Density-based continuity equations were used to model strain patterns and size effects in confined plastic flow: shearing of thin films and micro-bending. A representation in terms of coupled equations for the densities of screw and edge components was used. It was shown that these equations were derived from a more general formulation in a higher-dimensional configuration space. The new factor was the incorporation, into previous continuum formulations, of geometrical features and interactions of dislocation lines that could not be neglected or averaged-out within a 3-dimensional treatment of plasticity at the μm- and nm-scales.

Modelling Size Effects using 3D Density-Based Dislocation Dynamics. M.Zaiser, N.Nikitas, T.Hochrainer, E.C.Aifantis: Philosophical Magazine, 2007, 87[8-9], 1283-306