The directional instability problem in systems with frictional contacts

Computer Methods in Applied Mechanics and Engineering

Volumn 193, Issue 3-5, 2004, Pages 357-384

  Pinto da Costa, A ^a   Martins, J A C ^a   Figueiredo, I N ^b   Judice J J ^b  

^a INSTITUTO SUPERIOR TÉCNICO   (Portugal)

^b UNIVERSITY OF COIMBRA   (Portugal)

Author keywords

Angular bifurcation; Complementarity problems; Coulomb friction; Directional instability; Finite elements

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; FRICTION; NUMERICAL METHODS; SURFACE PROPERTIES;

COMPLEMENTARITY FORMULATIONS; DIRECTIONAL INSTABILITY;

MECHANICAL ENGINEERING;

FRICTION; INSTABILITY;

EID: 0347300437     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2003.09.013     Document Type: Article

References (40)

1. Andersson L.-E. Klarbring A. Existence and uniqueness for quasistatic contact problems with friction Martins J.A.C. Monteiro Marques M.D.P. Contact Mechanics, Proceedings of the 3rd Contact Mechanics International Symposium, Praia da Consolação, Peniche, Portugal, 17-21 June 2001 Solid Mechanics and Its Applications vol. 103 2002 245-260 Kluwer Academic Publishers
2. Bigoni D. Bifurcation and instability of non-associative elastoplastic solids Petryk H. Material Instabilities in Elastic and Plastic Solids CISM Courses and Lectures vol. 414 2000 1-52 Springer-Verlag
3. Björkman G. Path following and critical points for contact problems Comput. Mech. 10 1992 231-246
4. Brace W.F. Byerlee J.D. Stick slip as a mechanism for earthquakes Science 153 1966 990-992
5. Chateau X. Nguyen Q.-S. Buckling of elastic structures in unilateral contact with or without friction Eur. J. Mech., A/Solids 10 1 1991 71-89
6. Martins J.A.C. Raous M. Friction and Instability CISM Courses and Lecture vol. 457 2002 Springer-Verlag Wien New York
7. Cottle R.W. Pang J.-S. Stone R.E. The Linear Complementarity Problem 1992 Academic Press Boston
8. Dirkse S.P. Ferris M.C. The PATH solver: a non-monotone stabilization scheme for mixed complementarity problems Optim. Methods Software 5 1995 123-156
9. Duran J. Sands, Powders and Grains: An Introduction to the Physics of Granular Materials 2000 Springer-Verlag
10. Earles S.W.E. Lee C.K. Instabilities arising from the frictional interaction of a pin-disk system resulting in noise generation ASME, J. Engrg. Ind. February 1976 81-86
11. Earles S.W.E. Badi M.N.M. Oscillatory instabilities generated in a double-pin and disc undamped system: a mechanism of disc-brake squeal Proc. Inst. Mech. Engrs. 198C 4 1984 43-50
12. Hill R. A general theory of uniqueness and stability in elastic-plastic solids J. Mech. Phys. Solids 6 1958 236-249
13. Ibrahim R.A. Friction-induced vibration, chatter, squeal and chaos. Part I: Mechanics of contact and friction Appl. Mech. Rev. 47 7 1994 209-226
14. Ibrahim R.A. Friction-induced vibration, chatter, squeal and chaos. Part II: Dynamics and modeling Appl. Mech. Rev. 47 7 1994 227-253
15. Klarbring A. On discrete and discretized non-linear elastic structures in unilateral contact (stability, uniqueness and variational principles) Int. J. Solids Struct. 24 5 1988 459-479
16. Klarbring A. Examples of non-uniqueness and non-existence of solutions to quasistatic contact problems with friction Ingenieur-Archiv. 56 1990 529-541
17. Klarbring A. Björkman G. Solution of large displacement contact problems with friction using Newton's method for generalized equations Int. J. Num. Meth. Engrg. 34 1992 249-269
