Neunteufel, M., Pechstein, A. S., & Schöberl, J. (2021). Three-field mixed finite element methods for nonlinear elasticity. Computer Methods in Applied Mechanics and Engineering, 382, Article 113857. https://doi.org/10.1016/j.cma.2021.113857
E101-03 - Forschungsbereich Scientific Computing and Modelling
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Journal:
Computer Methods in Applied Mechanics and Engineering
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ISSN:
0045-7825
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Date (published):
15-Aug-2021
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Number of Pages:
28
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Peer reviewed:
Yes
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Keywords:
Computer Science Applications; Mechanical Engineering; Mechanics of Materials; General Physics and Astronomy; Computational Mechanics
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Abstract:
In this paper, we extend the tangential-displacement normal-normal-stress continuous (TDNNS) method from Pechstein and Schöberl (2011) to nonlinear elasticity. By means of the Hu-Washizu principle, the distributional derivatives of the displacement vector are lifted to a regular strain tensor. We introduce three different methods, where either the deformation gradient, the Cauchy-Green strain tensor, or both of them are used as independent variables. Within the linear sub-problems, all stress and strain variables can be locally eliminated leading to an equation system in displacement variables, only. The good performance and accuracy of the presented methods are demonstrated by means of several numerical examples.
