Large Plastic Deformation of Polycrystals

This paper is devoted to the description of the general relationships between micro- and macroscales in non-linear mechanics. After a thermodynamical presentation of these relations, we point out some particular cases of non-linearities, especially the case of polycrystalline aggregates in finite strain. In the case of the single crystal, the energy is well defined in the frame of the crystal lattice, the deformation of which is essentially reversible. The plastic deformation preserves the orientation and the structure of the lattice. In the case of the polycrystal, the constitutive law has the same form as the single-crystal orne, the evolution of a triad of vectors is necessary to describe the evolution of the microstructure and to ensure uniqueness of the decomposition of the deformation gradient in a reversible and a plastic part.The problem of the evolution of the internal state of a single crystal and of a polycrystal is investigated, including the symmetry of the rate boundary-value problem.