been solved, fracture mechanics quantities are calculated as mechanical and electrical field intensity factors. Thereby, the properties of the introduced crack tip elements are utilized, i.e., by performing a limiting process over the elements in the ligament. The developed BEM-techniques are applied to three-dimensional example problems. The results are in good agreement with known solutions.