Mortar contact formulations for deformable-deformable contact: Past contributions and new extensions for enriched and embedded interface formulations

Computer Methods in Applied Mechanics and Engineering

Volumn 205-208, Issue 1, 2012, Pages 3-15

  Laursen, Tod A ^a   Puso, Michael A ^b   Sanders, Jessica ^c  

^a KHALIFA UNIVERSITY   (United Arab Emirates)

^b LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

^c USA   (United States)

Author keywords

Contact; Interface; Mortar formulations; Stabilization

Indexed keywords

CONTACT MECHANICS; CONVERGENCE RATES; DOMAIN DECOMPOSITIONS; EMBEDDED INTERFACE; IMPACT INTERACTION; INTERFACE MECHANICS; LARGE DEFORMATIONS; LARGE SLIDING; MORTAR FORMULATIONS; MORTAR METHODS; NEW RESULTS; NONCONFORMING MESH; NONSMOOTH EQUATION; STRESS RECOVERY;

CONTACTS (FLUID MECHANICS); DEFORMATION; DOMAIN DECOMPOSITION METHODS; FINITE ELEMENT METHOD; INTERFACES (MATERIALS); NONLINEAR EQUATIONS; STABILIZATION;

MORTAR;

EID: 84655164991     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2010.09.006     Document Type: Article

References (39)

