A finite-strain elastic–plastic Cosserat theory for polycrystals with grain rotations

We investigate geometrically exact generalized continua of Cosserat micropolar type. A variational form of these models is recalled and extended to finite-strain elasto-plasticity based on the multiplicative decomposition of the deformation gradient. The stress driving the plastic evolution is the Eshelby energy momentum tensor. No plastic Cosserat rotation is introduced and the plastic spin is set to zero. It is argued that the traditional Cosserat couple modulus μc should be set to zero for polycrystal specimens liable to fracture in shear, still leading to a complete Cosserat theory with independent rotations in the geometrically exact case in contrast to the infinitesimal, linearized model. A geometrical linearization of the presented finite-strain plasticity model is already shown to be well posed.