A yield-limited Lagrange multiplier formulation for frictional contact

International Journal for Numerical Methods in Engineering

Volumn 48, Issue 8, 2000, Pages 1127-1149

  Jones, Reese E ^a,b   Papadopoulos, Panayiotis ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b SANDIA NATIONAL LABORATORIES   (United States)

Author keywords

Contact mechanics; Finite element method; Friction

Indexed keywords

COMPUTER SIMULATION; FINITE ELEMENT METHOD; FRICTION; FUNCTIONS; KINEMATICS; SOLIDS;

CONTACT MECHANICS; FRICTIONAL CONTACT; PLANAR QUASISTATIC PROBLEM; PREDICTOR CORRECTOR SCHEME; YIELD FUNCTION;

LAGRANGE MULTIPLIERS;

CONTACT RESISTANCE; FINITE ELEMENT METHOD; FRICTION; LAGRANGIAN ANALYSIS;

EID: 0034234562     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(20000720)48:8<1127::AID-NME937>3.0.CO;2-C     Document Type: Article

References (29)

1. Amontons G. De la resistance causée dans des machines. Mémories de l'Académie Royale A 1699; 275-282.
2. Suh NP, Sin H-C. The genesis of friction. Wear 1981; 69:91-114.
3. Rabinowicz E. Friction and Wear of Materials (2nd edn). Wiley: New York, 1995.
4. Bowden FP, Brookes CA, Hanwell AE. Anisotropy of friction in crystals. Nature 1964; 203:27-30.
5. Ruina A. Slip instability and state variable friction laws. Journal of Geophysical Research 1983; 88:10,359-10,370.
6. Godet M, Play D, Berthe D. An attempt to provide a unified treatment of tribology through load carrying capacity, transport and continuum mechanics. Journal of Lubrication Technology 1980; 102:153-164.
7. Michalowski R, Mróz Z. Associated and non-associated sliding rules in contact friction problems. Archives of Mechanics 1978; 30:259-276.
8. Curnier A. A theory of friction. International Journal of Solids and Structures 1984; 20:637-647.
9. Papadopoulos P, Solberg JM. A Lagrange multiplier method for the finite element solution of frictionless contact problems. Mathematical and Computer Modelling 1998; 28:373-384.
10. Truesdell C, Toupin RA. Principles of classical mechanics and field theory. In Handbuch der Physik, vol. III/1, Flügge S (ed.). Springer: Berlin, 1960.
11. Kosiński W. Field Singularities and Wave Analysis in Continuum Mechanics. Wiley: New York, 1986.
12. He Q-C, Curnier A. Anisotropic dry friction between two orthotropic surfaces undergoing large displacements. European Journal of Mechanics, A/Solids 1993; 12:631-666.
13. Casey J. On finitely deforming rigid-plastic materials. International Journal of Plasticity 1986; 2:247-277.
14. Casey J. A treatment of internally constrained materials. Journal of Applied Mechanics 1995; 62:542-544.
15. Panagiotopoulos PD. A nonlinear programming approach to the unilateral contact-, and friction-boundary value problem in the theory of elasticity. Ingenieur Archive 1975; 44:421-432.
16. Fredriksson B. Finite element solution of surface nonlinearities with special emphasis to contact and fracture mechanics problems. Computers and Structures 1976; 6:281-290.
17. Feijoo RA, Barbosa HJC, Zouain N. Numerical formulations for contact problems with friction. Journal de Mécanique Théorique et Appliquee 1988; 7 (Suppl. 1):129-144.
18. Wriggers P, Vu Van T, Stein E. Finite element formulation of large deformation impact-contact problems with friction. Computers and Structures 1990; 37:319-331.
19. Klarbring A, Björkman G. Solution of large displacement contact problems with friction using Newton's method for generalized equations. International Journal for Numerical Methods in Engineering 1992; 34:249-269.
20. Laursen TA, Simo JC. A continuum-based finite element formulation for the implicit solution of multibody, large deformation frictional contact problems. International Journal for Numerical Methods in Engineering 1993; 36:3451-3486.
21. Bathe K-J, Mijailovich S. Finite element analysis of frictional contact problems. Journal de Mécanique Théorique et Appliquée 1988; 7:31-45 (Special issue, Suppl.).
22. Ju J-W, Taylor RL. A perturbed Lagrangian formulation for the finite element solution matrix of non-linear frictional contact problems. Journal de Mécanique Théorique et Appliquée 1988; 7:1-14 (Special issue, Suppl.).
23. Chawla V, Laursen TA. Energy consistent algorithms for frictional contact problems. International Journal for Numerical Methods in Engineering 1998; 42:799-827.
24. Hughes TJR, Taylor RL, Sackman JL, Curnier A, Kanoknukulchai W. A finite element method for a class of contact-impact problems. Computer Methods in Applied Mechanics and Engineering 1976; 8:249-276.
25. Curnier A, Alart P. A generalized Newton method for contact problems with friction. Journal de Mécanique Théorique et Appliquée 1988; 7:67-82 (Special issue, Suppl.).
26. Taylor RL. FEAP - a Finite Element Analysis Program, Users Manual. University of California, Berkeley, 1998, http://www.ce.berkeley.edu/rlt.
27. Papadopoulos P, Taylor RL. A mixed formulation for the finite element solution of contact problems. Computer Methods in Applied Mechanics and Engineering 1992; 94:373-389.
28. Cattaneo C. Sur contatto di due corpi elastici: distribuzione locale degli sforzi. Rendiconti dell' Accademia Nazionale dei Lincei 27, Series 1938; 6:342-348, 434-436, 474-478.
29. Mindlin RD. Compliance of elastic bodies in contact. Journal of Applied Mechanics 1949; 16:259-268.