Some implications of work hardening and ideal plasticity

The purpose of this note is to point out the severe restriction imposed on possible stress-strain relations by a mathematical formulation of the concepts of work hardening and ideal plasticity. Using this condition, an algebraic derivation and extension is given of Prager’s extension of the Mises plastic potential function. A brief discussion is also given of the meaning of stability of plastic deformation as contrasted with stability of non-conservative systems in general.