Computational visco-plasticity for kinematically constrained crystals

Crystals possessing less than five independent slip systems cannot undergo any arbitrary isochoric deformation. For these kinematically deficient crystal structures, besides incompressibility, extra constraints need to be taken into account. A visco-plastic constitutive model, based on crystallographic slip, is formulated for these materials, incorporating the kinematic deficiency. A finite element formulation is presented that enforces these kinematic restrictions by an approximate weighting method. The procedure is applicable for large deformations. The orientation of the crystal lattice is incrementally updated. The formulation is applied to a fictitious two-dimensional analogon of a kinematically constrained crystal.