Screw dislocation and elliptic inhomogeneity of a confocal crack in magnetoelectroelastic medium: Comparison of energy release rate and strain energy density

Abstract

This work is devoted to investigate the magnetoelectroelastic interaction between a generalized screw dislocation and an elliptic inhomogeneity containing a confocal crack in piezoelectric/piezomagnetic composite subjected to remote anti-plane shear stress field, in-plane electric and magnetic field. By using the complex variable method of elasticity, the closed-form expressions of complex potentials of matrix and inhomogeneity are obtained for the dislocation locating both in matrix and inhomogeneity. The expressions of the generalized stress/strain field, image force, the generalized stress intensity factor and energy release rate of crack tip, and strain energy density are derived explicitly. Then, the influence laws of material parameters, the shape of elliptic inhomogeneity and remote loading on these quantities are analyzed. The results show that the image force has different variation laws in magnetoelectroelastic materials with that in elastic materials; stress intensity factor has the same distributing law as electric displacement intensity factor, but is different from magnetic induction intensity factor; the energy release rate (ERR) can be positive and negative depending on the combined action of applied fields, the in-plane electric field and magnetic field. This makes the ERR interpretation unphysical. ERR is not permitted to change sign. The strain energy density function is shown to be positive definite under all conditions.