  This paper is an extension of the result by Christowiak and Kreisbeck (2017),
which addresses the Gamma-convergence approach to a homogenization problem for
composite materials consisting of two distinct types of parallel layers. In
Christowiak et al. (2017), one of the layers of the material undergoes only
local rotations while the other allows local rotation and plastic deformation
along a single slip system. On the other hand, real materials show an interplay
of multiple directions of slip. Here we obtain the Gamma-limit for the problem
where the number of slip directions is increased to two. When the slip systems
are orthogonal, we derive the full homogenized energy based on generalized
convex envelopes of the original energy density. Since these envelopes are not
completely known for angles between slip directions differing from the right
angle, we present a partial, conditional homogenization result in this general
case. The analysis is based on a modification of the classical construction of
laminate microstructures but several nontrivial difficulties arise due to
nonconvex constraints being present in the composite energy.
