A phenomenological mesoscopic field dislocation mechanics model was developed, extending continuum plasticity theory for studying initial-boundary value problems of small-scale plasticity. Phenomenological mesoscopic field dislocation mechanics results from an elementary space-time averaging of the equations of field dislocation mechanics, followed by a closure assumption from any strain-gradient plasticity model that attempts to account for effects of geometrically necessary dislocations only in work hardening. The specific lower-order gradient plasticity model chosen to substantiate this work required one additional material parameter compared to its conventional continuum plasticity counterpart. The further addition of dislocation mechanics required no additional material parameters. The model (a) retains the constitutive dependence of the free-energy only on elastic strain as in conventional continuum plasticity with no explicit dependence on dislocation density, (b) did not require higher-order stresses, and (c) did not require a constitutive specification of a back-stress in the expression for average dislocation velocity/plastic strain rate. However, long-range stress effects of average dislocation distributions were predicted by the model in a mechanistically rigorous sense. Plausible boundary conditions (with obvious implication for corresponding interface conditions) were considered from a physical point of view. Energetic and dissipative aspects of the model were also considered. The framework developed was a continuous-time model of averaged dislocation plasticity, without having to rely on the notion of incremental work functions, their convexity properties, or their minimization. The tangent modulus relating stress rate and total strain rate in the model was the positive-definite tensor of linear elasticity, and this was not an impediment to the development of idealized microstructure in the theory and computations, even when such a convexity property was preserved in a computational scheme. A model of finite deformation, mesoscopic single crystal plasticity was also presented, motivated by the above considerations.

Size Effects and Idealized Dislocation Microstructure at Small Scales - Predictions of a Phenomenological Model of Mesoscopic Field Dislocation Mechanics – I. A.Acharya, A.Roy: Journal of the Mechanics and Physics of Solids, 2006, 54[8], 1687-710