Skip to main content
SpringerLink
Log in

Granular statistical mechanics – a personal perspective

  • Review
  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract

The science of granular matter has expanded from an activity for specialised engineering applications to a fundamental field in its own right. This has been accompanied by an explosion of research and literature, which cannot be reviewed in one paper. A key to progress in this field is the formulation of a statistical mechanical formalism that could help develop equations of state and constitutive relations. This paper aims at reviewing some milestones in this direction. An essential basic step toward the development of any static and quasi-static theory of granular matter is a systematic and useful method to quantify the grain-scale structure and we start with a review of such a method. We then review and discuss the ongoing attempt to construct a statistical mechanical theory of granular systems. Along the way, we will clarify a number of misconceptions in the field, as well as highlight several outstanding problems.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. W.O. Smith, P.D. Foote, P.F. Busang, Phys. Rev. 34, 1271 (1929)

    Article  ADS  Google Scholar 

  2. T. Kallstenius, W. Bergau, Proc. 5th Int. Conf. Soil Mech. Found. Eng. 1, 165 (1961)

    Google Scholar 

  3. T. Mogami, Soils Found. 5, 26 (1965)

    Article  Google Scholar 

  4. M. Oda, Soils Found. 14, 13 (1974)

    Article  Google Scholar 

  5. C.B. Brown, “The use of maximum entropy in the characterization of granular materials”, in Continuum Mechanical and Statistical Approaches in the Mechanics of Granular Materials, edited by C.S. Cowin, M. Satake (Gakujutsu Bunken Fukyu-kai, 1978), p. 98

  6. M. Oda, S. Nemat-Nasser, M.M. Mehrabadi, Int. J. Numer. Anal. Meth. Geomech. 6, 77 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  7. H. Herrmann, Physica A 263, 51 (1999)

    Article  ADS  Google Scholar 

  8. S.F. Edwards, R.B. Oakeshott, Physica A 157, 1080 (1989)

    Article  MathSciNet  ADS  Google Scholar 

  9. S.F. Edwards, IMA Bull. 25, 94 (1989)

    Google Scholar 

  10. A. Mehta, S.F. Edwards, Physica A 157, 1091 (1989)

    Article  MathSciNet  ADS  Google Scholar 

  11. N. Xu, J. Blawzdziewicz, C.S. O’Hern, Phys. Rev. E 71, 061306 (2005)

    Article  ADS  Google Scholar 

  12. G.-J. Gao, J. Blawzdziewicz, C.S. O’Hern, Phys. Rev. E 74, 061304 (2006)

    Article  ADS  Google Scholar 

  13. G.-J. Gao, J. Blawzdziewicz, C.S. O’Hern, M. Shattuck, Phys. Rev. E 80, 061304 (2009)

    Article  ADS  Google Scholar 

  14. S. Henkes, C.S. O’Hern, B. Chakraborty, Phys. Rev. Lett. 99, 038002 (2007)

    Article  ADS  Google Scholar 

  15. L.A. Pugnaloni, I. Sánchez, P.A. Gago, J. Damas, I. Zuriguel, D. Maza, Phys. Rev. E 82, 050301(R) (2010)

    Article  ADS  Google Scholar 

  16. S.F. Edwards, R. Blumenfeld, in Powders and Grains, Stuttgart, edited by R. Garcia-Rojo, H.J. Herrmann, and S. McNamara (Balkema, Leiden, Netherlands, 2005), p. 3

  17. R. Blumenfeld, J.F. Jordan, S.F. Edwards, Phys. Rev. Lett. 109, 238001 (2012)

    Article  ADS  Google Scholar 

  18. R.C. Ball, R. Blumenfeld, Phys. Rev. Lett. 88, 115505 (2002)

    Article  ADS  Google Scholar 

  19. R. Blumenfeld, S.F. Edwards, Phys. Rev. Lett. 90, 114303 (2003)

    Article  ADS  Google Scholar 

  20. R. Blumenfeld, S.F. Edwards, Eur. Phys. J. E 19, 23 (2006)

    Article  Google Scholar 

  21. V.A. Luchnikov, N.N. Medvedev, L. Oger, J.-P. Troadec, Phys. Rev. E. 59, 72057212 (1999)

    Article  Google Scholar 

  22. T. Aste, Phys. Rev. Lett. 96, 018002 (2006)

    Article  ADS  Google Scholar 

  23. C. Song, P. Wang, H.A. Makse, Nature 453, 629 (2008)

    Article  ADS  Google Scholar 

  24. M.P. Ciamarra, Phys. Rev. Lett. 99, 089401 (2007)

    Article  ADS  Google Scholar 

  25. R. Blumenfeld, S.F. Edwards, Phys. Rev. Lett. 99, 089402 (2007)

    Article  ADS  Google Scholar 

  26. G. Voronoi, J. Reine Ang. Math. 133, 97 (1908)

    MATH  Google Scholar 

  27. B. Delaunay, Bulletin de l’Académie des Sci. de l’URSS, Classe des Sci. Mathématiques et Naturelles 6, 793 (1934)

    Google Scholar 

  28. A. Okabe, B. Boots, K. Sugihara, Spatial Tessellations. Concepts and Applications of Voronoi Diagrams (J. Wiley and Sons, Chichester, New York, Brisbane, Toronto and Singapore, 1992)

  29. R. Blumenfeld, “Stress transmission and isostatic states of non-rigid particulate systems”, in IMA Volume in Mathematics and its Applications, Vol. 141, Modeling of Soft Matter, edited by M.-C.T. Calderer, E.M. Terentjev (Springer-Verlag, 2005), p. 235

  30. T. Matsushima, R. Blumenfeld, Phys. Rev. Lett. 112, 098003 (2014)

    Article  ADS  Google Scholar 

  31. T. Matsushima, R. Blumenfeld, Powders and Grains (2013)

  32. J.F. Jordan, R. Blumenfeld (in preparation) (2014)

  33. S.F. Edwards, R. Blumenfeld, “Basic laws of granular materials”, in Physics of Granular Materials, edited by A. Mehta (Cambridge University Press, Cambridge, 2007)

  34. R. Blumenfeld, S.F. Edwards, J. Phys. Chem. B 113, 3981 (2009)

    Article  Google Scholar 

  35. J.F. Jordan, R. Hihinashvili, R. Blumenfeld (in preparation) (2014)

  36. R. Blumenfeld, J.F. Jordan, S.F. Edwards, Powders and Grains (2013)

Download references

Author information

Authors and Affiliations

  1. ESE, Imperial College London, London, SW7 2AZ, UK

    R. Blumenfeld

  2. Gonville and Caius College, Trinity St., Cambridge, CB2 1TA, UK

    R. Blumenfeld

  3. College of Science, National Univ. of Defence Technology, Changsha, 410073, China

    R. Blumenfeld

  4. Cavendish Laboratory, Cambridge, CB3 0HE, UK

    S.F. Edwards

Authors
  1. R. Blumenfeld
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S.F. Edwards
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. Blumenfeld.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Blumenfeld, R., Edwards, S. Granular statistical mechanics – a personal perspective. Eur. Phys. J. Spec. Top. 223, 2189–2204 (2014). https://doi.org/10.1140/epjst/e2014-02258-y

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjst/e2014-02258-y

Keywords

Search

Navigation