Discrete dislocation simulations of 2 boundary value problems were used as numerical test-beds in order to explore the extent to which Gurtin’s non-local crystal plasticity theory could reproduce their predictions. In one problem, the simple shear of a constrained strip was analyzed. The other problem concerned a 2-dimensional model composite with elastic reinforcements in a crystalline matrix that was subjected to macroscopic shear. In the constrained layer problem, boundary layers developed that gave rise to size-effects. In the composite problem, the discrete dislocation solutions exhibited a composite hardening that depended upon the reinforcement morphology; with a size-dependence of the overall stress–strain response for some morphologies, and a strong Bauschinger effect upon unloading. In neither problem were the qualitative features of the discrete dislocation results reproduced by conventional continuum crystal plasticity. The non-local plasticity calculations reproduced the behavior, that was seen in discrete dislocation simulations, to a remarkable degree.

A Comparison of Non-Local Continuum and Discrete Dislocation Plasticity Predictions. E.Bittencourt, A.Needleman, M.E.Gurtin, E.Van der Giessen: Journal of the Mechanics and Physics of Solids, 2003, 51[2], 281-310