A Selection of Benchmark Problems in Solid Mechanics and Applied Mathematics

Jörg Schröder, Thomas Wick, Stefanie Reese, Peter Wriggers, Ralf Müller, Stefan Kollmannsberger, Markus Kästner, Alexander Schwarz, Maximilian Igelbüscher, Nils Viebahn, Hamid Reza Bayat, Stephan Wulfinghoff, Katrin Mang, Ernst Rank, Tino Bog, Davide D’Angella, Mohamed Elhaddad, Paul Hennig, Alexander Düster, Wadhah GarhuomSimeon Hubrich, Mirjam Walloth, Winnifried Wollner, Charlotte Kuhn, Timo Heister

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


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 Non-Standard Discretisation Methods, Mechanical and Mathematical Analysis’.

Original languageEnglish
Pages (from-to)713-751
Number of pages39
JournalArchives of Computational Methods in Engineering
Issue number2
StatePublished - Mar 2021


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