Some steps towards a continuum representation of 3D dislocation systems

We outline a method for representing the dynamics of interacting curved dislocations in a continuum framework. Starting from a pseudo-continuum representation of the kinematics of discrete lines, we demonstrate how this can be used to derive a set of coupled equations for the densities of screw and edge components. We discuss how long- and short-range dislocation interactions can be treated within this framework, and apply the resulting equations to a simple model of channel slip.