A variational viscosity-limit approach to the evolution of microstructures in finite crystal plasticity

A micromechanical model for finite single crystal plasticity was introduced by Kochmann & Hackl (2011Contin. Mech. Thermodyn. 23, 63–85 (doi:10.1007/s00161-010-0714-5 )). This model is based on thermodynamic variational principles and leads to a non-convex variational problem. Based on the Lagrange functional, an incremental strategy was outlined to model the time-continuous evolution of a first-order laminate microstructure. Although this model provides interesting results on the material point level, owing to the global minimization in the evolution equations, the calculation time and numerical instabilities may cause problems when applying this model to macroscopic specimens. In this paper, a smooth transition zone between the laminates is introduced to avoid global minimization, which makes the numerical calculations cumbersome compared with the model in Kochmann & Hackl. By introducing a smooth viscous transition zone, the dissipation potential and its numerical treatment have to be adapted. We outline rate-dependent time-evolution equations for the internal variables based on variational techniques and show as first examples single-slip shear and tension/compression tests.