The European Physical Journal Special Topics

, Volume 223, Issue 11, pp 2227–2240 | Cite as

Generalized formulation of the interactions between soft spheres

  • F. Alonso-Marroquín
  • S. McNamara
Part of the following topical collections:
  1. Dynamic Systems: From Statistical Mechanics to Engineering Applications


The goal of this paper is to identify the most general formulation that consistently links the different degrees of freedom in a contact between spherical soft particles. These contact laws have two parts: a set of “generalized contact velocities” that characterize the relative motion of the two particles, and a set of “generalized contact forces” that characterize the interparticle forces. One well known constraint on contact models is that the contact velocities must be objective. This requirement fixes the number of linearly independent contact velocities. We also present a previously unnoticed (in this context) constraint, namely, that the velocities and forces must be related in such a way that the stiffness matrix is symmetric. This constraint also places restrictions on the coupling between the contact forces. Within our generalized contact model, we discuss the expression for rolling velocity that need to be used in the calculation of rolling resistance, and the risk or producing perpetual mobile when other expressions of rolling velocity are using instead.


Contact Force European Physical Journal Special Topic Contact Model Rolling Resistance Rolling Velocity 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    P.A. Cundall, O.D. Strack, Geotech. 29, 47 (1979)CrossRefGoogle Scholar
  2. 2.
    H.J. Herrmann, J. Hovi, S. Luding, NATO-ASI Series E 350 (Kluwer academic publishers, Dordrecht, 1998)Google Scholar
  3. 3.
    H.M. Jaeger, S.R. Nagel, R.P. Behringer, Rev. Mod. Phys. 68, 1259 (1996)CrossRefADSGoogle Scholar
  4. 4.
    C. Goldenberg, I. Goldhirsch, Phys. Rev. E 77, 041303 (2008)CrossRefADSGoogle Scholar
  5. 5.
    D.M. Mueth, H.M. Jaeger, S.R. Nagel, Phys. Rev. E 57, 3164 (1998)CrossRefADSGoogle Scholar
  6. 6.
    Y. Fukumoto, H. Sakaguchi, A. Murakami, Granular Matter 15, 175 (2013)CrossRefGoogle Scholar
  7. 7.
    M. Oda, J. Konishi, S. Nemat-Nasser, Mech. Mater. 1, 269 (1982)CrossRefGoogle Scholar
  8. 8.
    K. Iwashita, M. Oda, J. Eng. Mech. 124, 285 (1998)CrossRefGoogle Scholar
  9. 9.
    R. Fuchs, T. Weinhart, J. Meyer, H. Zhuang, T. Staedler, X. Jiang, S. Luding, Granular Matter 16(3), 281 (2014)CrossRefGoogle Scholar
  10. 10.
    K. Iwashita, M. Oda, Powder Technol. 109, 192 (2000)CrossRefGoogle Scholar
  11. 11.
    A. Tordesillas, D. Walsh, Powder Technol. 124, 106 (2002)CrossRefGoogle Scholar
  12. 12.
    R. Kirsch, U. Bröckel, L. Brendel, J. Török, Granular Matter 13, 517 (2011)CrossRefGoogle Scholar
  13. 13.
    S. Luding, Granular Matter 10, 235 (2008)CrossRefzbMATHGoogle Scholar
  14. 14.
    Y. Wang, P. Mora, Pure Appl. Geophys. 165, 609 (2008)CrossRefADSGoogle Scholar
  15. 15.
    K. Iwashita, M. Oda, J. Eng. Mech. 124, 286 (1998)CrossRefGoogle Scholar
  16. 16.
    A. Tordesillas, D. Walsh, Powder Technol. 124, 106 (2002)CrossRefGoogle Scholar
  17. 17.
    H.M. Shodja, E.G. Nezami, Int. J. Numer. Anal. Meth. Geomech. 27, 403 (2003)CrossRefzbMATHGoogle Scholar
  18. 18.
    K. Bagi, M.R. Kuhn, J. Appl. Mech 71, 493 (2004)CrossRefzbMATHADSGoogle Scholar
  19. 19.
    M.R. Kuhn, K. Bagi, J. Eng. Mech. 130, 826 (2004)CrossRefGoogle Scholar
  20. 20.
    F. Alonso-Marroquin, I. Vardoulakis, H. Herrmann, D. Weatherley, P. Mora, Phys. Rev. E 74, 031306 (2006)CrossRefADSGoogle Scholar
  21. 21.
    J. Ai, J.F. Chen, J.M. Rotter, J.Y. Ooi, Powder Technol. 206, 269 (2011)CrossRefGoogle Scholar
  22. 22.
    A. Mohamed, M. Gutierrez, Granular Matter 12, 527 (2010)CrossRefzbMATHGoogle Scholar
  23. 23.
    L. Brendel, J. Török, R. Kirsch, U. Bröckel, Granular Matter 13, 777 (2011)CrossRefGoogle Scholar
  24. 24.
    M. Jiang, H.S. Yu, D. Harris, Comput. Geotech. 32, 340 (2005)CrossRefGoogle Scholar
  25. 25.
    Y.C. Wang, F. Alonso-Marroquin, S. Xue, J. Xie, Particuology, available online 18 August (2014)Google Scholar
  26. 26.
    J. Roux, Phys. Rev. E 61, 6802 (2000)MathSciNetCrossRefADSGoogle Scholar
  27. 27.
    T.R. Chandrupatla, A.D. Belegundu, T. Ramesh, C. Ray, Introduction to Finite Elements in Engineering (Prentice-Hall Englewood Cliffs, New Jersey, 1991)Google Scholar
  28. 28.
    K. Bagi, M.R. Kuhn, J. Appl. Mech. 71, 493 (2004)CrossRefzbMATHADSGoogle Scholar
  29. 29.
    M.R. Kuhn, K. Bagi, Int. J. Solids Struct. 41, 5793 (2004)CrossRefzbMATHGoogle Scholar
  30. 30.
    A. Singh, V. Magnanimo, S. Luding, Powder Technol. (2013)Google Scholar
  31. 31.
    N.J. Brown, J.F. Chen, J.Y. Ooi, Granular Matter., 1 (2014)Google Scholar

Copyright information

© EDP Sciences and Springer 2014

Authors and Affiliations

  • F. Alonso-Marroquín
    • 1
  • S. McNamara
    • 2
  1. 1.School of Civil Engineering, The University of SydneySydneyAustralia
  2. 2.Institut de Physique de Rennes, Université de Rennes 1RennesFrance

Personalised recommendations