We determine the effective behavior of a class of composites in finite-straincrystal plasticity, based on a variational model for materials made of fineparallel layers of two types. While one component is completely rigid in thesense that it admits only local rotations, the other one is softer featuring asingle active slip system with linear self-hardening. As a main result, weobtain explicit homogenization formulas by means of {\Gamma}-convergence. Dueto the anisotropic nature of the problem, the findings depend critically on theorientation of the slip direction relative to the layers, leading to threequalitatively different regimes that involve macroscopic shearing and blockingeffects. The technical difficulties in the proofs are rooted in the intrinsicrigidity of the model, which translates into a non-standard variational problemconstraint by non-convex partial differential inclusions. The proof of thelower bound requires a careful analysis of the admissible microstructures and anew asymptotic rigidity result, whereas the construction of recovery sequencesrelies on nested laminates.
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