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Karabelas, E; Haase, G; Plank, G; Augustin, CM.
Versatile stabilized finite element formulations for nearly and fully incompressible solid mechanics.
Comput Mech. 2020; 65(1):193-215 Doi: 10.1007/s00466-019-01760-w [OPEN ACCESS]
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Führende Autor*innen der Med Uni Graz
Augustin Christoph
Karabelas Elias
Co-Autor*innen der Med Uni Graz
Plank Gernot

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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 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.

Find related publications in this database (Keywords)
Incompressible elasticity
Large strain elasticity
Mixed finite elements
Piecewise linear interpolation
Transient dynamics
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