Journal
COMPUTATIONAL MECHANICS
Volume 52, Issue 5, Pages 1153-1167Publisher
SPRINGER
DOI: 10.1007/s00466-013-0869-0
Keywords
Incompressible nonlinear elasticity; Stability; Mixed finite elements
Funding
- European Commission [FoF-ICT-2011.7.4, 284981]
- European Research Council [259229 ISO-BIO, 205004 GeoPDEs]
- Italian MIUR through the FIRB Futuro in Ricerca Grant [RBFR08CZ0S]
- Italian MIUR through the PRIN [2010BFXRHS]
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Several finite element methods for large deformation elastic problems in the nearly incompressible and purely incompressible regimes are considered. In particular, the method ability to accurately capture critical loads for the possible occurrence of bifurcation and limit points, is investigated. By means of a couple of 2D model problems involving a very simple neo-Hookean constitutive law, it is shown that within the framework of displacement/pressure mixed elements, even schemes that are inf-sup stable for linear elasticity may exhibit problems when used in the finite deformation regime. The roots of such troubles are identified, but a general strategy to cure them is still missing. Furthermore, a comparison with displacement-based elements, especially of high order, is presented.
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