A new formulation was developed for the elastic boundary value problem of dislocations in bounded crystals. This was based upon the ansatz that the stress field of dislocations in bounded domains could be constructed as the sum of a contribution corresponding to the classical infinite-domain solution, plus a correction that was deduced from a mathematically well posed problem. The formulation of the elastic boundary value problem given here ensured that the equilibrium of the overall stress field was rigorously satisfied; in particular, when dislocations intersected the boundary. The implications of this new formalism for dislocation dynamics simulation were considered for the cases of bounded crystals and for crystal volumes which were representative of uniformly loaded infinite crystals. An approximate computational solution of the elastic boundary value problem was presented that was based upon the concept of virtual dislocations and the use of a non-singular form of the infinite-domain solution of the dislocation stress field. This computational solution addressed the issues of singularity and of global equilibrium of the boundary traction associated with the corrective field. Results were presented, for the internal stress in bounded crystals containing 3-dimensional dislocation configurations, using the dislocation dynamics simulation method. The results illustrated the statistical character of the internal elastic field.

On the Elastic Boundary Value Problem of Dislocations in Bounded Crystals. J.Deng, A.El-Azab, B.C.Larson: Philosophical Magazine, 2008, 88[30-32], 3527-48