A comparison of nonlocal continuum and discrete dislocation plasticity predictions

Abstract

Discrete dislocation simulations of two boundary value problems are used as numerical experiments to explore the extent to which the nonlocal crystal plasticity theory of Gurtin (J. Mech. Phys. Solids 50 (2002) 5) can reproduce their predictions. In one problem simple shear of a constrained strip is analyzed, while the other problem concerns a two-dimensional model composite with elastic reinforcements in a crystalline matrix subject to macroscopic shear. In the constrained layer problem, boundary layers develop that give rise to size effects. In the composite problem, the discrete dislocation solutions exhibit composite hardening that depends on the reinforcement morphology, a size dependence of the overall stress–strain response for some morphologies, and a strong Bauschinger effect on unloading. In neither problem are the qualitative features of the discrete dislocation results represented by conventional continuum crystal plasticity. The nonlocal plasticity calculations here reproduce the behavior seen in the discrete dislocation simulations in remarkable detail.