Kinetic toy model for crystal plasticity

Abstract

We propose a kinetic toy model to describe the dynamics of sliding layers as it occurs in the plastic deformation of single crystals. As its basic ingredient, the distribution function of relative strains between adjacent crystal layers is introduced with time evolution described by a diffusion equation with periodic boundary conditions. The model highlights the conceptual difference in the dynamics of the elastic and plastic strains, the latter being related to an average hopping rate that captures the evolving reference state. We illustrate the model by calculation of the stress response for both stationary and transient conditions.