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 -