A stochastic finite-strain crystal plasticity model with continuum dislocation dynamics

A stochastic finite-deformation continuum dislocation dynamics–crystal plasticity (CDD–CP) framework is developed for simulating the coupled evolution of dislocation microstructures and macroscopic mechanical response in heterogeneous crystalline materials. The formulation couples finite-strain crystal plasticity with higher-dimensional CDD transport equations for total dislocation density, geometrically necessary dislocation density, and curvature density, with stochastic initial dislocation fields, source distributions, grain morphologies, and crystallographic orientations as inputs. A consistent algorithmic tangent enables robust Newton-based solution under strongly heterogeneous stochastic fields, and the CDD equations are discretized by a nodal discontinuous Galerkin method with diagonally implicit Runge–Kutta time integration.
The framework is assessed in single-slip simple shear, single-crystal tension, and polycrystalline tension, and compared with a small-deformation CDD–CP formulation. Single-slip simulations capture three distinct regimes governed by the competition between dislocation multiplication and boundary escape. The Frank–Read source term acts as a continuum simplification for physical multiplication, admitting natural extensions to annihilation, cross-slip, and junction reactions within the same mathematical structure. ... mehrIn single crystals, finite-deformation effects are modest macroscopically but drive additional slip-system activation through lattice rotation. In polycrystals, grain-boundary constraints cause the two formulations to diverge immediately at the onset of plastic flow, providing a first quantitative assessment of this difference in a transport-based CDD–CP setting. The exponential-map plastic update outperforms backward-Euler in robustness under the chosen time-stepping strategy. An ensemble of 64 stochastic polycrystalline simulations demonstrates measurable realization-to-realization variability in both macroscopic response and dislocation microstructure, constituting a first step toward uncertainty-aware dislocation-based crystal plasticity.