  The starting point for this work is a static macroscopic model for a
high-contrast layered material in single-slip finite crystal plasticity,
identified in [Christowiak & Kreisbeck, Calc. Var. PDE (2017)] as a
homogenization limit via {\Gamma}-convergence. First, we analyze the minimizers
of this limit model, addressing the question of uniqueness and deriving
necessary conditions. In particular, it turns out that at least one of the
defining quantities of an energetically optimal deformation, namely the
rotation and the shear variable, is uniquely determined, and we identify
conditions that give rise to a trivial material response in the sense of
rigid-body motions. The second part is concerned with extending the static
homogenization to an evolutionary {\Gamma}- convergence-type result for
rate-independent systems in specific scenarios, that is, under certain
assumptions 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, the
limiting system is purely energetic, which can be interpreted as a loss of
dissipation through homogenization.
