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Session Chair: Jörg Schröder, UDE Session Chair: Alexander Schwarz, University of Duisburg-Essen
Location:Auditorium Wolfsburg
Presentations
The Stability of Mixed Polygonal Finite Element Formulations in Nearly-Incompressible Hyperelasticity
Björn Sauren, Sven Klinkel
RWTH Aachen Universtity, Germany
In this work, we assess the stability of the lower-order mixed displacement-pressure formulation on polygonal and quadrilateral meshes in both linear and nonlinear analysis. We address the inf-sup stability and especially the occurrence of spurious pressure modes (checkerboard modes). It is shown that, in both linear and nonlinear analysis, the existence of spurious pressure modes is purely dependent on the chosen discretization technique. A comparison between quadrilateral and Voronoi discretizations demonstrates that spurious modes are suppressed on Voronoi meshes without the need for any type of stabilization method. To discretize Voronoi meshes, a polygonal mixed displacement-pressure element based on the scaled boundary parameterization [1] is used. Several numerical examples in both nearly-incompressible linear elasticity and nonlinear hyperelasticity are presented. In particular, the absence of spurious checkerboard modes on Voronoi meshes in each Newton iteration is shown in the large strain regime.
References
[1] B. Sauren, S. Klarmann, L. Kobbelt and S. Klinkel, A mixed polygonal finite element formulation for nearly-incompressible finite elasticity. Comput. Methods Appl. Mech. Engrg., Vol. 403, pp. 115656, 2023
