Computational visco-plasticity for kinematically constrained crystals

Crystals possessing less than ve independent slip systems cannot undergo any arbitrary isochoric deformation. For these kinematically de cient 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 de ciency. A nite 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 ctitious two-dimensional analogon of a kinematically constrained crystal.