Abstract
Abstract
Computational formulations for large strain, polyconvex, nearly incompressible elasticity have been extensively studied, but research on enhancing solution schemes that offer better tradeoffs between accuracy, robustness, and computational efficiency remains to be highly relevant. In this paper, we present two methods to overcome locking phenomena, one based on a displacement-pressure formulation using a stable finite element pairing with bubble functions, and another one using a simple pressure-projection stabilized $$\mathbb {P}_1 - \mathbb {P}_1$$P1-P1 finite element pair. A key advantage is the versatility of the proposed methods: with minor adjustments they are applicable to all kinds of finite elements and generalize easily to transient dynamics. The proposed methods are compared to and verified with standard benchmarks previously reported in the literature. Benchmark results demonstrate that both approaches provide a robust and computationally efficient way of simulating nearly and fully incompressible materials.
Funder
Austrian Science Fund
BioTechMed-Graz
H2020 Marie Skłodowska-Curie Actions
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Computational Theory and Mathematics,Mechanical Engineering,Ocean Engineering,Computational Mechanics
Reference87 articles.
1. Aguirre M, Gil AJ, Bonet J, Arranz Carreño A (2014) A vertex centred finite volume Jameson–Schmidt–Turkel (JST) algorithm for a mixed conservation formulation in solid dynamics. J Comput Phys 259:672–699
2. Alnæs MS, Blechta J, Hake J, Johansson A, Kehlet B, Logg A, Richardson C, Ring J, Rognes ME, Wells G N (2015) The FEniCS Project Version 1.5, Archive of Numerical Software 3.100
3. Arnold DN, Brezzi F, Fortin M (1984) A stable finite element for the Stokes equations. Calcolo 21:337–344
4. Atluri SN, Reissner E (1989) On the formulation of variational theorems involving volume constraints. Comput Mech 5(5):337–344
5. Augustin CM, Neic A, Liebmann M, Prassl AJ, Niederer SA, Haase G, Plank G (2016) Anatomically accurate high resolution modeling of cardiac electromechanics: a strongly scalable algebraic multigrid solver method for non-linear deformation. J Comput Phys 305:622–646
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