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The starting point for this work is a static macroscopic model for ahigh-contrast layered material in single-slip finite crystal plasticity,identified in [Christowiak & Kreisbeck, Calc. Var. PDE (2017)] as ahomogenization limit via {\Gamma}-convergence. First, we analyze the minimizersof this limit model, addressing the question of uniqueness and derivingnecessary conditions. In particular, it turns out that at least one of thedefining quantities of an energetically optimal deformation, namely therotation and the shear variable, is uniquely determined, and we identifyconditions that give rise to a trivial material response in the sense ofrigid-body motions. The second part is concerned with extending the statichomogenization to an evolutionary {\Gamma}- convergence-type result forrate-independent systems in specific scenarios, that is, under certainassumptions on the slip systems and suitable regularizations of the energies,where energetic and dissipative effects decouple in the limit. Interestingly,when the slip direction is aligned with the layered microstructure, thelimiting system is purely energetic, which can be interpreted as a loss ofdissipation through homogenization.

On static and evolutionary homogenization in crystal plasticity for stratified composites