The node-to-segment algorithm for 2D frictionless contact: Classical formulation and special cases

Computer Methods in Applied Mechanics and Engineering

Volumn 198, Issue 41-44, 2009, Pages 3428-3451

  Zavarise, Giorgio ^a   De Lorenzis, Laura ^a  

^a UNIVERSITY OF SALENTO   (Italy)

Author keywords

Contact mechanics; Corner cases; Node to segment; Penalty method

Indexed keywords

CONTACT ELEMENTS; CONTACT MECHANICS; CORNER CASES; DISCRETIZATIONS; FRICTIONLESS CONTACTS; GEOMETRIC RELATIONSHIPS; LARGE DEFORMATIONS; NODE-TO-SEGMENT; NON MATCHING MESHES; NUMERICAL EXAMPLE; PENALTY METHOD; RESIDUAL VECTORS; TWO-DIMENSION;

MECHANICS; STIFFNESS MATRIX; TWO DIMENSIONAL;

ALGORITHMS;

EID: 69549119957     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2009.06.022     Document Type: Article

References (22)

1. Bathe K.J., and Chaudhary A.B. A solution method for planar and axisymmetric contact problems. Int. J. Numer. Methods Engrg. 21 (1985) 65-88
2. Chen X., and Hisada T. Development of a finite element contact analysis algorithm to pass the patch test. Jpn. Soci. Mech. Eng. Int. J. Ser. A 49 4 (2006) 483-491
3. Crisfield M.A. Revisiting the contact patch test. Int. J. Numer. Methods Engrg. 44 (2000) 1334-1355
4. El-Abbasi N., and Bathe K.J. Stability and patch test performance of contact discretizations and a new solution algorithm. Comput. Struct. 79 (2001) 1473-1486
5. J.O. Hallquist, Nike2D: an implicit, finite deformation, finite element code for analyzing the static and dynamic response of two-dimensional solids. Technical Report UCRL-52678, University of California, Lawrence Livermore National Laboratory, Livermore, 1979.
6. Hallquist J.O., Goudreau G.L., and Benson D.J. Sliding interfaces with contact-impact in large-scale Lagrange computations. Comput. Methods Appl. Mech. Engrg. 51 (1985) 107-137
7. Hughes T.R.J., Taylor R.L., Sackman J., Curnier A., and Kanoknukulchai W. A finite element method for a class of contact-impact problems. Comput. Methods Appl. Mech. Engrg. 8 3 (1976) 249-276
8. Hughes T.R.J., Taylor R.L., and Kanoknukulchai W. A finite element method for large displacement contact and impact problems. In: Bathe K.J. (Ed). Formulations and Computational Algorithms in FE Analysis (1977), MIT Press, Boston 468-495
9. Luenberger D.G. Linear and Nonlinear Programming (1984), Addison-Wesley, Massachusetts
10. Paggi M., Carpinteri A., and Zavarise G. A unified interface constitutive law for the study of fracture and contact problems in heterogeneous materials. Analysis and Simulation of Contact Problems. In: Wriggers P., and Nackenhorst U. (Eds). Lecture Notes in Applied and Computational Mechanics vol. 27 (2006), Springer, Berlin 297-304
11. 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
12. 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
13. Tan D. Mesh matching and contact patch test. Comput. Mech. 31 (2003) 135-152
14. Taylor R.L., and Papadopoulos P. On a patch test for contact problems in two dimensions. In: Wriggers P., and Wanger W. (Eds). Computational Methods in Nonlinear Mechanics (1991), Springer-Verlag, Berlin 690-702
15. Wriggers P., Van T.V., and Stein E. Finite element formulation of large deformation impact-contact problems with friction. Comput. Struct. 37 (1990) 319-333
16. Wriggers P., and Zavarise G. Computational contact mechanics. In: Stein E., De Borst R., and Huges T.J.R. (Eds). Encyclopedia of Computational Mechanics. Solids and Structures vol. 2 (2004), John Wiley & Sons, Ltd., Chichester 195-226
17. P. Wriggers, Computational Contact Mechanics, Springer Ed., 2006, 518 pp.
18. Wriggers P., and Simo J.C. A note on tangent stiffness for fully nonlinear contact problems. Commun. Appl. Numer. Methods 1 (1985) 199-203
19. Zavarise G., Wriggers P., Stein E., and Schrefler B.A. A numerical model for thermomechanical contact based on microscopic interface laws. Mech. Res. Commun. 19 3 (1992) 173-182
20. Zavarise G., and De Lorenzis L. A modified node-to-segment algorithm passing the contact patch test. Int. J. Numer. Methods Engrg. 79 (2009) 379-416
21. G. Zavarise, L. De Lorenzis, A strategy for frictionless contact problems with large initial penetrations, in preparation.
22. Zavarise G., and Taylor R.L. A force control method for contact problems with large penetrations. In: Owen D.R.J., Oñate E., and Hinton E. (Eds). Proceedings of the Fifth International Conference on Computational Plasticity (1997), Pineridge Press, Barcelona, Spain 280-285