The choice of objective rates in finite elastoplasticity: General results on the uniqueness of the logarithmic rate. (Q2713395)

Every Eulerian rate formulation of finite elastoplasticity is a composite one comprising a rate equation for elastic behaviour and a plastic flow equation with the loading-unloading condition, as well as an evolution equation for the back stress. It is realized that each such composite rate formulation must fulfil certain consistency criteria in order to avoid contradictions. Here two such criteria, i.e. Prager's yielding-stationarity criterion and the self-consistency criterion for rate characterization of elastic behaviour, are introduced and their implications for the choice of objective rates in finite elastoplastic formulation are investigated. Prager's yielding-stationarity criterion narrows the choice of objective rates to objective corotational rates, and the self-consistency criterion for rate characterization of elastic behaviour further leads to the unique choice of logarithmic rate. The two consistency criteria in conjunction with the objectivity criterion are just the physical essence behind the uniqueness of logarithmic rate in finite elastoplasticity. It is shown that the just-stated criterion is necessary for a composite Eulerian rate formulation of finite elastoplasticity to be consistent, and means that the stress rate must be a corotational rate.