The dynamics behavior of an assembly of parallel dislocations is investigated at different length scales. In the first part, it is shown that a discrete dislocation system is able to reproduce several important features of plastic deformation. Then, a self-consistent field continuum model is derived. Finally, a stochastic approach is outlined, which can be considered as an intermediate scale description between the discrete and the continuum models. ? 2001 Elsevier Science B.V. All rights reserved.

We present an extension of the fast-multipole method of Greengard and Rokhlin to the case of the long-range interactions between parallel edge (in arbitrary orientations) and screw dislocations. By finding complex potentials from which the stress terms can be calculated, and expanding those potentials in multipole series, we convert a computationally difficult O(N2) poroblem into a much faster O(N) approach. To reach sufficient numerical accuracy, only a few terms are needed in the multipole expansions (four screws and six for edges) so that the interactions between millions of dislocations can be calculated in a few minutes on a workstation. We present results of a study of the relaxed configurations of 16384 edge dislocations of arbitrary orientations.