Skip to main content

A 3D study of the contact interface behavior using elastic-plastic constitutive equations

  • Chapter
Analysis and Simulation of Contact Problems

Part of the book series: Lecture Notes in Applied and Computational Mechanics ((LNACM,volume 27))

  • 2586 Accesses

Abstract

In this work a homogenization method presented by Bandeira et al [2,3,4] is enhanced in order to obtain by numerical simulation the interface law for the normal contact pressure based on statistical surface models. For this purpose elasticplastic behavior of the asperities is considered. Statistical evaluations of numerical simulations lead to a constitutive law for the contact pressure. The resulting law compared with other laws stemming from analytical investigations, like those presented by Greenwood Williamson [11] and Yovanovich [19, 32]. The non-penetration condition and the interface model for contact that takes into account the surface microstructure are investigated in detail.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alart, P.; Curnier, A. A Mixed Formulation for Frictional Contact Problems prone to Newton like Solution Methods. Computational Methods in Applied Mechanics and Engineering, v. 92, p. 353–375, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  2. Bandeira, A. A., Wriggers, P., Pimenta, P. M. Numerical Derivation of Contact Mechanics Interface Laws using a Finite Element Approach for large 3D Deformation. International Journal for Numerical Methods in Engineering: IJNME, 2005 (presented in 3rd contact mechanics international symposium: cnds, peniche, Portugal, 2001).

    Google Scholar 

  3. Bandeira, A. A., Wriggers, P., Pimenta, P. M. Numerical Simulation of 3D Contact Problems under Finite Elastic-Plastic Deformation. 7th US National Congress on Computational Mechanics, Albuquerque, New Mexico, USA, 2003.

    Google Scholar 

  4. Bandeira, A. A., Wriggers, P., Pimenta, P. M. Computational Analysis of Contact Mechanics Undergoing Large 3D Deformation. European Conference on Computational Mechanics: ECCM, Krakow, Poland, 2001.

    Google Scholar 

  5. Bertsekas, D. P. Nonlinear programming. Belmont, Athena Scientific, 1995.

    MATH  Google Scholar 

  6. Bertsekas, D. P. Constrained optimization and Lagrange multiplier methods. N. Y., Academic Press, 1984.

    MATH  Google Scholar 

  7. Curnier, A. A Theory of Friction. International Journal for Solids Structures, v. 20, p. 637–47, 1984.

    Article  MATH  Google Scholar 

  8. Evseev, D. G.; Medvedev, B. M.; Grigoriyan, G. G. Modification of the elastic-plastic model for the contact of rough surfaces. Wear, v. 150, p. 79–88, 1991.

    Article  Google Scholar 

  9. Farin, G. Curves and Surfaces for Computer Aided Geometric Design: A Practical Guide. Department of Computer Science, Arizona State University, Arizona.

    Google Scholar 

  10. Fletcher, R. Practical methods of optimization. Chichester, John Wiley & Sons, 1980. 2v.

    Google Scholar 

  11. Greenwood, J. A; Williamson, J. B. P. Contact of nominally flat surfaces. Burndy Corporation Research Division, Norwalk, Connecticut, U.S.A, 1966.

    Google Scholar 

  12. Heegaard, J. H.; Curnier, A. An Augmented Lagrangian Method for Discrete Large-Slip Contact Problems. International Journal for Numerical Methods in Engineering, v. 36, p. 569–93, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  13. Kardestuncer, H; Norrie, D. H. Finite Element Handbook. McGRAW-HILL Book Company, 1987.

    Google Scholar 

  14. Kragelsky, I.V; Dobychin, M. N.; Kombalov, V. S. Friction and Wear – Calculation Methods. (Translated from The Russian by N. Standen). Pergamon Press, 1982.

    Google Scholar 

  15. Laursen, T. A.; Maker, B. N. An augmented Lagrangian quasi-Newton solver for constrained nonlinear finite element applications. International Journal for Numerical Methods in Engineering, v. 38, p. 3571–90, 1995.

    Article  MATH  Google Scholar 

  16. Laursen, T. A.; Simo, J. C. A Continuum-Based Finite Element Formulation for the Implicit Solution of Multibody, Large Deformation Frictional Contact Problems. International Journal for Numerical Methods in Engineering, v. 36, p. 3451–85, 1993a.

