Total Lagrange implementation of a finite-deformation continuum dislocation dynamics model of mesoscale plasticity

We present a computational algorithm for solving the recently developed finite-deformation continuum dislocation dynamics theory of mesoscale plastic deformation single crystals (Starkey et al., 2020). This CDD is based on vector density representation dislocations governed by curl-type transport-reaction equations subjected to divergence-free constraint appropriate density. These evolution are be solved simultaneously with crystal mechanics. Specifically, our aims solve referential form governing representative volume element (RVE) subject remote uniform loading. The mechanical fields at thus split into RVE-averages plus fluctuating components and treated using strain-driven homogenization scheme. A virtual work-based total Lagrange formulation was used discretize mechanics equations. first-order system least squares finite transport two schemes coupled in staggered fashion. As part discretization, we derive consistent tangent modulus show that stress update this model both linear global. comes cost every time step distortion caused motion. Several test problems given, demonstrating ability discretization scheme problem, including expansion loop-like bundles under constant velocity driven mean gradient, dynamic recovery oppositely oriented tilt boundaries crystal, uniaxial tension one slip activated. In most these examples, behavior regime demonstrated.