An internal variable theory of inelastic behaviour derived from the uniaxial rigid-perfectly plastic law

In the general framework provided by the internal variable theories of associated inelastic behaviour the formulation of constitutive relations is addressed in this paper. Attention is focused on the basic properties of the evolution relation involving rates of internal variables and dual thermodynamic forces. It is shown that a suitable generalization of the uniaxial rigid-perfectly plastic law can be performed by introducing the definition of step-shaped constitutive maps. This definition allows us to derive a general theory of associated inelastic behaviour with its characteristic properties: convexity of the elastic locus, normality rule, existence of a sublinear dissipation functional and of a canonical yield functional. Finally the formulation of the constitutive relation in terms of yield functionals and related inelastic multipliers is discussed. The analysis is performed on the basis of a chain rule of subdifferential calculus, recently contributed by the authors, which provides an effective tool to develop the theory of Kuhn-Tucker vectors in optimization problems. © 1993