Energy density and release rate study of an elliptic-arc interface crack in piezoelectric solid under anti-plane shear

The anti-plane problem of an elliptical inhomogeneity with an interfacial crack in piezoelectric materials is investigated. The system is subjected to arbitrary singularity loads (point charge and anti-plane concentrated force) and remote anti-plane mechanical and in-plane electrical loads. Using the complex variable method, the explicit series form solutions for the complex potentials in the matrix and the inclusion regions are derived. The electroelastic field intensity factors, the corresponding energy release rates and the generalized strain energy density at the cracks tips are then provided. The influence of the aspect ratio of the ellipse, the crack geometry and the electromechanical coupling coefficient on the energy release rate and the strain energy density is discussed and shown in graphs. The results indicate that the energy release rate increases with increment of the aspect ratio of the ellipse and the influence of electromechanical coupling coefficient on the energy release rate is significant. The strain energy density decreases with increment of the aspect radio of the ellipse and it is always positive for the cases discussed. The energy release rate, however, can be negative when both mechanical and fields are applied.