  In the framework of the rate-independent large-strain Cosserat theory of
plasticity we calculate analytically explicit solutions of a two-dimensional
shear problem. We discuss two cases where the micro-rotations are stationary
solutions of an Allen-Cahn equation. Thus, for a certain parameter range,
patterning arises and the domain is partitioned into subsets with approximate
constant rotations. This describes a possible mechanism for the formation of
grains and subgrains in deformed solids.
