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Microplane modelling and particle modelling of cohesive-frictional materials

  • E. Kuhl
  • G. A. D’Addetta
  • M. Leukart
  • E. Ramm
Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 568)

Abstract

This paper aims at comparing the microplane model as a particular representative of the class of continuous material models with a discrete particle model which is of discontinuous nature. Thereby, the constitutive equations of both approaches will be based on Voigt’s hypothesis defining the strain state on the individual microplanes as well as the relative particle displacements. Through an appropriate constitutive assumption, the microplane stresses and the contact forces can be determined. In both cases, the equivalence of microscopic and macroscopic virtual work yields the overall stress strain relation. An elastic and an elasto-plastic material characterization of the microplane model and the particle model are derived and similarities of both approaches are illustrated.

Keywords

Contact Force Tangential Contact Granular Assembly Contact Vector Plastic Multiplier 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    R. J. Bathurst, L. Rothenburg: J. Appl. Mech. 55, 17 (1988)CrossRefGoogle Scholar
  2. 2.
    Z. P. Bažant, P. G. Gambarova: J. Struct. Eng. 110, 2015 (1984)CrossRefGoogle Scholar
  3. 3.
    Z. P. Bažant and B. H. Oh: ZAMM 66, 37 (1986)CrossRefzbMATHGoogle Scholar
  4. 4.
    Z. P. Bažant, P. Prat: J. Eng. Mech. 114, 1672 (1988)CrossRefGoogle Scholar
  5. 5.
    B. Cambou, P. Dubujet, F. Emeriault, F. Sidoro.: Eur. J. Mech. A / Solids 14, 255 (1995)zbMATHGoogle Scholar
  6. 6.
    I. Carol, Z. P. Bažant, P. Prat: Int. J. Solids & Structures 29, 1173 (1992)CrossRefGoogle Scholar
  7. 7.
    C. S. Chang: ‘Dislocation and plasticity of granular materials with frictional contacts’. In: Powders & Grains 93, ed. Thornton, pp. 105–110, (1993)Google Scholar
  8. 8.
    C. S. Chang: ‘Numerical and analytical modelling of granulates’. In: Computer Methods and Advances in Geomechanics, ed. by Yuan, pp. 105–114, (1997)Google Scholar
  9. 9.
    J. Christoffersen, M. M. Mehrabadi, S. Nemat-Nasser: J. Appl. Mech. 48, 339 (1981)zbMATHCrossRefGoogle Scholar
  10. 10.
    P. A. Cundall, O. D. L. Strack: Géotechnique 29, 47 (1979)CrossRefGoogle Scholar
  11. 11.
    A. Drescher, G. de Josselin de Jong: J. Mech. Phys. Solids 20, 337 (1972)CrossRefADSGoogle Scholar
  12. 12.
    F. Emeriault, B. Cambou: Int. J. Solids & Structures 33, 2591 (1996)zbMATHCrossRefGoogle Scholar
  13. 13.
    H. Hertz: J. für die reine u. angew. Math. 92, 156 (1881)Google Scholar
  14. 14.
    K.-I. Kanatani: Int. J. Eng. Sci. 22, 149 (1984)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    N. P. Kruyt, L. Rothenburg: J. Appl. Mech. 118, 706 (1996)CrossRefGoogle Scholar
  16. 16.
    E. Kuhl, E. Ramm: Mech. Coh. Fric. Mat. 3, 343 (1998)CrossRefGoogle Scholar
  17. 17.
    E. Kuhl, G. A. D’Addetta, H. J. Herrmann, E. Ramm: Granular Matter 2, 113 (2000)CrossRefGoogle Scholar
  18. 18.
    M. Lätzel, S. Luding, H. J. Herrmann: Granular Matter 2, 123 (2000)CrossRefGoogle Scholar
  19. 19.
    C.-L. Liao, T.-P. Chang, D.-H. Young and C. S. Chang: Int. J. Solids & Structures 34, 4087 (1997)zbMATHCrossRefGoogle Scholar
  20. 20.
    V. A. Lubarda, D. Krajcinovic: Int. J. Solids & Structures 30, 2859 (1993)zbMATHCrossRefGoogle Scholar
  21. 21.
    O. Mohr: Zeitschrift des Vereins Deutscher Ingenieure, 46, pp. 1524–1530, 1572-1577, (1900)Google Scholar
  22. 22.
    L. Rothenburg, A. P. S. Selvadurai: ‘A micromechanical definition of the Cauchy stress tensor for particulate media’. In: Proceedings of the International Symposium on Mechanical Behavior of Structured Media, ed. by Selvadurai, pp. 469–486, (1981)Google Scholar
  23. 23.
    A. Suiker, H. Askes, L. J. Sluys: ‘Micro-mechanically based 1-d gradient damage models’. To appear in: Proceedings of the ECCOMAS 2000 Google Scholar
  24. 24.
    K. Walton: J. Mech. Phys. Solids 35, 213 (1987)zbMATHCrossRefADSGoogle Scholar
  25. 25.
    O. C. Zienkiewicz, G. N. Pande: Int. J. Num. Anal. Meth. Geom. 1, 219 (1977)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • E. Kuhl
    • 1
  • G. A. D’Addetta
    • 1
  • M. Leukart
    • 1
  • E. Ramm
    • 1
  1. 1.Institute of Structural MechanicsUniversity of StuttgartStuttgartGermany

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