On unifying concrepts in plasticity theory and related matters in numerical analysis

Abstract

This paper summarizes a rate-independent theory for multiple-mode plastic straining which unifies constitutive equations of macroscopic solids and single crystals at both infinitesimal and finite strain. A basic symmetry postulate plays a key role in the general theory. This postulate enables stress and plastic mechanism rates to be derived from a saddle potential function and leads to connections between uniqueness of solution and minimum principles. One such principle permits the independent variation of displacement and plastic mechanism rates. This is significant to the investigation of convergence of the finite element method in incremental boundary value problems. The theory also has noteworthy consequences for the finite distortion of single crystals and the analysis of crystalline aggregates.