Details
| Original language | English |
|---|---|
| Pages (from-to) | 479-492 |
| Number of pages | 14 |
| Journal | Computational mechanics |
| Volume | 60 |
| Issue number | 3 |
| Publication status | Published - 5 May 2017 |
Abstract
In this work we investigate different mixed finite element formulations for the detection of critical loads for the possible occurrence of bifurcation and limit points. In detail, three- and two-field formulations for incompressible and quasi-incompressible materials are analyzed. In order to apply various penalty functions for the volume dilatation in displacement/pressure mixed elements we propose a new consistent scheme capturing the non linearities of the penalty constraints. It is shown that for all mixed formulations, which can be reduced to a generalized displacement scheme, a straight forward stability analysis is possible. However, problems based on the classical saddle-point structure require a different analyses based on the change of the signature of the underlying matrix system. The basis of these investigations is the work from Auricchio et al. (Comput Methods Appl Mech Eng 194:1075–1092, 2005, Comput Mech 52:1153–1167, 2013).
Keywords
- Condensed formulations, Signature of a matrix, Stability analysis, Three-field and two-field mixed FEM
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Ocean Engineering
- Engineering(all)
- Mechanical Engineering
- Computer Science(all)
- Computational Theory and Mathematics
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Computational mechanics, Vol. 60, No. 3, 05.05.2017, p. 479-492.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On the stability analysis of hyperelastic boundary value problems using three- and two-field mixed finite element formulations
AU - Schröder, Jörg
AU - Viebahn, Nils
AU - Wriggers, Peter
AU - Auricchio, Ferdinando
AU - Steeger, Karl
N1 - Funding information: The authors gratefully acknowledge Gerhard Starke, Fleurianne Bertrand and Rainer Niekamp for helpful discussions. The authors appreciate the support by the Deutsche Forschungsgemeinschaft in the Priority Program 1748 “Novel finite elements for anisotropic media at finite strain” under the project “Reliable Simulation Techniques in Solid Mechanics, Development of Non-standard Discretization Methods, Mechanical and Mathematical Analysis” (SCHR 570/23-1) (WR 19/50-1).
PY - 2017/5/5
Y1 - 2017/5/5
N2 - In this work we investigate different mixed finite element formulations for the detection of critical loads for the possible occurrence of bifurcation and limit points. In detail, three- and two-field formulations for incompressible and quasi-incompressible materials are analyzed. In order to apply various penalty functions for the volume dilatation in displacement/pressure mixed elements we propose a new consistent scheme capturing the non linearities of the penalty constraints. It is shown that for all mixed formulations, which can be reduced to a generalized displacement scheme, a straight forward stability analysis is possible. However, problems based on the classical saddle-point structure require a different analyses based on the change of the signature of the underlying matrix system. The basis of these investigations is the work from Auricchio et al. (Comput Methods Appl Mech Eng 194:1075–1092, 2005, Comput Mech 52:1153–1167, 2013).
AB - In this work we investigate different mixed finite element formulations for the detection of critical loads for the possible occurrence of bifurcation and limit points. In detail, three- and two-field formulations for incompressible and quasi-incompressible materials are analyzed. In order to apply various penalty functions for the volume dilatation in displacement/pressure mixed elements we propose a new consistent scheme capturing the non linearities of the penalty constraints. It is shown that for all mixed formulations, which can be reduced to a generalized displacement scheme, a straight forward stability analysis is possible. However, problems based on the classical saddle-point structure require a different analyses based on the change of the signature of the underlying matrix system. The basis of these investigations is the work from Auricchio et al. (Comput Methods Appl Mech Eng 194:1075–1092, 2005, Comput Mech 52:1153–1167, 2013).
KW - Condensed formulations
KW - Signature of a matrix
KW - Stability analysis
KW - Three-field and two-field mixed FEM
UR - http://www.scopus.com/inward/record.url?scp=85018773836&partnerID=8YFLogxK
U2 - 10.1007/s00466-017-1415-2
DO - 10.1007/s00466-017-1415-2
M3 - Article
AN - SCOPUS:85018773836
VL - 60
SP - 479
EP - 492
JO - Computational mechanics
JF - Computational mechanics
SN - 0178-7675
IS - 3
ER -