Deformation patterning in three-dimensional large-strain Cosserat plasticity

• Derivation of a rate-independent large-strain Cosserat model of plasticity.
• Computation of analytic solutions for two 3D-shear problems.
• Linking of micro-rotations to the Allen–Cahn model explains deformation patterning.

In the framework of the rate-independent large-strain Cosserat theory of plasticity explicit analytic solutions are computed in three space dimensions. It is shown that the micro-rotations can be computed by solving stationary Allen–Cahn equations. While the material parameters are within a certain range, this explains the occurrence of patterning leading to a partitioning of the domain into subsets with approximately constant rotations.