Current advances in the size-dependent continuum plasticity of crystals were summarized, in particular the rate-independent (quasi-static) formulation, on the basis of dislocation mechanics. Particular emphasis was placed on the relaxation of slip at interfaces. This unsolved problem was deemed to be one of the current frontiers of research in the plasticity of crystalline materials. A framework for further investigation was outlined, based upon theory developed for the bulk crystal. The latter was based upon the concept of geometrically necessary dislocations; specifically, configurations where dislocations piled up against interfaces. The average spacing of slip planes provided a characteristic length for the theory. The physical interpretation of the free energy included the error in elastic interaction energies resulting from coarse representation of dislocation density fields. Continuum kinematics was determined by the fact that dislocation pile-ups had a singular distribution, which permitted representation of the dense dislocation field at the boundary as a super-dislocation. That is, the jump in the slip field. Associated with this jump was a slip-dependent interface energy, which in turn, made this formulation suitable for the analysis of interface relaxation mechanisms.

Plasticity of Crystals and Interfaces - From Discrete Dislocations to Size-Dependent Continuum Theory. S.D.Mesarovic: Theoretical Applied Mechanics, 2010, 37[4], 289–332