Skip to main content

An Adaptive Finite Element Method for Large Deformation Frictional Contact Problems

  • Conference paper
IUTAM Symposium on Discretization Methods in Structural Mechanics

Part of the book series: Solid Mechanics and its Applications ((SMIA,volume 68))

Abstract

Frictional contact problems in engineering are often associated with very complex geometries and nonlinear material behaviour. For such problems only numerical methods yield the required solution and especially the finite element method has proved to be a flexible numerical tool in this context. Since numerical methods yield approximate solutions it is necessary to control the errors inherited in the method. During the last years adaptive finite element techniques have been developed, providing automatically a numerical model which is accurate and reliable. Here we introduce an adaptive method for frictional contact problems which ensures successive improvement of the numerical solution via an iterative solution procedure to refine the finite element mesh.

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. Laursen, T. A., Simo, J. C., A Continuum-based Finite Element Formulation for the Implicit Solution of Multibody, Large Deformation Frictional Contact Problems, Int. J. Num. Meth. Engng., 36, 3451–3485, 1993

    Article  MathSciNet  MATH  Google Scholar 

  2. Wriggers, P., Miehe, C., Contact Constraints within Coupled Thermomechanical Analysis, Comp. Meth. Appl. Mech. Engrg., 113, 301–319, 1994

    Article  MathSciNet  MATH  Google Scholar 

  3. Ogden, R. W., Non-linear Elastic Deformations, Ellis Horwood, Chichester, 1984

    Google Scholar 

  4. Curnier, A., He, Q. C., Telega, J. J., Formulation of Unilateral Contact between Two Elastic Bodies Undergoing Finite Deformations, C. R. Acad. Sci. Paris, 314, 1–6, 1992

    MATH  Google Scholar 

  5. Kikuchi, N., and Oden, J. T., Contact Problems in Elasticity, SIAM, Philadelphia, 1988

    MATH  Google Scholar 

  6. Wriggers, P., On Consistent Tangent Matrices for Frictional Contact Problems, in: Proc. NUMETA 87 Conj., eds. Middleton et al., Nijhoff Publishers, Dorbrecht, 1987

    Google Scholar 

  7. Wriggers, P., Finite Element Algorithms for Contact Problems, Arch. Comp. Meth. Engng., 4, 1–49, 1995

    Article  MathSciNet  Google Scholar 

  8. Wriggers, P., Scherf, O., Carstensen, C., Adaptive Techniques for the Contact of Elastic Bodies, in: Recent Developments in Finite Element Analysis, eds. Hughes et al., CIMNE, Barcelona, 1994

    Google Scholar 

  9. Rheinboldt, W. C., Error Estimates for Nonlinear Finite Element Computations, Comp. Struct., 20, 91–98, 1985

    Article  MathSciNet  MATH  Google Scholar 

  10. Johnson, C., Adaptive Finite Element Methods for the Obstacle Problem, Technical Report, Chalmers University of Technology, Göteborg, 1991

    Google Scholar 

  11. Wriggers, P., Scherf, O., An Adaptive Finite Element Technique for Nonlinear Contact Problems, in: Contact Mechanics, Proc. 2nd Contact Mech. Int. Sym. 1994, eds. Raous et al., Plenum Publishing, London, 1995

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer Science+Business Media Dordrecht

About this paper

Cite this paper

Scherf, O., Wriggers, P. (1999). An Adaptive Finite Element Method for Large Deformation Frictional Contact Problems. In: Mang, H.A., Rammerstorfer, F.G. (eds) IUTAM Symposium on Discretization Methods in Structural Mechanics. Solid Mechanics and its Applications, vol 68. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4589-3_4

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-4589-3_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-5942-8

  • Online ISBN: 978-94-011-4589-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics