Skip to main content
SpringerLink
Log in

Objective Rates in Finite Elastoplasticity

  • Conference paper
Book cover IUTAM Symposium on Computational Mechanics of Solid Materials at Large Strains

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

Abstract

An Eulerian rate formulation of finite elastoplasticity is a composite one, in which objective Eulerian tensor rates are used. Among a large variety of objective rates, how to choose suitable ones has been one of the crucial points in finite elastoplasticity. It is realized that the foregoing composite formulation of elastoplasticity should fulfill certain criteria in order to avoid inconsistencies or contradictions.

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

Access this chapter

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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bruhns, O.T., Xiao, H. and Meyers, A. (1999). Self-consistent Eulerian rate type elastoplasticity models based upon the logarithmic stress rate. Int. J. Plasticity, 15, 479–520.

    Article  MATH  Google Scholar 

  2. Dafalias, Y.F. (1985). The plastic spin. J. Appl. Mech., 52, 865–871.

    Article  ADS  MATH  MathSciNet  Google Scholar 

  3. Dienes, J.K. (1979). On the analysis of rotation and stress rate in deforming bodies. Acta Mechanica, 32, 217–232.

    Article  MATH  MathSciNet  Google Scholar 

  4. Green, A.E. and Naghdi, P.M. (1965) A general theory of an elastic-plastic continuum. Arch. Rat. Mech. Anal., 18, 251–281.

    Article  MATH  MathSciNet  Google Scholar 

  5. Hill, R. (1958). A general theory of uniqueness and stability in elastic-plastic solids. J. Mech. Phys. Solids, 6, 236–249.

    Article  ADS  MATH  Google Scholar 

  6. Hill, R. (1978). Aspects of invariance in solid mechanics. Adv. Appl. Mech., 18, 1–75.

    Article  MATH  Google Scholar 

  7. Hoger, A. (1987). The stress conjugate to the logarithmic strain. Int. J. Solids Struct., 23, 1645–1656.

    Article  MATH  MathSciNet  Google Scholar 

  8. Lee, E.H. (1969). Elastic-plastic deformation at finite strains. J. Appl. Mech., 36, 1–6.

    Article  ADS  MATH  Google Scholar 

  9. Lee, E.H., Mallett, R.L. and Wertheimer, T.B. (1983). Stress analysis for anisotropic hardening in finite deformation plasticity. J. Appl. Mech., 50, 554–560.

    Article  ADS  MATH  Google Scholar 

  10. Lehmann, Th. (1962). Zur Beschreibung großer plasticher Formänderungen unter Berücksichtigung der Werkstoffverfestigung. Rheologica Acta, 2, 247–254.

    Article  Google Scholar 

  11. Nagtegaal, J.C. and De Jong, J.E. (1982). Some aspects of non-isotropic work-hardening in finite strain plasticity. In: Plasticity of Metals at Finite Strain: Theory, Computation and Experiment, E.H. Lee and R.L. Mallet (eds.), Stanford University, pp.65–102.

    Google Scholar 

  12. Nemat-Nasser, S. (1982). On finite deformation elastoplasticity. Int. J. Solids Struct., 18, 857–872.

    Article  MATH  Google Scholar 

  13. Prager, W. (1960). An elementary discussion of definitions of stress rate. Q. Appl. Math., 18, 403–407.

    MathSciNet  Google Scholar 

  14. Simó, J.C. and Pister, K.S. (1984). Remarks on rate constitutive equations for finite deformation problem: computational implications. Comp. Meth. Appl. Mech. Engng., 46, 201–215.

    Article  MATH  Google Scholar 

  15. Truesdell, C.A. and Noll, W. (1965). The nonlinear field theories of mechanics. In: Handbuch der Physik, S. Flügge (ed.), vol. III/3, Berlin: Springer-Verlag.

    Google Scholar 

  16. Xiao, H., Bruhns, O.T. and Meyers, A. (1997). Logarithmic strain, logarithmic spin and logarithmic rate. Acta Mechanica, 124, 89–105.

    Article  MATH  MathSciNet  Google Scholar 

  17. Xiao, H., Bruhns, O.T. and Meyers, A. (1998). On objective corotational rates and their defining spin tensors. Int. J. Solids Struct., 35, 4001–4014.

    Article  MATH  MathSciNet  Google Scholar 

  18. Xiao, H., Bruhns, O.T. and Meyers, A. (1998). Objective corotational rates and unified work-conjugacy relation between Lagrangean and Eulerian stress and strain measures. Arch. Mech., 50, 913–943.

    Google Scholar 

  19. Xiao, H., Bruhns, O.T. and Meyers, A. (2000). A consistent finite elastoplasticity theory combining additive and multiplicative decomposition of the stretching and the deformation gradient. Int. J. Plasticity, 16, 143–177.

    Article  MATH  Google Scholar 

  20. Xiao, H., Bruhns, O.T. and Meyers, A. (2000). The choice of objective rates in finite elastoplasticity: general results on the uniqueness of the logarithmic rate. Proc. Roy. Soc. London, A 456, 1865–1882.

    ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mechanics, Ruhr- University Bochum, Universitätsstraße 150, 44780, Bochum, Germany

    O. T. Bruhns

Authors
  1. O. T. Bruhns
    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

Bruhns, O.T. (2003). Objective Rates in Finite Elastoplasticity. 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_13

Download citation

  • DOI: https://doi.org/10.1007/978-94-017-0297-3_13

  • 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