Domain partitioning as a result of deformation in the framework of large-strain Cosserat plasticity

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.