    Article  MathSciNet  Google Scholar 

  17. Laursen, T. A.; Simo, J. C. Algorithmic Symmetrization of Coulomb Frictional Problems using Augmented Lagrangians. Computer Methods in Applied Mechanics and Engineering, v. 108, p. 133–46, 1993b.

    Article  MathSciNet  Google Scholar 

  18. Luenberger, D. G. Linear and Nonlinear Programming. 2. ed. Reading, Addison-Wesley Publishing Company, Massachusetts, 1984.

    MATH  Google Scholar 

  19. Yovanovich, M. M. Thermal Contact Correlations. AIAA Paper, p. 81–1164, 1981.

    Google Scholar 

  20. Oden, J. T.; Pires, E. B. Algorithms and Numerical Results for Finite Element Approximations of Contact Problems with Non-Classical Friction Laws. Computer & Structures, v. 19, p. 137–47, 1983a.

    Article  Google Scholar 

  21. Parisch, H. A Consistent Tangent Stiffness Matrix for Three-Dimensional Non-Linear Contact Analysis. International Journal for Numerical Methods in Engineering, v. 28, p. 1803–12, 1989.

    Article  MATH  Google Scholar 

  22. Pimenta, P. M. Finite deformation soil plasticity on principal axes, in: Proceedings of the Third International Conference on Computational Plasticity, Fundamentals and applications, ed. by D.R.J. Owen, E. Onate & E. Hinton, Pineridge Press Limited, Swansea, U.K., 1992, pp 859–870.

    Google Scholar 

  23. Press, W. H. Numerical recipes in C: the art of scientific computing. 2 ed. Cambridge, University Press, 1995.

    Google Scholar 

  24. Simo, J. C.; Laursen, T. A. An augmented Lagrangian Treatment of Contact Problems Involving Friction. Computers & Structures, v. 42, p. 97–116, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  25. Song, S.; Yovanovich, M. M. Explicit relative contact pressure expression: dependence upon surface roughness parameters and Vickers microhardness coefficients. AIAA Paper, p. 87–152, 1987.

    Google Scholar 

  26. Tabor, D. Friction — The Present State of Our Understanding. Journal of Lubrication Technology, v. 103, p. 169–116, 1981.

    Google Scholar 

  27. Wriggers, P. Finite Element Algorithms for Contact Problems. Archives of Computational Methods in Engineering, v. 2, n.° 4, p. 1–49, 1995.

    MATH  MathSciNet  Google Scholar 

  28. Wriggers, P.; Simo, J. C. A Note on Tangent Stiffness for Fully Nonlinear Contact Problems. Communications in Applied Numerical Methods, v. 1, p. 199–203, 1985.

    Article  MATH  Google Scholar 

  29. Wriggers, P.; Simo, J. C.; Taylor, R. L. Penalty and Augmented Lagrangian Formulations for Contact Problems. In Proceedings of NUMETA 85 Conference, eds. J. Middleton & G. N. Pande, Balkema, Rotterdam, 1985.

    Google Scholar 

  30. Wriggers, P.; Vu Van, T.; Stein, E. Finite Element Formulation of Large Deformation Impact-Contact Problems with Friction. Computers & Structures, v. 37, p. 319–31, 1990.

    Article  MATH  Google Scholar 

  31. Wriggers, P.; Zavarise, G. On the Application of Augmented Lagrangian Techniques for Nonlinear Constitutive Laws in Contact Interfaces. Comm. Num. Meth. Engng., v. 9, p. 815–24, 1993.

    Article  MATH  Google Scholar 

  32. Yovanovich, M. M. Thermal Contact Correlations. AIAA Paper, p. 81–1164, 1981.

    Google Scholar 

  33. Zavarise, G; Schrefler, B. A; Wriggers, P. Consistent Formulation for Ther-momechanical Contact based on Microscopic Interface Law, in Proceedings of COMPLAS III, eds. D.R.J. Owen, E. Hilton, E. E. Onate, Pineridge Press, 1992.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer

About this chapter

Cite this chapter

Bandeira, A., Pimenta, P., Wriggers, P. (2006). A 3D study of the contact interface behavior using elastic-plastic constitutive equations. In: Wriggers, P., Nackenhorst, U. (eds) Analysis and Simulation of Contact Problems. Lecture Notes in Applied and Computational Mechanics, vol 27. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-31761-9_35

Download citation

  • DOI: https://doi.org/10.1007/3-540-31761-9_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-31760-9

  • Online ISBN: 978-3-540-31761-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics