Skip to main content
SpringerLink
Log in
Book cover

IUTAM Symposium on Computational Mechanics of Solid Materials at Large Strains pp 385–394Cite as

Goal-Oriented Error Control for Large Strain Viscoplasticity

  • Conference paper

  • 442 Accesses

Part of the book series: Solid Mechanics and Its Applications ((SMIA,volume 108))

Abstract

In this paper we investigate the possibility for, and characteristics of, reliable and efficient a posteriori error computation at the integration of the constitutive relations pertinent to large strain viscoplasticity. An important feature is the possibility to select “goal-oriented” error measures with great freedom. A key task is to identify and solve the pertinent dual problem.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Becker, R. and Rannacher, R. (1996). A feed-back approach to error control in finite element methods: basic analysis and examples. East-West J. Numer. Math., 4, 237–264.

    MATH  MathSciNet  Google Scholar 

  2. Cirak, F. and Ramm, E. (1998). A posteriori error estimation and adaptivity for linear elasticity using the reciprocal theorem. Computer Methods in Applied Mechanics and Engineering, 156, 351–362.

    Article  ADS  MATH  MathSciNet  Google Scholar 

  3. Cirak, F. and Ramm, E. (2000). A posteriori error estimation and adaptivity for elastoplasticity using the reciprocal theorem. International Journal for Numerical Methods in Engineering, 47, 379–393.

    Article  ADS  MATH  MathSciNet  Google Scholar 

  4. Eriksson, K. and Johnson, C. (1991). Adaptive finite element methods for parabolic problems I: A linear model problem. SIAM Journal on Numerical Analysis, 28, 43–77.

    Article  MATH  MathSciNet  Google Scholar 

  5. Eriksson, K., Estep, D., Hansbo, P. and Johnson C. (1995). Introduction to adaptive methods for differential equations. Acta Numerica, 105–158.

    Google Scholar 

  6. Johnson, C. and Hansbo, P. (1992). Adaptive finite element methods in computational mechanics. Computer Methods in Applied Mechanics and Engineering, 101, 143–181.

    Article  ADS  MATH  MathSciNet  Google Scholar 

  7. Ladevèze, P., Moës, N. and Douchin, B. (1999). Constitutive relation errors (visco)plastic finite element analysis with softening. Computer Methods in Applied Mechanics and Engineering, 176, 247–264.

    Article  ADS  MATH  MathSciNet  Google Scholar 

  8. Ladevèze, P. (2001). Constitutive relation errors for F.E. analysis considering (visco)plasticity and damage. International Journal for Numerical Methods in Engineering, 52, 527–542.

    Article  ADS  MATH  MathSciNet  Google Scholar 

  9. Larsson, F., Runesson, K. and Hansbo, P. (2001). Computation of goal-oriented a posteriori error measures in space-time finite elements for viscoplasticity. In: Trends in Computational Structural Mechanics, Wall, W.A., Bletzinger, K.-U., Schweizerhof, K. (eds.), CIMNE, Barcelona, 499–510.

    Google Scholar 

  10. Larsson, F., Runesson, K. and Hansbo, P. Time finite elements and error computation for (visco)plasticity with hardening or softening. International Journal for Numerical Methods in Engineering, in print.

    Google Scholar 

  11. Larsson, F., Hansbo, P. and Runesson, K. Space-time finite elements and an adaptive strategy for the coupled thermoelasticity problem. International Journal for Numerical Methods in Engineering, in print.

    Google Scholar 

  12. Larsson, F., Hansbo, P. and Runesson, K. Strategies for computing goal-oriented a posteriori error measures in nonlinear elasticity. International Journal for Numerical Methods in Engineering, submitted.

    Google Scholar 

  13. Oden, J.T. and Prudhomme, S. (2001). Goal-oriented error estimation and adaptivity for the finite element method. Computers and Mathematics with Applications, 41, 735–756.

    Article  MATH  MathSciNet  Google Scholar 

  14. Ohnimus, S., Rüter, M. and Stein, E. A global and local a posteriori error estimator in finite elasticity. Computational Mechanics, submitted.

    Google Scholar 

  15. Prudhomme, S. and Oden, J.T. (1999). On goal-oriented error estimation for elliptic problems: application to the control of pointwise errors. Computer Methods in Applied Mechanics and Engineering, 176, 313–331.

    Article  ADS  MATH  MathSciNet  Google Scholar 

  16. Rannacher, R. (1999). Error control in finite element computations. An introduction to error estimation and mesh-size adaptation. NATO ASI series Series C. Mathematical and physical sciences, 536, 247–278.

    MathSciNet  Google Scholar 

  17. Rannacher, R. (2001). An optimal control approach to a posteriori error estimation in finite element methods. Preprint 2001–14 (SFB 359), University of Heidelberg.

    Google Scholar 

  18. Rannacher, R. and Suttmeier F.T. (1999). A posteriori error estimation and mesh adaptation for finite element models in elasto-plasticity. Computer Methods in Applied Mechanics and Engineering, 176, 333–361.

    Article  ADS  MATH  MathSciNet  Google Scholar 

  19. Rüter, M., Stein, E., Larsson, F., Hansbo, P. and Runesson, K. (2001). Strategies for goaloriented error measures in nonlinear elasticity. Proceedings: 2nd European Conference on Computational Mechanics.

    Google Scholar 

  20. Steeb, H. and Ramm, E. (2000). A general framework for local error estimation applied to material nonlinear problems. Proceedings: European Congress on Computational Methods in Applied Sciences and Engineering.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mechanics, Chalmers University of Technology, Hörsalsvägen 7, 41296, Göteborg, Sweden

    F. Larsson, K. Runesson & P. Hansbo

Authors
  1. F. Larsson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. Runesson
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. Hansbo
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of Stuttgart, Germany

    Christian Miehe

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer Science+Business Media Dordrecht

About this paper

Cite this paper

Larsson, F., Runesson, K., Hansbo, P. (2003). Goal-Oriented Error Control for Large Strain Viscoplasticity. In: Miehe, C. (eds) IUTAM Symposium on Computational Mechanics of Solid Materials at Large Strains. Solid Mechanics and Its Applications, vol 108. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0297-3_35

Download citation

  • DOI: https://doi.org/10.1007/978-94-017-0297-3_35

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-6239-0

  • Online ISBN: 978-94-017-0297-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation