A family of simple two-pass dual formulations for the finite element solution of contact problems

Computer Methods in Applied Mechanics and Engineering

Volumn 196, Issue 4-6, 2007, Pages 782-802

  Solberg, Jerome M ^a,b   Jones, Reese E ^a,c   Papadopoulos, Panayiotis ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

^c SANDIA NATIONAL LABORATORIES   (United States)

Author keywords

Auto contact; Convergence; Dual formulation; Finite element method; LBB condition; Two body contact; Unbiased method

Indexed keywords

ALGORITHMS; FINITE ELEMENT METHOD; INTERPOLATION; KINEMATICS;

COMPUTATIONAL MECHANICS; DUAL FORMULATION; TWO-BODY CONTACT; UNBIASED METHOD;

FRICTION;

ALGORITHMS; FINITE ELEMENT METHOD; FRICTION; INTERPOLATION; KINEMATICS;

EID: 33750452734     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2006.05.011     Document Type: Article

References (18)

1. Solberg J.M., and Papadopoulos P. An analysis of dual formulations for the finite element solution of two-body contact problems. Comput. Methods Appl. Mech. Engrg. 194 (2005) 2734-2780
2. Hughes T.J.R. The Finite Element Method; Linear Static and Dynamic Finite Element Analysis (1987), Prentice-Hall, Englewood Cliffs
3. Papadopoulos P., and Solberg J.M. A Lagrange multiplier method for the finite element solution of frictionless contact problems. Math. Comput. Model. 28 (1998) 373-384
4. Belgacem F.B., Hild P., and Laborde P. The mortar finite element method for contact problems. Math. Comput. Model. 28 (1998) 263-271
5. Wieners C., and Wohlmuth B. Duality estimates and multigrid analysis for saddle point problems arising from mortar discretizations. SIAM J. Sci. Comput. 24 (2003) 2163-2184
6. Lamichhane B.P., and Wohlmuth B.I. Mortar finite elements for interface problems. Computing 72 (2004) 333-348
7. Puso M.A., and Laursen T.A. A mortar segment-to-segment contact method for large deformation solid mechanics. Comput. Methods Appl. Mech. Engrg. 193 (2004) 601-629
8. Flemisch B., Puso M.A., and Wohlmuth B.I. A new dual mortar method for curved interfaces: 2D elasticity. Int. J. Numer. Methods Engrg. 63 (2005) 813-832
9. Fischer K.A., and Wriggers P. Frictionless 2D contact formulations for finite deformations based on the mortar method. Comput. Mech. 36 (2005) 226-244
10. Truesdell C., and Toupin R.A. The classical field theories. In: Flügge S. (Ed). Handbuch der Physik III/1 (1960), Springer Verlag, Berlin 226-793
11. Jones R.E., and Papadopoulos P. A novel three-dimensional contact finite element based on smooth pressure interpolations. Int. J. Numer. Methods Engrg. 51 (2001) 791-811
12. Barbosa H.J.C., and Hughes T.J.R. The finite element method with Lagrange multipliers on the boundary: circumventing the Babuška-Brezzi condition. Comput. Methods Appl. Mech. Engrg. 85 (1991) 109-128
13. Kikuchi N., and Oden J.T. Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods vol. 8 (1988), SIAM, Philadelphia
14. Simo J.C., Wriggers P., and Taylor R.L. A perturbed Lagrangian formulation for the finite element solution of contact problems. Comput. Methods Appl. Mech. Engrg. 50 (1985) 163-180
15. Papadopoulos P., and Taylor R.L. A mixed formulation for the finite element solution of contact problems. Comput. Methods Appl. Mech. Engrg. 94 (1992) 373-389
16. Papadopoulos P., and Taylor R.L. A simple algorithm for three-dimensional finite element analysis of contact problems. Comput. Struct. 46 (1993) 1107-1118
17. Puso M.A. A 3D mortar method for solid mechanics. Int. J. Numer. Methods Engrg. 59 (2004) 315-336
18. Heegard J.H., and Curnier A. An augmented Lagrangian method for discrete large slip contact problems. Int. J. Numer. Methods Engrg. 36 (1993) 569-593