Skip to main content

Hierarchical Adaptive FEM at Finite Elastoplastic Deformations

  • Conference paper
Parallel Algorithms and Cluster Computing

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 52))

  • 1425 Accesses

Abstract

The simulation of non-linear problems of continuum mechanics was a crucial point within the framework of the subproject “Efficient parallel algorithms for the simulation of the deformation behaviour of components of inelastic materials”. Nonlinearity appears with the occurence of finite deformations as well as with special material behaviour as e.g. elastoplasticity.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight 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. 1. T. Apel, R. Mücke and J.R. Whiteman. An adaptive finite element technique with a-priori mesh grading. Report 9, BICOM Institute of Computational Mathematics, 1993.

    Google Scholar 

  2. 2. N. Aravas. Finite strain anisotropic plasticity: Constitutive equations and computational issues. Advances in finite deformation problems in materials processing and structures. ASME 125 : 25–32, 1991.

    Google Scholar 

  3. 3. R. Asaro. Crystal plasticity. J Appl Mech 50 : 921–934, 1983.

    Article  MATH  Google Scholar 

  4. 4. I. Babuška, W.C. Rheinboldt. A-posteriori error estimates for the finite element method. Int J Numerical Meth Eng 12 : 1597–1615, 1978.

    Article  MATH  Google Scholar 

  5. 5. I. Babuška, A. Miller. A-posteriori error estimates and adaptive techniques for the finite element method. Technical report, Institute for Physical Science and Technology, University of Maryland, 1981.

    Google Scholar 

  6. 6. D. Besdo. Zur anisotropen Verfestigung anfangs isotroper starrplastischer Medien. ZAMM 51 : T97–T98, 1971.

    Article  Google Scholar 

  7. 7. A. Bucher. Deformationsgesetze für große elastisch-plastische Verzerrungen unter Berücksichtigung einer Substruktur. PhD thesis, TU Chemnitz, 2001.

    Google Scholar 

  8. 8. A. Bucher, U.-J. Görke and R. Kreißig. A material model for finite elasto-plastic deformations considering a substructure. Int. J. Plasticity 20 : 619–642, 2004.

    Article  MATH  Google Scholar 

  9. 9. A. Bucher, A. Meyer, U.-J. Görke, R. Kreißig. A contribution to error estimation and mapping algorithms for a hierarchical adaptive FE-strategy in finite elastoplasticity. Comput. Mech. 36 : 182–195, 2005.

    Article  MATH  Google Scholar 

  10. 10. C. Carstensen, J. Alberty. Averaging techniques for reliable a posteriori FEerror control in elastoplasticity with hardening. Comput. Method. Appl. Mech. Engrg. 192 : 1435–1450, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  11. 11. H. Cramer, M. Rudolph, G. Steinl, W. Wunderlich. A hierarchical adaptive finite element strategy for elastic-plastic problems. Comput. Struct. 73 : 61–72, 1999.

    Article  MATH  Google Scholar 

  12. 12. Y.F. Dafalias. A missing link in the macroscopic constitutive formulation of large plastic deformations. In: Plasticity today, (Sawczuk, A., Bianchi, G. eds.), from the International Symposium on Recent Trends and Results in Plasticity, Elsevier, Udine, p.135, 1983.

    Google Scholar 

  13. 13. Y.F. Dafalias. On the microscopic origin of the plastic spin. Acta Mech. 82 : 31– 48, 1990.

    Article  MathSciNet  Google Scholar 

  14. 14. J.P. Gago, D. Kelly, O.C. Zienkiewicz and I. Babuška. A-posteriori error analysis and adaptive processes in the finite element method. Part I: Error analysis. Part II: Adaptive processes. Int. J. Num. Meth. Engng., 19/83 : 1593–1656, 1983.

    Google Scholar 

  15. 15. P. Haupt. On the concept of an intermediate configuration and its application to a representation of viscoelastic-plastic material behavior. Int. J. Plasticity, 1 : 303–316.

    Google Scholar 

  16. 16. R. Hill. A theory of yielding and plastic flow of anisotropic metals. Proc. Roy. Soc. of London A 193, 281–297, 1948.

