Kinetic view on dynamic plasticity of crystalline solids

Abstract

Plastic deformation in crystalline solids arises from discrete microstructural rearrangements driven by energy exchange and crystallographic constraints. Conventional continuum plasticity models, even when enriched with crystal anisotropy, rely on prescribed flow rules and struggle to represent the emergence of internal length and time scales during the early stages of plastic flow. Here, we propose a fully discrete statistical framework for crystalline plasticity based on polytopal cell complexes (PCCs), in which elementary plastic events are represented as probabilistic microslips defined on crystallographically admissible face–edge pairs. The framework captures several physically interpretable features associated with non-equilibrium plastic flow, including strain-rate sensitivity, stress-dependent activation of slip systems, discrete activation spectra arising from crystallographic topology and the appearance of a minimum representative volume (MRV) for statistically stable plastic activity. Characteristic relaxation times (CRTs) and effective deformation rates arise naturally from the dynamics of internal energy dissipation, providing an intrinsic mapping between stochastic evolution and physical time. While the present study is restricted to illustrative simulations of face-centred cubic (FCC) single crystals under relatively simple loading conditions, the results demonstrate the potential of the proposed discrete framework for mesoscale investigations of crystallographically constrained stochastic plasticity.