ON UNIFYING CONCEPTS IN PLASTICITY THEORY AND RELATED MATTERS IN NUMERICAL ANALYSIS.

This paper reviews a rate-independent theory (or class of theories) of multiple-mode plastic straining which unifies various constitutive equations of macroscopic solids and single crystals. Some consideration is given to the relationship between the multiple-mode theory and thermodynamic concepts, including physical aspects of finite distortion of metal crystals. Uniqueness criteria and related minimum principles in incremental (or ″rate-type″ ) boundary value problems are presenated for the general class at finite strain. Special circumstances (one being infinitesimal strain) are defined under which the uniqueness criteria assure convergence of a form of finite element approximation in the boundary value problem.