Image singularities of planar magnetoelectroelastic bimaterials for generalized line forces and edge dislocations

This study presents two-dimensional explicit full-field solutions of transversely isotropic magnetoelectroelastic bimaterials subjected to generalized line forces and edge dislocations using the Fourier-transform technique. One of the major objectives of this study is to analyze the physical meaning and the structure of the solution. Complete solutions for this problem consist only of the simplest solutions for an infinite medium. The solutions include Green's function of originally applied singularities in an infinite medium and thirty-two image singularities which are induced to satisfy interface continuity conditions. It is shown that the physical meaning of the solution is the image method. The mathematical method used in this study provides an automatic determination for the locations and magnitudes of image singularities. The locations and magnitudes of image singularities are dependent on the roots of the characteristic equation for bimaterials. The number and distribution for image singularities are discussed according to characteristic roots features. With the aid of the generalized Peach-Koehler formula, the explicit expressions of image forces acting on generalized edge 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 bimaterials are presented. 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.