Discrete dislocation and continuum descriptions of plastic flow

Conventional continuum mechanics models of inelastic deformation processes are size scale independent. In contrast, there is considerable experimental evidence that plastic flow in crystalline materials is size-dependent over length scales of the order of tens of microns and smaller. Geometrically necessary dislocations play a key role in this regard. At present there is no generally accepted framework for analyzing the size-dependent response of a plastically deforming crystal. Dislocation-based plasticity can provide information on the form of the governing equations and the boundary conditions, as well as material properties. Two model problems that highlight the limitations of conventional continuum plasticity are considered. For each problem, solutions using discrete dislocation plasticity and a recently proposed nonlocal continuum formulation are compared. The capabilities and limitations of the currently available nonlocal continuum theories are discussed.