A 2-dimensional non-local version of continuum crystal plasticity theory was proposed, which was based upon a statistical-mechanics description of the collective behavior of dislocations coupled to standard small-strain crystal continuum kinematics for single slip. It involves a set of transport equations for the total dislocation density field and for the net-Burgers vector density field, which include a slip system back stress associated to the gradient of the net-Burgers vector density. The theory was applied to the problem of shearing of a 2-dimensional composite material with elastic reinforcements in a crystalline matrix. The results were compared to those of discrete dislocation simulations of the same problem. The continuum theory was shown to be able to pick up the distinct dependence on the size of the reinforcing particles for one of the morphologies being studied. Also, its predictions were consistent with the discrete dislocation results during unloading, showing a pronounced Bauschinger effect. None of these features were captured by standard local plasticity theories.

A Comparison of a Statistical Mechanics-Based Plasticity Model with Discrete Dislocation Plasticity Calculations. S.Yefimov, I.Groma, E.van der Giessen: Journal of the Mechanics and Physics of Solids, 2004, 52[2], 279-300