On the elastic–plastic response of hemitropic Cosserat solids

Abstract

A model for the elastic–plastic response of solids is formulated on the basis of the concept of a materially uniform Cosserat continuum. Plastic deformation and rotation tensors are defined in terms of invertible mappings of a local archetypal state, encoding the constitutive response of the material, to a neighborhood of a material point in an assigned reference configuration. The archetype is mapped to a neighborhood of this material point in a current configuration by corresponding elastic kinematic descriptors. These in turn furnish the arguments of a strain-energy function that describes the response of the archetype. In the specialization to hemitropic solids, the plastic rotation is effectively eliminated from the theory by exploiting the degree of freedom afforded by material symmetry. An appropriate version of Eshelby’s tensor is identified as the driving force for dissipation and used in the construction of a yield criterion and associated flow rule for plastic evolution. In a further specialization to decoupled strain-energy functions, the force and torque balances are found to be coupled solely by the plastic deformation. Moreover, in this case, a model of kinematic hardening emerges as a natural outcome of the theory. The present work is offered as a framework for the prediction of texture development due to local grain reorientation accompanying plastic deformation in polycrystalline metals.