Multilevel models of inelastic deformation of materials and their application for description of internal structure evolution

The paper considers a general formulation of multilevel models of inelastic deformation of materials as applied to the description of their internal structure evolution. Key problems for further development of this class of models and their solutions are put forward. An original variant of making constitutive relations of differing scale (differently scaled one-type characteristics) consistent is proposed; the consistency simultaneously provides unambiguous description of macroscale geometric nonlinearity by specifying the Cauchy stress tensor derivative independent of the choice of a reference frame. The general formulation is used to construct a two-level model of polycrystalline metals and a three-level model of semi-crystalline polymers for which hardening and lattice rotation laws of lower scales are derived from physical analysis. Numerical experiments performed with the developed algorithms of multilevel models for simple loading are described and their results are analyzed.