Volume 27, 2021Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
|Number of page(s)||32|
|Published online||01 March 2021|
Duality results and regularization schemes for Prandtl–Reuss perfect plasticity*
Department of Mathematics, Humboldt-Universität zu Berlin,
Unter d. Linden 6,
** Corresponding author: email@example.com
Accepted: 1 January 2018
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.
Mathematics Subject Classification: 74C05 / 49M15 / 49K20 / 49M29
Key words: Perfect plasticity / Prandtl–Reuss plasticity / small-strain / Fenchel duality / semismooth Newton
This research was carried out in the framework of Matheon supported by the Einstein Foundation Berlin within the ECMath projects OT1, SE5 and SE15 as well as project A-AP24. The authors further gratefully acknowledge the support of the DFG through the DFG-SPP 1962: Priority Programme “Non-smooth and Complementarity-based Distributed Parameter Systems: Simulation and Hierarchical Optimization” within Projects 10, 11 and 13.
© EDP Sciences, SMAI 2021
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