Duality results and regularization schemes for Prandtl–Reuss perfect plasticity

We consider the time-discretized problem of quasi-static evolution in perfect plasticity posed a non-reflexive Banach space. Based on novel equivalent reformulation reflexive space, primal is characterized as Fenchel dual classical incremental stress problem. This allows to obtain necessary and sufficient optimality conditions for time-discrete problems plasticity. Furthermore, consistency primal-dual stabilization scheme proven. As consequence, not only stresses, but also displacements strains are shown converge solution original suitable topology. The corresponding has simpler structure turns out be well-suited numerical purposes. For resulting subproblems an efficient algorithmic approach infinite-dimensional setting based semismooth Newton method proposed.