Analysis of the constraint equations of micro and macro states taking into account the anisotropy of material particles

Abstract

The continuous transition from the reversible to irreversible state of polycrystalline material’s loading is realizing on the hypothesis of plastic relaxation of stresses at microscopic scale, which doesn’t support experimental checks, in the reference works of E. Kroner (1961), R. Hill (1965), M. Berveriller and A. Zaoui (1979). In contrast to the traditional approaches, the way of concretizing the relations of transition from thermomechanical states to microscopic to macroscopic state is examined on the basis of general principles, formulated in [1-3], valid for reversible and irreversible processes. Based on the obtained computational relationships, the variance laws of the discrepancy of the macroscopic measure with the average value of the appropriate microscopic analogue are examined. The effects related to the dependence of the elastic constants on a macroscopic scale are described, depending on the accommodated plastic deformation.