Application of the theory of Cosserat media to the elasto-plastic behaviour of polycrystals

Abstract

Professor Germain has proposed in [Germain, 1973] a theory of Cosserat continua obtained through the principle of virtual power. We propose here an application of that theory to the elastoplastic behaviour of polycrystals. We put forward a model of continuum with microstructure representing a material body, the elements of which are single crystals. Crystals may deform with elasto-plastic behavior, with the plastic rules given through a multiple slip method.The field of orientation of the crystal lattice is a microscopic kinematic descriptor of the system; correspondingly the lattice spin is a kinematic unknown. As customary in the theory of continua with microstructure, a balance condition for the micro-momentum is associated with this unknown.First we recall the main equations of Cosserat continua, then we present a kinematic description of polycrystals and, finally, we establish the constitutive equations for the case at issue.KeywordsSlip SystemSlip RateMaterial ElementVirtual PowerMultiple SlipThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.