On constitutive relations in non-smooth elasto/viscoplasticity

A general treatment of constitutive relations in elastoplasticity and elasto/viscoplasticity is presented. The treatment holds for general non-smooth problems and it applies to non-smooth yield criteria and to functions characterized by non-differentiability. The formulation is developed by resorting to the tools provided by convex analysis and subdifferential calculus which are the appropriate instruments for dealing with convex criteria and non-smooth functions. General formulations of constitutive relations and evolutive laws are presented for elastoplasticity and elasto/viscoplasticity and connections are illustrated between the general elastoplastic model problem and the general elasto/viscoplastic model problem. The presented generalized treatment proves to be well-suited for the development of variational formulations for structural problems in elastoplasticity and elasto/viscoplasticity.