There is a thesis from 1980 that shows equivalence between strain and stress envelopes. It proves mathematically, that all stress envelopes, can be expressed using strain envelopes. (P.J.Yoder, 1980, Derivation and implementation of strain space plasticity).
One peculiar feature, that caught noone's attention in the 80's is - the strain envelope makes simulation run as a parallel spring system. At the time, there were no GPU cards, so they concluded the 1% increase in computation time is not important... not important enough to re-write conventional formulation.
The thing is, strain (not stress) envelopes allow to run simulations in pure parallel mode. In onve giant, fully closed GPU loop. And convergence can be controlled using PID principles, rather than extremely computation costly rebuilding of inverse stiffness matrices. That way... it is plausible to run explicit nonlinear dynamic FEM simulations in fully parallel computation mode.
I got it to run in 1D... with 1 million bar elements. In a fully closed GPU loop using MATLAB. But it was a spare time project during a Ph.D... makes me wonder what a professional or an expert could achieve. If a student with 2h spare time per day can get that far... how far could someone qualitfied for it take it?
