A three-dimensional (3D) mesoscopic model to simulate the collective d
ynamic behavior of a large number of curved dislocations of finite len
gths has been developed for the purpose of analyzing deformation patte
rns and instabilities, including the formation of dislocation cell str
uctures. Each curved dislocation is approximated by a piecewise contin
uous array of straight line segments. The interactions among the segme
nts, including line-tension and self-interactions, are treated explici
tly. For longer-range interactions, the space is divided into a regula
r cellular array and the elastic fields of the dislocations in a remot
e cell approximated by a multipolar expansion, leading to an order N a
lgorithm for the description of a cell containing N dislocations. For
large arrays, the simulation volume is divided into cubical cells. A d
iscrete random starting array is selected for the master cell and its
nearest neighbors, which constitute an order 2 cell. Reflection bounda
ry conditions are imposed for near-neighbor order 2 cells and so forth
, creating an NaCl-type lattice array. The boundaries between the cell
s are considered to be relaxed grain boundaries. That is, recovery wit
hin the boundaries and rotation across them are considered to occur so
that the boundaries have no associated elastic fields. This cell hier
archy, coupled with the multipole expansion, is suitable for the use o
f massively parallel computation, with individual cells assigned to se
parate processors. (C) 1997 Published by Elsevier Science Ltd.