Green’s functions were used to obtain new explicit expressions for the interaction force. These new solutions led to new physical interpretations. It was shown that, for the infinite space and the half-space with a traction-free surface, the interaction force was independent of the Burgers vectors. The force was zero if either vector lay along the x-axis. The force was independent of the skew angle if the projections of the Burgers vectors on the x = 0 plane lay along a pair of conjugate radii of an ellipse. For other half-spaces and bimaterials, the force (on one dislocation) was zero when its vector, and bxv lay along the x-axis; where v was the axial vector of a skew-symmetric matrix. Thus b was arbitrary when v = 0 (the case of a half-space with a slippery surface and of certain bimaterials). The force on one dislocation was independent of the skew angle when its vector lay along the x-axis, and b was coplanar with v and the x-axis.

On Nix’s Theorem for Two Skew Dislocations in Anisotropic Elastic Half-Spaces and Bimaterials. T.C.T.Ting, D.M.Barnett: Mathematics and Mechanics of Solids, 2001, 6[1], 3-27