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

Professor Germain has proposed in [Germain, 1973] a theory of Cosserat con- tinua 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 element 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 to this unknown. First we recall the main equations of Cosserat continua, then we present a kine- matic description of polycrystals and, finally, we establish the constitutive equationsfor the case at issue.