Consistent treatment of boundaries with mortar contact formulations using dual Lagrange multipliers

Computer Methods in Applied Mechanics and Engineering

Volumn 200, Issue 9-12, 2011, Pages 1317-1332

  Cichosz, T ^a   Bischoff, M ^a  

^a UNIVERSITY OF STUTTGART   (Germany)

Author keywords

Consistency; Dual Lagrange multipliers; Large deformations; Mortar finite element method; Multibody contact; Primal dual active set strategy

Indexed keywords

CONSISTENCY; DUAL LAGRANGE MULTIPLIERS; LARGE DEFORMATIONS; MORTAR FINITE ELEMENT METHOD; MULTI-BODY; PRIMAL-DUAL ACTIVE SET STRATEGY;

ALGORITHMS; COERCIVE FORCE; DEFORMATION; FINITE ELEMENT METHOD; FREQUENCY MULTIPLYING CIRCUITS; FUNCTION EVALUATION; MORTAR; STIFFNESS MATRIX;

LAGRANGE MULTIPLIERS;

EID: 79251627756     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2010.11.004     Document Type: Article

References (31)

1. Wriggers P. Computational Contact Mechanics 2002, John Wiley & Sons, Chichester, UK.
2. Hughes T.J.R., Taylor R.L., Kanoknukulchai W. A finite element method for large displacement contact and impact problems. Formulations and Computational Algorithms in FE Analysis 1977, 468-495. MIT Press, Boston. K.J. Bathe (Ed.).
3. J.O. Hallquist, Nike2d: an implicit, finite deformation, finite element code for analyzing the static and dynamic response of two-dimensional solids, Tech. Rep. UCRL-52678, Lawrence Livermore National Laboratory, University of California, Livermore, 1979.
4. Hallquist J.O., Goudreau G.L., Benson D.J. Sliding interfaces with contact-impact in large-scale lagrange computations. Comput. Methods Appl. Mech. Engrg. 1985, 51:107-137.
5. Wriggers P., Van T.V., Stein E. Finite element formulation of large deformation impact-contact problems with friction. Comput. Struct. 1990, 37:319-333.
6. R.L. Taylor, P. Wriggers, Smooth surface discretization for large deformation frictionless contact, Tech. Rep. UCB/SEMM-99-04, University of California, Berkeley, 1999.
7. Puso M.A., Laursen T.A. A 3d contact smoothing method using gregory patches. Int. J. Numer. Methods Engrg. 2002, 54:1161-1194.
8. Papadopoulos P., Taylor R.L. A mixed formulation for the finite element solution of contact problems. Comput. Methods Appl. Mech. Engrg. 1992, 94:373-389.
9. Simo J.C., Wriggers P., Taylor R.L. A perturbed lagrangian formulation for the finite element solution of contact problems. Comput. Methods Appl. Mech. Engrg. 1985, 50:163-180.
10. Zavarise G., Wriggers P. A segment-to-segment contact strategy. Math. Comput. Model. 1998, 28:497-515.
11. Bernardi C., Maday Y., Patera A.T. Domain decomposition by the mortar element method. Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters 1993, 269-286. Kluwer Academic Publishers, Dordrecht, The Netherlands. H.G.G.M. Kasper (Ed.).
12. C. Bernardi, Y. Maday, A.T. Patera, A new nonconforming approach to domain decomposition: the mortar element method, in: H. Brezis, J.L. Lions (Eds.), Nonlinear partial differential equations and their applications, vol. XI, College de France Seminar, Longman, Harlow, 1994, pp. 13-51.
13. Ganis B., Yotov I. Implementation of a mortar mixed finite element method using a multiscale flux basis. Comput. Methods Appl. Mech. Engrg. 2009, 198:3989-3998.
14. Belgacem F., Hild P., Laborde P. The mortar finite element method for contact problems. Math. Comput. Model. 1998, 28:263-271.
15. McDewitt T.W., Laursen T.A. A mortar-finite element formulation for frictional contact problems. Int. J. Numer. Methods Engrg. 2000, 48:1525-1547.
16. Puso M.A., Laursen T.A. A mortar segment-to-segment contact method for large deformation solid mechanics. Comput. Methods Appl. Mech. Engrg. 2004, 193:601-629.
17. Puso M.A., Laursen T.A. A mortar segment-to-segment frictional contact method for large deformation. Comput. Methods Appl. Mech. Engrg. 2004, 193:4891-4913.
18. Yang B., Laursen T.A., Meng X. Two dimensional mortar contact methods for large deformation frictional sliding. Int. J. Numer. Methods Engrg. 2005, 62:1183-1225.
19. Fischer K.A., Wriggers P. Frictionless 2d contact formulation for finite deformations based on the mortar method. Comput. Mech. 2005, 36:226-244.
20. Fischer K.A., Wriggers P. Mortar based frictional contact formulation for higher order interpolations using the moving friction cone. Comput. Methods Appl. Mech. Engrg 2006, 195:5020-5036.
21. Puso M.A., Laursen T.A., Solberg J. A segment-to-segment mortar contact method for quadratic elements and large deformations. Comput. Methods Appl. Mecha. Engrg. 2008, 197:555-566.
22. Yang B., Laursen T.A. A large deformation mortar formulation of self contact with finite sliding. Comput. Methods Appl. Mech. Engrg. 2008, 197:756-772.
23. Wohlmuth B. A mortar finite element method using dual spaces for the lagrange multiplier. SIAM J. Numer. Anal. 2000, 38:989-1012.
24. Hintermüller M., Ito K., Kunisch K. The primal-dual active set strategy as a semismooth newton method. SIAM J. Optim. 2003, 13:865-888.
25. G. Stadler, Infinite-dimensional semi-smooth newton and augmented lagrangian methods for friction and contact problems in elasticity, Ph.D. thesis, TU-Graz, 2004.
26. Hüeber S., Wohlmuth B.I. A primal-dual active set strategy for non-linear multibody contact problems. Comput. Methods Appl. Mech. Engrg. 2005, 194:3147-3166.
27. Hartmann S., Brunssen S., Ramm E., Wohlmuth B. Unilateral non-linear dynamic contact of thin-walled structures using a primal-dual active set strategy. Int. J. Numer. Methods Engrg. 2007, 70:883-912.
28. Hartmann S., Ramm E. A mortar based contact formulation for non-linear dynamics using dual lagrange multipliers. Finite Elem. Anal. Des. 2008, 44:245-258.
29. Popp A., Gee M.W., Wall W.A. A finite deformation mortar contact formulation using a primal-dual active set strategy. Int. J. Numer. Methods Engrg. 2009, 79:1354-1391.
30. S. Hartmann, Kontaktanalyse dünnwandiger Strukturen bei großen Deformationen, Ph.D. thesis, Universität Stuttgart, 2007.
31. Hüeber S., Mair M., Wohlmuth B.I. A priori error estimates and an inexact primal-dual active set strategy for linear and quadratic finite elements applied to multibody contact problems. Appl. Numer. Math. 2005, 54:555-576.