Journal
COMPUTATIONAL MECHANICS
Volume 65, Issue 1, Pages 193-215Publisher
SPRINGER
DOI: 10.1007/s00466-019-01760-w
Keywords
Incompressible elasticity; Large strain elasticity; Mixed finite elements; Piecewise linear interpolation; Transient dynamics
Funding
- Medical University of Graz
- European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Action H2020-MSCA-IF-2016 InsiliCardio [750835]
- Austrian Science Fund (FWF) [F3210-N18, I2760-B30]
- BioTechMed award
- BioTechMed-Graz
- Marie Curie Actions (MSCA) [750835] Funding Source: Marie Curie Actions (MSCA)
- Austrian Science Fund (FWF) [I2760] Funding Source: Austrian Science Fund (FWF)
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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 P-1 - P-1 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.
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