Link between the individual and continuum approaches of the description of the collective behavior of dislocations

The properties of a system of parallel edge dislocations is investigated by numerical and analytical methods. Although the considered 2D assembly is a strong simplification compared to the dislocation systems which develop in real crystals, computer simulations show that it can reproduce several important features of the plastic behavior of single crystals. In the second half of the paper a self consistent field description is derived from the equation of motion of the individual dislocations. The outlined method creates a link between the individual and continuum descriptions of the behavior of the dislocations without any ad hoc assumption. In the model the precise form of the elastic interaction of the dislocations is taken into account. Within this framework the stability of the homogeneous dislocation distribution is investigated.