Duality results and regularization schemes for Prandtl--Reuss perfect plasticity
- Hintermüller, Michael
- Rösel, Simon
2010 Mathematics Subject Classification
- 74C05 49M15 49K20 49M29
- perfect plasticity, Prandtl-Reuss plasticity, small-strain, Fenchel duality, semismooth Newton
We consider the time-discretized problem of the quasi-static evolution problem in perfect plasticity posed in a non-reflexive Banach space and we derive an equivalent version in a reflexive Banach space. A primal-dual stabilization scheme is shown to be consistent with the initial problem. As a consequence, not only stresses, but also displacement and strains are shown to converge to a solution of the original problem in a suitable topology. This scheme gives rise to a well-defined Fenchel dual problem which is a modification of the usual stress problem in perfect plasticity. The dual problem has a simpler structure and turns out to be well-suited for numerical purposes. For the corresponding subproblems an efficient algorithmic approach in the infinite-dimensional setting based on the semismooth Newton method is proposed.
- ESAIM Control Optim. Calc. Var., published online on 01.03.2021, DOI 10.1051/cocv/2018004 .