Based on the complex variable method, the magnetoelectroelastic interaction of a generalized screw dislocation with an elliptical inhomogeneity containing a electrically conductive confocal rigid line under remote anti-plane shear stresses, in-plane electric and magnetic loads is dealt with. The generalized screw dislocation is located inside either the inhomogeneity or the matrix. The analytical-functions of complex potentials for stresses, electric displacement fields and magnetic induction fields in both the inhomogeneity and the matrix are derived. The image force acting on the dislocation are also calculated explicitly. The results show that the influence of the rigid line on the interaction effect between a generalized screw dislocation and an elliptical inhomogeneity is significant. In addition, the material behavior also plays an important role on the image force.

The paper is aim to investigate the interaction of a screw dislocation in strained reinforcement with a lip-shaped crack under remote longitudinal shear load using complex variable method of Elasticity. The exact solution of complex function of the matrix and the renforcement layer are obtain in series form; then, the expressions of stress field, image force and stress intensity factor of crack tip can be derived; finally, numerical disccusions are pesented and the results shows that the lip-shaped crack in reinforcement layer has interference effect on the interaction of dislocation and reinforcement layer, and the eigenstrain in x-direction has little effect on image force; however, the eigenstrain in y-direction has great influence on image force.

The interaction between a screw dipole inside the matrix and an elastic elliptical inhomogeneity containing a confocal crack under longitudinal shear is investigated. By using the complex method of elasticity, singularity analysis of stress function and Riemann boundary problem, the complex functions of matrix and inhomogeneity are obtained in the series form. And the singularity stress field of matrix, the image force and image torque acting on the center of screw dipole and the stress intensity factor of crack tip are deduced. Then the influence of the dip angle of screw dipole, the size of inhomogeneity and the misfit of materials on image force, torque of couple and the stress intensity are analyzed. The results show that the image force varies periodically as and there is two critical value of to make image force getting its maximum and minimum; the decreasing of relative shear modulus and the increasing of inhomogeneity may lead to the increasing of image force; the variation of will change the direction of screw dipole on stress intensity factor.

The interaction between a screw dislocation and a reinforced lip-shaped crack embedded in an infinite matrix subjected to a remote longitudinal shear load is investigated in this paper. By combining the sectionally holomorphic function theory, Cauchy singular integral, singularity analysis of complex functions and Riemann boundary problem, the problem is reduced to solve an elementary complex potentials equation. The general expressions of complex function in the matrix and the reinforcement layer are derived explicitly in series form for the case when the screw dislocation is located in the matrix. The image force acting on the screw dislocation and the stress intensity factor are also calculated. Some numerical results are provided to discuss the effects of dislocation position, material parameters, geometric configurations and eigenstrain on the image force.