A consistent approach to continuum and discrete rate elastoplastic structural problems

The rate elasto-plastic structural problem with hardening is presented and is cast within the general theory of structural models with convex constraints. A consistent derivation of the constitutive variational principles is performed and the equivalence with the elastic predictor-plastic corrector scheme of computational plasticity is proved. Following general concepts of convex analysis and of potential theory, the more general variational formulation is derived. The space discretization is achieved by the finite element approach. The definition of a global yield function instead of a local one leads to a unique scalar plastic multiplier instead of a field of plastic multipliers and avoids their discretization. Mixed variational principles can thus be derived from the continuous ones and related computational schemes are also presented.