BEM analysis of electrically limited permeable cracks considering Coulomb tractions in piezoelectric materials

In this paper, the electrically limited permeable piezoelectric cracks considering the induced Coulomb tractions on the crack faces are studied with respect to the dielectric constant of the crack medium by BEM. As limiting cases, the permeable and impermeable electric crack-face boundary conditions are also considered. Based on the dual boundary integral equations, the crack-tip field intensity factors and the energy release rate are evaluated by the displacement extrapolation method and the J-integral method, respectively. The crack-face part of the contour integral is then handled by two approaches, namely numerical quadrature and approximate formula. The analytical solutions for a Griffith crack are also presented for verification purpose. Three examples are presented to check the efficiency and the accuracy of these approaches. The effects of the dielectric constant of the crack medium and the induced Coulomb tractions on the crack-tip field intensity factors and the energy release rate are also discussed.