Variational principles for a class of finite step elastoplastic problems with non-linear mixed hardening

A class of elastoplastic relations with non-linear mixed hardening is addressed in the framework of an internal variable theory. The relevant finite step structural problem, resulting from the time integration of the constitutive laws according to a backward difference scheme, is then formulated in a geometrically linear range. Convex analysis and potential theory for monotone multi-valued operators are shown to provide the rationale for the development of a consistent variational theory. As a special result, a convex minimum principle in the final values of displacements, plastic strains and plastic parameters is formulated and a critical comparison with an analogous result proposed in the literature is presented. © 1993.