Mesoscale modelling of defect dynamics and plasticity of defects crystals

Crystalline matter under external forces responds by plastic deformations which involve the nucleation of crystal defects, non-local interactions between them and their dissipative dynamics. As materials are scaled in down to micron scale and below, the cooperative effects of interacting defects are increasingly evident through the emergence of strong fluctuations in the plastic response prior to ductile flow and eventual material failure. In this regime, critical-like nonequilibrium phenomena is observed challenging theoretical approaches.
We propose a mesoscopic theory of defected crystals where defect kinetics, core structure and mutual interactions are emergent from a more fundamental description based on symmetry broken states and their topological constraints. Within the phase field crystal model, we show that the defect velocity is determined by the evolution of the order parameter and in certain limits reduces to the classical Peach-Koehler force. The separation of timescale between the dissipative motion of defects and fast relaxation of elastic perturbations is a challenging task in many of these mesoscale formulations. We constrain the mechanical equilibrium on a coarse-grained stress field, which is shown to be a reasonable and robust observable for mechanical distortions at least for small distortions.