Effect of variable particle stiffness on force propagation and mechanical response of a composite granular material

  • Wei Du
  • Dengming WangEmail author
  • Yang Yang
Regular Article


The force propagation and mechanical response are important for understanding the elasticity and deformation of a composite granular packings. In this paper, a 2D composite granular layers composed of particles with variable stiffness is proposed, and the effect of stiffness ratio between component particles on mechanical response is mainly considered. The results show that the decrease of stiffness ratio broadens the linear range of mechanical response and enhances the elasticity of the response in a composite granular system, showing a role similar with the friction in a monodisperse granular packings. Furthermore, a phase diagram for the crossover between a single-peaked and a double-peaked response is proposed, in which the critical stiffness ratio corresponding to the occurrence of the crossover decreases with the magnitude of external loading and increases with the friction. Finally, the microscopic mechanism of the crossover of the response is further discussed based on changes in contact network and force network.

Graphical abstract


Flowing Matter: Granular Matter 


  1. 1.
    H.M. Jaeger, S.R. Nagel, R.P. Behringer, Rev. Mod. Phys. 68, 1259 (1996)ADSCrossRefGoogle Scholar
  2. 2.
    B. Andreotti, Y. Forterre, O. Pouliquen, Granular Media: Between Fluid and Solid (Cambridge University Press, Cambridge, 2013)Google Scholar
  3. 3.
    G. Reydellet, E. Clément, Phys. Rev. Lett. 86, 3308 (2001)ADSCrossRefGoogle Scholar
  4. 4.
    J. Geng, D. Howell, E. Longhi, R.P. Behringer, G. Reydellet, L. Vanel et al., Phys. Rev. Lett. 87, 035506 (2001)ADSCrossRefGoogle Scholar
  5. 5.
    J. Geng, G. Reydellet, E. Clément, R.P. Behringer, Physica D 182, 274 (2003)ADSCrossRefGoogle Scholar
  6. 6.
    M.J. Spannuth, N.W. Mueggenburg, H.M. Jaeger, S.R. Nagel, Granular Matter 6, 215 (2004)Google Scholar
  7. 7.
    A.P.F.Atman, P. Brunet, J. Geng, G. Reydellet, G. Combe, P. Claudin et al., J. Phys: Condens. Matter 17, S2391 (2005)ADSGoogle Scholar
  8. 8.
    N. Gland, P. Wang, H.A. Makse, Eur. Phys. J. E 20, 179 (2006)CrossRefGoogle Scholar
  9. 9.
    C. Goldenberg, I. Goldhirsch, Phys. Rev. E 77, 041303 (2008)ADSCrossRefGoogle Scholar
  10. 10.
    C. Goldenberg, I. Goldhirsch, Nature (London) 435, 188 (2005)ADSCrossRefGoogle Scholar
  11. 11.
    C. Goldenberg, I. Goldhirsch, Phys. Rev. Lett. 89, 084302 (2002)ADSCrossRefGoogle Scholar
  12. 12.
    Y.H. Yang, D.M. Wang, Q. Qin, Powder Technol. 26, 272 (2014)Google Scholar
  13. 13.
    S. Ostojic, D. Panja, Phys. Rev. Lett. 97, 208001 (2006)ADSCrossRefGoogle Scholar
  14. 14.
    A.P.F. Atman, P. Claudin, G. Combe, R. Mari, EPL 101, 44006 (2013)ADSCrossRefGoogle Scholar
  15. 15.
    A.P.F. Atman, P. Claudin, G. Combe, G.H.B. Martins, Granular Matter 16, 193 (2014)CrossRefGoogle Scholar
  16. 16.
    R.M. Nedderman, Statics and Kinematics of Granular Flows (Cambridge University Press, Cambridge, UK, 1992)Google Scholar
  17. 17.
    S.B. Savage, in Physics of Dry Granular Media, edited by H.J. Herrmann, J.P. Hovi, S. Luding, NATO Advanced Studies Institute, Series B: Physics (Kluwer, Dordrecht, 1998) pp. 25--95Google Scholar
  18. 18.
    W. Wu, E. Bauer, D. Kolymbas, Mech. Mater. 23, 45 (1996)CrossRefGoogle Scholar
  19. 19.
    G. Gudehus, K. Nübel, Geotechnique 54, 187 (2004)CrossRefGoogle Scholar
  20. 20.
    J.P. Bouchaud, M.E. Cates, P. Claudin, J. Phys. I 5, 639 (1995)Google Scholar
  21. 21.
    J.P. Wittmer, M.E. Cates, P. Claudin, J. Phys. I 7, 39 (1997)Google Scholar
  22. 22.
    J.P. Bouchaud, P. Claudin, E. Clément, M. Otto, G. Reydellet, C. R. Phys. 3, 141 (2002)ADSCrossRefGoogle Scholar
  23. 23.
    D.A. Head, A.V. Tkachenko, T.A. Witten, Eur. Phys. J. E 6, 99 (2001)CrossRefGoogle Scholar
  24. 24.
    J.P. Bouchaud, P. Claudin, D. Levine, M. Otto, Eur. Phys. J. E 4, 451 (2001)CrossRefGoogle Scholar
  25. 25.
    M. Otto, J.P. Bouchaud, P. Claudin, J.E.S. Socolar, Phys. Rev. E 67, 031302 (2003)ADSCrossRefGoogle Scholar
  26. 26.
    C. Daraio, V.F. Nesterenko, E.B. Herbold, S. Jin, Phys. Rev. Lett. 96, 058002 (2006)ADSCrossRefGoogle Scholar
  27. 27.
    P.J. Wang, J.H. Xia, Y.D. Li, C.S. Liu, Phys. Rev. E 76, 041305 (2007)ADSCrossRefGoogle Scholar
  28. 28.
    S. Viridi, S.N. Khotimah, AIP Conf. Proc. 1454, 219 (2012) arXiv:1110.1906 ADSCrossRefGoogle Scholar
  29. 29.
    S.F. Pinto, M.S. Couto, A.P.F. Atman, S.G. Alves, A.T. Bernardes, H.F.V. de Resende et al., Phys. Rev. lett. 99, 068001 (2007)ADSCrossRefGoogle Scholar
  30. 30.
    P.A. Cundall, O.D.L. Strack, Geotechnique 29, 47 (1979)CrossRefGoogle Scholar
  31. 31.
    J. Shäfer, S. Dippel, D. Wolf, J. Phys. I 6, 5 (1996)Google Scholar
  32. 32.
    A.P.F. Atman, P. Claudin, G. Combe, Comput. Phys. Commun. 180, 612 (2009)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Key Laboratory of Mechanics on Disaster and Environment in Western China attached to the Ministry of Education of ChinaLanzhou UniversityLanzhouPRC
  2. 2.Department of Mechanics and Engineering Science, School of Civil Engineering and MechanicsLanzhou UniversityLanzhouPRC

Personalised recommendations