Duality results and regularization schemes for Prandtl–Reuss perfect plasticity
| Autor: | Michael Hintermüller, S. Rösel |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Control and Optimization
010102 general mathematics Prandtl number Banach space Duality (optimization) Plasticity 01 natural sciences Regularization (mathematics) Small strain 010101 applied mathematics Computational Mathematics symbols.namesake Control and Systems Engineering symbols Applied mathematics Stress Problem 0101 mathematics Newton's method Mathematics |
| Zdroj: | ESAIM: Control, Optimisation and Calculus of Variations. 27:S1 |
| ISSN: | 1262-3377 1292-8119 |
| Popis: | We consider the time-discretized problem of the quasi-static evolution problem in perfect plasticity posed in a non-reflexive Banach space. Based on a novel equivalent reformulation in a reflexive Banach space, the primal problem is characterized as a Fenchel dual problem of the classical incremental stress problem. This allows to obtain necessary and sufficient optimality conditions for the time-discrete problems of perfect plasticity. Furthermore, the consistency of a primal-dual stabilization scheme is proven. As a consequence, not only stresses, but also displacements and strains are shown to converge to a solution of the original problem in a suitable topology. The corresponding dual problem has a simpler structure and turns out to be well-suited for numerical purposes. For the resulting subproblems an efficient algorithmic approach in the infinite-dimensional setting based on the semismooth Newton method is proposed. |
| Databáze: | OpenAIRE |
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