1. Bernardi C., Maday Y., Patera A. A new nonconforming approach to domain decomposition: the mortar element method. Nonlinear Partial Differential Equations and their Applications 1992, 13-51. Pitman and Wiley. H. Brezia, J. Lions (Eds.).
2. Kim C., Lazarov R., Pasciak J., Vassilevski P. Multiplier spaces for the mortar finite element method in three dimensions. SIAM J. Numer. Anal. 2001, 38:519-538.
3. Wohlmuth B. Discretization Methods and Iterative Solvers Based on Domain Decomposition 2001, Springer-Verlag, Heidelberg.
4. Strang G., Fix G. An Analysis of the Finite Element Method 1973, Prentice-Hall, Englewood Cliffs, New Jersey.
5. Hughes T. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis 2000, Dover.
6. Laursen T. Computational Contact and Impact Mechanics: Fundamentals of Modeling Interfacial Phenomena in Nonlinear Finite Element Analysis 2003, Springer, Berlin.
7. Belgacem F., Maday Y. The mortar element method for three dimensional finite elements. Rairo - Math. Model. Numer. Anal. 1997, 31:289-302.
8. Seshayer P., Suri M. hp Submeshing via non-conforming finite element methods. Comput. Methods Appl. Mech. Engrg. 2000, 189:1011-1030.
9. Belgacem F., Hild P., Laborde P. Approximation of the unilateral contact problem by the mortar finite element method. CR Acad. Sci. 1991, 324:123-127.
10. Hild P. Numerical implementation of two nonconforming finite element methods for unilateral contact. Comput. Methods Appl. Mech. Engrg. 2000, 184:99-123.
11. McDevitt T., Laursen T. A mortar-finite element formulation for frictional contact problems. Int. J. Numer. Methods Engrg. 2000, 48:1525-1547.
12. J. Hallquist, NIKE2D: A Vectorized Implicit, Finite Deformation Finite Element Code for Analyzing the Static and Dynamic Response of 2-D Solids with Interactive Rezoning and Graphics, Technical Report UCID-19677, Lawrence Livermore National Laboratory, University of California, 1986 (Revision 1).
13. Simo J., Wriggers P., Taylor R. A perturbed Lagrangian formulation for the finite element solution of contact problems. Comput. Methods Appl. Mech. Engrg. 1985, 50:163-180.
14. Papadopoulos P., Taylor R. A mixed formulation for the finite element solution of contact problems. Comput. Methods Appl. Mech. Engrg. 1992, 94:373-389.
15. Zavarise G., Wriggers P. A segment-to-segment contact strategy. Math. Comput. Modell. 1998, 28:497-515.
16. Puso M., Laursen T. A mortar segment-to-segment contact method for large deformation solid mechanics. Comput. Methods Appl. Mech. Engrg. 2004, 193:601-629.
17. Hueber S., Wohlmuth B. A primal-dual active set strategy for non-linear multibody contact problems. Comput. Methods Appl. Mech. Engrg. 2005, 194:3147-3166.
18. Puso M. A 3D mortar method for solid mechanics. Int. J. Numer. Methods Engrg. 2004, 59:601-629.
19. Flemisch B., Puso M., Wohlmuth B. A new dual mortar method for curved interfaces: 2d elasticity. Int. J. Numer. Methods Engrg. 2005, 63:813-832.
20. Popp A., Gitterle M., Gee M., Wall W. A dual mortar approach for 3d finite deformation contact with consistent linearization. Int. J. Numer. Methods Engrg. 2010, 83:1428-1465.
21. Puso M., Laursen T., Solberg J. A segment-to-segment mortar contact method for quadratic elements and large deformations. Comput. Methods Appl. Mech. Engrg. 2008, 197:556-566.
22. Luenberger D. Linear and Nonlinear Programming 1984, Addison-Wesley, Reading, Massachusetts. second ed.
23. Puso M., Laursen T. A mortar segment-to-segment contact method for large deformation solid mechanics. Comput. Methods Appl. Mech. Engrg. 2004, 193:601-629.
24. Puso M., Laursen T. A mortar segment-to-segment frictional contact method for large deformations. Comput. Methods Appl. Mech. Engrg. 2004, 193:601-629.
25. Fischer K., Wriggers P. Frictionless 2d contact formulations for finite deformations based on the mortar method. Comput. Mech. 2005, 36:226-244.
26. Fischer K., 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.
27. Yang B., Laursen T. A mortar segment-to-segment frictional contact method for large deformations. Int. J. Numer. Methods Engrg. 2005, 62:1183-1225.
28. Kikuchi N., Oden J. Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods 1988, SIAM, Philadelphia.
29. Laursen T., Simo J. On the formulation and numerical treatment of finite deformation frictional contact problems. Nonlinear Computational Mechanics - State of the Art 1991, 716-736. Springer-Verlag, Berlin. P. Wriggers, W. Wagner (Eds.).
30. Foley J., et al. Computer Graphics Principles and Practice 1997, Addison-Wesley, Reading. second ed.
31. Cowper G. Gaussian quadrature formulas for triangles. Int. J. Numer. Methods Engrg. 1973, 7:405-408.
32. Yang B., Laursen T. A large deformation mortar formulation of self contact with finite sliding. Comput. Methods Appl. Mech. Engrg. 2008, 197.
33. Yang B., Laursen T. A contact searching algorithm including bounding volume trees applied to finite sliding mortar formulations. Comput. Mech. 2008, 41:189-205.
34. Yang B., Laursen T. A mortar-finite element approach to lubricated contact problems. Comput. Methods Appl. Mech. Engrg. 2009, 198:3656-3669.
35. Sanders J., Dolbow J., Laursen T. On methods for stabilizing constraints over enriched interfaces in elasticity. Int. J. Numer. Methods Engrg. 2009, 78:1009-1036.
36. Moës N., Béchet E., Tourbier M. Imposing Dirichlet boundary conditions in the extended finite element method. Int. J. Numer. Methods Engrg. 2006, 67:1641-1669.
37. Nitsche J. über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilrä umen, die keinen Randbedingungen unterworfen sind. Comput. Methods Appl. Mech. Engrg. 1971, 191:1122-1145.
38. Becker R., Hansbo P., Stenberg R. A finite element method for domain decomposition with non-matching grids. ESAIM - Math. Model. Numer. Anal. 2003, 37:209-225.
39. Wriggers P., Zavarise G. A formulation for frictionless contact problems using a weak form introduced by Nitsche. Comput. Mech. 2008, 41:407-420.