Deformation patterning in the framework of large-strain Cosserat plasticity

In the framework of the rate-independent large-strain Cosserat theory of plasticity, analytically explicit solutions of a two-dimensional shear problem are computed. Two cases are discussed 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 approximately constant rotations. This describes a possible mechanism for the formation of grains and subgrains in deformed solids. (paper)