The structure of stress-strain relations in finite elasto-plasticity

The importance of the distinction between rotation in the continuum and material sense is emphasized. Starting from the stability of thin-walled tube test specimens, material stability at finite strains is formulated for any choice of conjugate stress and strain. Normality is investigated when total strain rates are non-integrable. It is the total strain rate minus the instantaneous elastic strain rate that follows normality. The general lack of normality exhibited by the rate of strain of the unloaded body element is evaluated quantitatively. A general criterion for convexity of the yield surface is established, and the effect on convexity of changing the stress definition is examined.