Dislocation group dynamics II. general solutions of the n-body problem

Abstract

The general motion of n dislocations under their mutual repulsion and an applied stress field is considered. When the applied field is a linear function of position and an arbitrary function of time, it is shown that a Stieitjes transformation turns the nonlinear equations of motion into a set of linear differential equations which are integrable to give an exact specification of the general motion. The motion of the centroid of the dislocation group and the mean square deviation about the centroid are shown to have particularly simple properties.