Integral expressions were derived for the elastic displacements and stress fields due to stationary or moving dislocation loops in finite samples. These general expressions were also valid for anisotropic media. In the case of the stress fields, a line integral representation was found; thus clearly revealing the independence of the stress fields with respect to the choice of slip planes. In the stationary case, the line-integral representation involved the calculation of a so-called vector potential which depended upon the specific geometry of the sample. The vector potential was explicitly determined for 2 geometries: the isotropic half-space and the thin plate. This reproduced some known results for these geometries.

Elastic Fields of Stationary and Moving Dislocations in Finite Samples R.Arias: Philosophical Magazine B, 1998, 78[2], 109-13