A Mesoscale Model of Plasticity: Dislocation Dynamics and Patterning (One-Dimensional)

In this study, we developed a physically based mesoscale model for dislocation dynamics systems to predict the deformation and spontaneous formation of spatio-temporal dislocation patterns over microscopic space and time. Dislocations and dislocation patterns are emblematic of plastic deformation, a nonlinear, dissipative process involving the dynamics of underlying dislocations as carriers of plastic deformation. The mesoscale model includes a set of nonlinear partial differential equations of reaction–diffusion type. Here, we consider the equations within a one-dimensional framework and analyze the stability of steady-state solutions for these equations to elucidate the associated patterns with their intrinsic length scale. The numerical solution to the model yields the spatial distribution of dislocation patterns over time and provides respective stress–strain curves. Finally, we compare the stress–strain curves associated with the dislocation patterns with the experimental results noted in the literature.