18. Klarbring A. Stability and critical points in large displacement frictionless contact problems Martins J.A.C. Raous M. Friction and Instabilities CISM Courses and Lectures vol. 457 2002 39-64 Springer-Verlag
19. Martins J.A.C. Barbarin S. Raous M. Pinto da Costa A. Dynamic stability of finite dimensional linearly elastic systems with unilateral contact and Coulomb friction Comput. Methods Appl. Mech. Engrg. 177 1999 289-328
20. Martins J.A.C. Pinto da Costa A. Stability of finite-dimensional nonlinear elastic systems with unilateral contact and friction Int. J. Solids Struct. 37 18 2000 2519-2564
21. Martins J.A.C. Pinto da Costa A. Simões F.M.F. Some notes on friction and instabilities Martins J.A.C. Raous M. Friction and Instabilities CISM Courses and Lectures vol. 457 2002 65-136 Springer-Verlag, Wien New York
22. Moore R.E. Methods and Applications of Interval Analysis 1979 SIAM--Studies in Applied Mathematics
23. Mróz Z. Plaut R.H. On the stability and post-critical behavior of elastic structures with dry friction Int. J. Solids Struct. 29 10 1992 1241-1253
24. Mróz Z. Contact friction models and stability problems Martins J.A.C. Raous M. Friction and Instabilities CISM Courses and Lectures vol. 457 2002 179-232 Springer-Verlag
25. K.G. Murty, Linear Complementarity, Linear and Nonlinear Programming, 1997. Available from
26. Neumaier A. Interval methods for systems of equations Rota G.-C. Encyclopedia of Mathematics and its Applications 1990 Cambridge University Press
27. Nguyen Q.-S. Stabilité et bifurcation des systèmes dissipatifs standards à comportement indépendant du temps physique C.R. Acad. Sci. Paris 310 Série II 1990 1375-1380
28. Nguyen Q.-S. Stabilité et Mécanique Non-Linéaire 2000 Hermes Science Publications Paris
29. Petryk H. Theory of bifurcation and instability in time-independent plasticity Nguyen Q.S. Bifurcation and Stability of Dissipative Systems CISM Courses and Lectures vol. 327 1993 95-152 Springer, Wien New York
30. Petryk H. Material instabilities in elastic and plastic solids CISM Courses and Lectures vol. 414 2000 Springer, Wien New York
31. Pinto da Costa A. Figueiredo I.N. Júdice J.J. Martins J.A.C. A complementarity eigenproblem in the stability analysis of finite dimensional elastic systems with frictional contact Ferris M.C. Mangasarian O.L. Pang J.-S. Complementarity: Applications, Algorithms and Extensions 2001 50 Kluwer Academic Publishers Dordrecht
32. Progri R. Villechaise B. Analyse des glissements dans un contact sec C.R. Acad. Sci. Paris 299 Série II, 12 1984 763-768
33. Raniecki B. Bruhns O.T. Bounds to bifurcation stresses in solids with non-associated plastic flow law at finite strain J. Mech. Phys. Solids 29 2 1981 153-172
34. Rice J.R. Ruina A.L. Stability of steady frictional slipping ASME, J. Appl. Mech. 50 1983 343-349
35. Rice J.R. New perspectives on crack and fault dynamics Aref H. Philips J.W. Mechanics for a New Millenium 2001 1-24 Kluwer Academic Publishers
36. Scholz C.H. The Mechanics of Earthquakes and Faulting 1990 Cambridge University Press Cambridge, UK
37. Shanley F.R. The column paradox J. Aeronaut. Sci. 13 12 1946 678
38. Shanley F.R. Inelastic column theory J. Aeronaut. Sci. 14 5 1947 261-267
39. Vola D. Raous M. Martins J.A.C. Friction and instability of steady sliding: squeal of a rubber/glass contact Int. J. Num. Meth. Engrg. 46 10 1999 1699-1720
40. T. Zeghloul, B. Villechaise, Stress waves in a sliding contact, Part 1: Experimental study, in: Proc. 22nd Leeds-Lyon symposium on Tribology, 5-8 September 1995