Analysis of elliptical hole edge-cracks in piezoelectric materials with the extended finite element method

Based on the XFEM, an elliptical hole edge-cracks problem in piezoelectric materials is analyzed. The stress field and the electrical displacement field around the crack tip are derived. The virtual crack closure method is used to calculate the energy release rate of different crack length under the mechanical load and electromechanical coupling load, respectively. According to the relationship between the energy release rate and the stress intensity factor, the crack tip stress intensity factor and the electric displacement intensity factor are calculated. The obtained results are excellent agreement with those from the analytical solutions. The influences of the geometries and the external loads on the field intensity factors are discussed. To show the accuracy of the present method, the numerical results from the XFEM are compared with the analytical reference solutions available in the literature and excellent agreements are found.