On Some New General and Complementary Energy Theorems for the Rate Problems in Finite Strain, Classical Elastoplasticity

Abstract

General variational theorems for the rate problem of classical elastoplasticity at finite strains, in both Updated Lagrangian (UL) and Total Lagrangian (TL) rate forms, and in terms of alternate measures of stress-rate and conjugate strain-rates, are critically studied from the point of view of their application. Attention. is primarily focused on the derivation of consistent complementary energy rate principles which could form the basis of consistent and rational assumed stress-type finite element methods, and two such principles, in both UL and TL forms, are newly stated. Systematic procedures to exploit these new principles in the context of a finite element method are discussed. Also discussed are certain general modified variational theorems which permit an accurate numerical treatment of near incompressible behavior at large plastic strains