Phenomenological mesoscopic field dislocation mechanics, lower-order gradient plasticity, and transport of mean excess dislocation density

Three practically useful reductions of phenomenological mesoscopic field dislocation mechanics (PMFDM) are explored to evaluate some of their capabilities and limitations. Lower-order gradient plasticity arises as one of these reduced frameworks, and a boundary condition appropriate for the modelling of constrained plastic flow in 3D is demonstrated through FEM simulation.To elaborate and fix ideas in a simplified context, we motivate the averaging procedure giving rise to PMFDM in a 1D context and show the possibility of obtaining a diffusion term in coarse evolution through a perturbative approach. Formally, the diffusion appears as a small, first-order correction to mean transport of excess dislocation density. Physically, it arises from a more refined modelling of the slip distortion rate and not as an additional energetic 'back' stress contribution. The approximate nature of the perturbative approach is assessed to highlight the importance of the transport term in the equation. We also comment on the emergence of stochasticity and memory effects in coarse response.

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