Interaction between a generalized screw dislocation in the matrix and an inhomogeneity containing an elliptic hole in piezoelectric–piezomagnetic composite materials

Abstract

The paper deals with the interaction of a generalized screw dislocation and an elliptic inhomogeneity containing a confocal elliptic hole in a magneto-electro-elastic composite material. Exact solutions are derived for the case where the generalized screw dislocation is located in the matrix under a remote anti-plane shear stress field, an in-plane electric field, and a magnetic field. Based on the complex variable method, the complex potentials of both the matrix and the inhomogeneity are obtained in series, and analytic expressions for the generalized stress and strain field, the image force, the generalized stress intensity factor of the blunt crack tip, and the energy release rate are derived explicitly. The presented solutions include some previous solutions, such as pure elastic, piezoelectric, piezomagnetic, and circular inclusions. Typical numerical examples are presented and the influences of the dislocation position, the volume of inhomogeneity, and the elliptic hole on these physical quantities are discussed. The results show that the magneto-electro-elastic coupling effect has a great influence on the image force and the equilibrium position of dislocation, especially when the dislocation approaches the interface; the coupling effect makes the image force on the screw dislocation follow different variation laws in piezoelectric–piezomagnetic composite materials compared with elastic materials.