Approximation of incompressible large deformation elastic problems

some unresolved issues

authored by: Ferdinando Auricchio, Lourenco Beirao Da Veiga, Carlo Lovadina, Alessandro Reali, Robert L. Taylor, Peter Wriggers
Abstract: 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 identi-fied, but a general strategy to cure them is still missing. Furthermore, a comparison with displacement-based elements, especially of high order, is presented.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): University of Milan - Bicocca (UNIMIB)
University of California at Berkeley
University of Pavia
Type: Article
Journal: Computational mechanics
Volume: 52
Pages: 1153-1167
No. of pages: 15
ISSN: 0178-7675
Publication date: 18.05.2013
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Ocean Engineering, Mechanical Engineering, Computational Theory and Mathematics, Computational Mathematics, Applied Mathematics
Electronic version(s): https://doi.org/10.1007/s00466-013-0869-0 (Access: Unknown)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{92258983aa774b759bdba84321ec484d,
title = "Approximation of incompressible large deformation elastic problems: some unresolved issues",
abstract = "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 identi-fied, but a general strategy to cure them is still missing. Furthermore, a comparison with displacement-based elements, especially of high order, is presented.",
keywords = "Incompressible nonlinear elasticity, Mixed finite elements, Stability",
author = "Ferdinando Auricchio and {Da Veiga}, {Lourenco Beirao} and Carlo Lovadina and Alessandro Reali and Taylor, {Robert L.} and Peter Wriggers",
note = "Funding information: The authors were partially supported by the European Commission through the FP7 Factory of the Future project TERRIFIC (FoF-ICT-2011.7.4, Reference: 284981), by the European Research Council through the FP7 Ideas Starting Grants n. 259229 ISOBIO and n. 205004 GeoPDEs, as well as by the Italian MIUR through the FIRB “Futuro in Ricerca” Grant RBFR08CZ0S and through the PRIN Project n. 2010BFXRHS. These supports are gratefully acknowledged.",
year = "2013",
month = may,
day = "18",
doi = "10.1007/s00466-013-0869-0",
language = "English",
volume = "52",
pages = "1153--1167",
journal = "Computational mechanics",
issn = "0178-7675",
publisher = "Springer Verlag",
number = "5",
}