    Article  MATH  Google Scholar 

  17. 17. C. Johnson, P. Hansbo. Adaptive finite element methods in computational mechanics. Comput. Methods Appl. Mech. Engrg. 101 : 143–181, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  18. 18. J. Kratochvil. Finite strain theory of cristalline elastic-plastic materials. Acta Mech. 16 : 127–142, 1973.

    Article  MATH  Google Scholar 

  19. 19. G. Kunert. Error estimation for anisotropic tetrahedral and triangular finite element meshes. Preprint SFB393/97–16, TU Chemnitz, 1997.

    Google Scholar 

  20. 20. G. Kunert. An a posteriori residual error estimator for the finite element method on anisotropic tetrahedral meshes. Numer. Math., 86(3) : 471–490, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  21. 21. G. Kunert. A local problem error estimator for anisotropic tetrahedral finite element meshes. SIAM J. Numer. Anal. 39 : 668–689, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  22. 22. G. Kunert. A posteriori l2 error estimation on anisotropic tetrahedral finite element meshes. IMA J. Numer. Anal. 21 : 503–523, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  23. 23. G. Kunert and R. Verfürth. Edge residuals dominate a posteriori error estimates for linear finite element methods on anisotropic triangular and tetrahedral meshes. Numer. Math., 86(2):283–303, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  24. 24. J. Mandel. Plasticité classique et viscoplasticité. CISM Courses and Lectures No.97, Springer-Verlag, Berlin, 1971.

    Google Scholar 

  25. 25. C. Miehe, J. Schotte, J. Schröder. Computational micro-macro transitions and overall moduli in the analysis of polycristals at large strains. Comp. Mat. Sci. 16 : 372–382, 1999.

    Article  Google Scholar 

  26. 26. J. Ning, E.C. Aifantis. On anisotropic finite deformation plasticity, Part I. A two-back stress model. Acta Mech. 106 : 55–72, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  27. 27. J. Ning, E.C. Aifantis. Anisotropic yield and plastic flow of polycristalline solids. Int. J. Plasticity 12 : 1221–1240, 1996.

    Article  MATH  Google Scholar 

  28. 28. E.T. Onat. Representation of inelastic behaviour in the presence of anisotropy and of finite deformations. In: Recent advances in creep and fracture of engineering materials and structures, Pineridge Press, Swansea, 1982.

    Google Scholar 

  29. 29. S.S. Rao. Engineering Optimization. John Wiley and Sons, New York, 1996.

    Google Scholar 

  30. 30. C. Sansour. On anisotropy at the actual configuration and the adequate formulation of a free energy function. IUTAM Symposium on Anisotropy, Inhomogenity and Nonlinearity in Solid Mechanics, 43–50, 1995.

    Google Scholar 

  31. 31. J.C. Simo. A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition: Part I. Continuum formulation. Comput. Methods Appl. Mech. Engrg. 66 : 199–219, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  32. 32. E. Steck. Zur Berücksichtigung von Vorgängen im Mikrobereich metallischer Werkstoffe bei der Entwicklung von Stoffmodellen. ZAMM 75 : 331–341, 1995.

    MATH  Google Scholar 

  33. 33. E. Stein (Ed.). Error-controlled Adaptive Finite Elements in Solid Mechanics. Wiley, Chichester, 2003.

    Google Scholar 

  34. 34. V. Ulbricht, H. Röhle. Berechnung von Rotationsschalen bei nichtlinearem Deformationsverhalten, PhD thesis, TU Dresden, 1975.

    Google Scholar 

  35. 35. H. Ziegler, D. Mac Vean. On the notion of an elastic solid. In: B. Broberg, J. Hult and F. Niordson, eds., Recent Progress in Appl. Mech. The Folke Odquist Volume, Eds. B. Broberg, J. Hult, F. Niordson, Almquist & Wiksell, Stockholm, 561–572, 1965.

    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 paper

Cite this paper

Kreißig, R., Bucher, A., Görke, UJ. (2006). Hierarchical Adaptive FEM at Finite Elastoplastic Deformations. In: Hoffmann, K.H., Meyer, A. (eds) Parallel Algorithms and Cluster Computing. Lecture Notes in Computational Science and Engineering, vol 52. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-33541-2_7

Download citation

Publish with us

Policies and ethics