A Selection of Benchmark Problems in Solid Mechanics and Applied Mathematics
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ORIGINAL PAPER
A Selection of Benchmark Problems in Solid Mechanics and Applied Mathematics Jörg Schröder1 · Thomas Wick2 · Stefanie Reese3 · Peter Wriggers4 · Ralf Müller5 · Stefan Kollmannsberger6 · Markus Kästner7 · Alexander Schwarz1 · Maximilian Igelbüscher1 · Nils Viebahn1 · Hamid Reza Bayat3 · Stephan Wulfinghoff12 · Katrin Mang2 · Ernst Rank6 · Tino Bog6 · Davide D’Angella6 · Mohamed Elhaddad6 · Paul Hennig7 · Alexander Düster8 · Wadhah Garhuom8 · Simeon Hubrich8 · Mirjam Walloth9 · Winnifried Wollner9 · Charlotte Kuhn10 · Timo Heister11 Received: 21 July 2020 / Accepted: 17 August 2020 © The Author(s) 2020
Abstract In this contribution we provide benchmark problems in the field of computational solid mechanics. In detail, we address classical fields as elasticity, incompressibility, material interfaces, thin structures and plasticity at finite deformations. For this we describe explicit setups of the benchmarks and introduce the numerical schemes. For the computations the various participating groups use different (mixed) Galerkin finite element and isogeometric analysis formulations. Some programming codes are available open-source. The output is measured in terms of carefully designed quantities of interest that allow for a comparison of other models, discretizations, and implementations. Furthermore, computational robustness is shown in terms of mesh refinement studies. This paper presents benchmarks, which were developed within the Priority Programme of the German Research Foundation ‘SPP 1748 Reliable Simulation Techniques in Solid Mechanics—Development of NonStandard Discretisation Methods, Mechanical and Mathematical Analysis’.
* Thomas Wick [email protected]‑hannover.de
Stephan Wulfinghoff [email protected]‑kiel.de
Jörg Schröder j.schroeder@uni‑due.de
Katrin Mang [email protected]‑hannover.de
Stefanie Reese stefanie.reese@rwth‑aachen.de
Ernst Rank [email protected]
Peter Wriggers [email protected]‑hannover.de
Tino Bog [email protected]
Ralf Müller [email protected]‑kl.de
Davide D’Angella [email protected]
Stefan Kollmannsberger [email protected]
Mohamed Elhaddad [email protected]
Markus Kästner markus.kaestner@tu‑dresden.de
Paul Hennig paul.hennig@tu‑dresden.de
Alexander Schwarz alexander.schwarz@uni‑due.de
Alexander Düster [email protected]
Maximilian Igelbüscher maximilian.igelbuescher@uni‑due.de
Wadhah Garhuom [email protected]
Nils Viebahn nils.viebahn@uni‑due.de
Simeon Hubrich [email protected]
Hamid Reza Bayat hamid.reza.bayat@rwth‑aachen.de
Mirjam Walloth [email protected]‑darmstadt.de
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J. Schröder et al.
1 Introduction Solving partial differential equations on complex geometries is perhaps one of the most important scientific achievement of the last decades. Analytical or manufactured solutions of such differential equations, e.g. from engineering or economics, is in most cases not available. Therefore, computeraided numerical algorithms play an important role. At this point we mention that
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