Dynamic Eulerian modeling of visco-plastic crystals

Abstract
We present a robust Eulerian numerical algorithm for a new rigid-visco-plastic single-crystal model. The Eulerian description seems more appropriate for applications involving large deformations and very high-strain rates. Furthermore, problems associated to mesh entangling and distortion are avoided. In the proposed model, plastic deformation is assumed to occur only by slip. The flow rule is obtained from Schmid law using an overstress approach. The evolution equations for the Burger vector and slip directions involve the rotations of the lattice and the plastic spin. A mixed finite-element and finite-volume strategy is developed. Specifically, the variational inequality for the velocity field is discretized using the finite element method and a finite volume method is adopted for the hyperbolic equation related to the orientation of the slip systems. To solve the velocity problem, a decomposition-coordination formulation coupled with the augmented Lagrangian method is used. This approach is accurate in detecting the viscoplastic regions, permit us to handle the rigid zones and capture the change in crystal orientations. Several two-dimensional boundary value problems for FCC crystals are selected to illustrate the predictive capabilities of the model.