Theoretical analysis of generalized loadings and image forces in a planar magnetoelectroelastic layered half-plane

The problem of a planar transversely isotropic magnetoelectroelastic layered half-plane subjected to generalized line forces and edge dislocations is analyzed. The complete solutions consist only of the simplest solutions for an infinite magnetoelectroelastic medium with applied loadings. The physical meaning of this solution is the image method. It is shown that the explicit solutions include Green's function for originally applied singularities in an infinite medium and the other image singularities are induced to satisfy free surface and interface continuity conditions. The mathematical method used in this study provides an automatic determination for the locations and magnitudes of all image singularities. The locations and magnitudes of image singularities are dependent on the roots of the characteristic equation which is related to the material constants of the layered half-plane. With the aid of the generalized Peach–Koehler formula, the explicit expressions of image forces acting on dislocations are easily derived from the full-field solutions of the generalized stresses. Numerical results for the full-field distributions of stresses, electric fields, and magnetic fields in the layered half-plane medium are presented based on the analytical solutions. The image forces and equilibrium positions of one dislocation, two dislocations, and an array of dislocations are presented by numerical calculations and are discussed in detail.