A proof of lothe's theorem

Abstract

A short proof is given of the result found by Lothe (1967) published in the preceding paper in this journal. In the course of the proof, it is shown how a knowledge of the stresses around infinite straight dislocations leads to a formal solution of dislocation problems in which there is a planar array of dislocations. The solution consists in finding the contribution to the stress at any point in the plane of the array due to an element of dislocation line situated at the origin; it is a kind of generalized Biot-Savart law, valid in particular for dislocations in anisotropic media.