TY - JOUR
T1 - Approximation of incompressible large deformation elastic problems
T2 - some unresolved issues
AU - Auricchio, Ferdinando
AU - Da Veiga, Lourenco Beirao
AU - Lovadina, Carlo
AU - Reali, Alessandro
AU - Taylor, Robert L.
AU - Wriggers, Peter
N1 - 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.
PY - 2013/5/18
Y1 - 2013/5/18
N2 - 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.
AB - 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.
KW - Incompressible nonlinear elasticity
KW - Mixed finite elements
KW - Stability
UR - http://www.scopus.com/inward/record.url?scp=84892969346&partnerID=8YFLogxK
U2 - 10.1007/s00466-013-0869-0
DO - 10.1007/s00466-013-0869-0
M3 - Article
AN - SCOPUS:84892969346
SN - 0178-7675
VL - 52
SP - 1153
EP - 1167
JO - Computational mechanics
JF - Computational mechanics
IS - 5
ER -