On some new general complementary energy theorems for the rate problems in finite strain, classical elastoplasticity

General variational theorems for the rate problem of classical elastoplastic. ity al nnite strains, in both Updated Lagransian (UL) and Total Lagrangian (TL) rate fonns, and in terms of alternate measures of stress-rate and conju-gate strain-rates, are cri tically studied from the point of view of their applica. tion. Attention, is primarily focused on the derivation of consistent complementary energy rate principles which could form the basis of consistent and rational assumed st ress-type finite element methods, and two such princi. pIes, in both UL and TL forms, are newly stated. Systematic procedures to exploit these new principles in the context of a finite dement method are dis· cussed. Also discussed are certain general modified variational theorems which permit an accurate numerical treatment of near incompressible behavior at large plastic strains