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Difficulties and limitation of statistical homogenization in granular materials

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Continuous and Discontinuous Modelling of Cohesive-Frictional Materials

Part of the book series: Lecture Notes in Physics ((LNP,volume 568))

Abstract

A global constitutive model for granular material can be obtained from a change of scale using a statistical homogenization procedure. This kind of approach uses various operators for the change of scale. This paper presents the difficulties encountered to define all these operators and analyzes the validity of the relations proposed in the literature. These different analyses are based on the results obtained from a 2 D numerical simulation using the DEM.

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References

  1. K. Bagi: Stress and strain in granular assemblies. Mechanics of Materials, 22, pp. 165–177 (1996).

    Article  Google Scholar 

  2. J. P. Bardet: Observations on the effects of particle rotations on the failure of idealized granular materials. Mechanics of Materials, 18, pp. 159–182 (1994).

    Article  Google Scholar 

  3. B. Cambou: Micromechanical approach in granular media, in: Behaviour of granular materials, ed. B. Cambou, pp. 171–216, Springer Verlag publisher (1998).

    Google Scholar 

  4. B. Cambou, Ph. Dubujet, F. Emeriault, F. Sidoro.: Homogenization for granular materials. European Journal of Mechanics, A/Solids, 14 (2), pp. 225–276,(1995).

    Google Scholar 

  5. C. S. Chang, C. L. Liao: Estimates of elastic modulus for media of randomly packed granule. Journal of applied mechanics, ASME, 48 (2), pp. 339–344,(1981).

    Google Scholar 

  6. J. Christofferson, M.M. Mehrabadi, S. Nemat-Nasser: A micromechanical description of granular material behavior. Journal of applied mechanics, ASME, 48 (2), pp. 339–344, (1981).

    Article  Google Scholar 

  7. P. A. Cundall, O. D. L. Strack: A discrete numerical model for granular assemblies. Geotechnique, 29, pp. 47–65,(1979).

    Article  Google Scholar 

  8. F. Dedecker, M. Chaze, Ph. Dubujet, B. Cambou: Specific features of strain in granular materials. Mechanics of Cohesive-Frictional Materials, 5, pp. 173–193,(2000).

    Article  Google Scholar 

  9. N. P. Kruyt, L. Rothenburg: Micromechanical definition of the strain tensor for granular materials. Journal of applied mechanics, 118, pp. 706–711,(1996).

    Article  Google Scholar 

  10. C. L. Liao, T. P. Chang, D. H. Young, C. S. Chang: Stress-Strain relationships for granular materials based on the Hypothesis of Best Fit. Int. J. Solids Structures, 34, pp. 4087–4100, (1997).

    Article  MATH  Google Scholar 

  11. E. Sanchez-Palencia, A. Zaoui: Homogenization techniques for composite media. Springer-Verlag, Berlin, (1987).

    MATH  Google Scholar 

  12. J. Weber: Recherche concernant les contraintes intergranulaires dans les milieux pulvérulents. Bulletin de liaison des Ponts et Chaussées, Paris, 20, pp. 1–20, (1966).

    Google Scholar 

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Author information

Authors and Affiliations

  1. Laboratoire de Tribologie et Dynamique des Systèmes, Ecole Centrale de Lyon, 69131, Ecully Cedex, France

    B. Cambou & Ph. Dubujet

Authors
  1. B. Cambou
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  2. Ph. Dubujet
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Editor information

Editors and Affiliations

  1. Institute of Geotechnical Engineering, University of Stuttgart, Pfaffenwaldring 35, 70569, Stuttgart, Germany

    Pieter A. Vermeer

  2. Institute of Computer Applications 1, University of Stuttgart, Pfaffenwaldring 27, 70569, Stuttgart, Germany

    Hans J. Herrmann  & Stefan Luding  & 

  3. Institute of Applied Mechanics, University of Stuttgart, Pfaffenwaldring 7, 70569, Stuttgart, Germany

    Wolfgang Ehlers  & Stefan Diebels  & 

  4. Institute of Structural Mechanics, University of Stuttgart, Pfaffenwaldring 27, 70569, Stuttgart, Germany

    Ekkehard Ramm

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© 2001 Springer-Verlag Berlin Heidelberg

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Cambou, B., Dubujet, P. (2001). Difficulties and limitation of statistical homogenization in granular materials. In: Vermeer, P.A., Herrmann, H.J., Luding, S., Ehlers, W., Diebels, S., Ramm, E. (eds) Continuous and Discontinuous Modelling of Cohesive-Frictional Materials. Lecture Notes in Physics, vol 568. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44424-6_15

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  • DOI: https://doi.org/10.1007/3-540-44424-6_15

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41525-1

  • Online ISBN: 978-3-540-44424-4

  • eBook Packages: Springer Book Archive

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