The equivalence of stress- and strain-based plasticity theories

Abstract

Strain space plasticity theory has been advocated by a number of researchers as a viable alternative to its stress space counterpart. However, there appears to be a certain level of uncertainty about the equivalence of stress- and strain-based plasticity theories. This paper attempts to clarify some issues raised by Casey and Naghdi [2] concerning the equivalence of these two theories. By providing the alternative conjugate expressions for the loading criteria, it will be shown that the two formulations are indeed equivalent in substance and produce equivalent expressions for the plastic strain rate, provided that the material laws used are identical in both approaches. The use of the strain space formulation in many cases, for example, when dealing with strain-softening materials, is deemed to be convenient and therefore desirable. Nevertheless, it is not essential. The findings in this article exemplify the statement made by Drucker [4]: ‘The use of a strain space or a stress space is equally permissible, but may not be equally convenient for one purpose or the other.’