A mechanism-based homogenization of a dislocation source model for bending

The homogenization of dislocation dynamics including the mechanisms of dislocation nucleation is a great challenge in dislocation based continuum formulations. Due to the loss of the local and temporal resolution in a continuum model, physical nucleation mechanisms have to be incorporated in an average sense. Consequences can be the over- or underestimation of the macroscopic production rate of dislocation density which results in artificial softening or hardening phenomena. In this paper, we derive a mechanism-based homogenization of a dislocation source model based on the theory of critical thickness, which accounts for the relation between the external loading condition and the resulting dislocation density production rate. The formulation is applied to pure and cantilever bending problems, validated in comparison to discrete dislocation dynamics simulations, and discussed for the discrete-continuum transition regime.