Journal of Physical Studies 25(1), Article 1401 [8 pages] (2021)
DOI: https://doi.org/10.30970/jps.25.1401

NONLINEAR WAVE DYNAMICS OF A DISPERSE GRANULAR LAYER STIMULATED BY AN INWARDS MOVING PISTON

Sergiy Mykulyak , Sergii Skurativskyi 

Subbotin Institute of Geophysics, NAS of Ukraine,
63B, Bohdan Khmelnytskyi St., Kyiv, UA-03142, Ukraine,
e-mail: mykulyak@ukr.net

Received 22 April 2020; in final form 15 November 2020; accepted 16 October 2020; published online 16 February 2021

Three-dimensional simulations of wave propagation in a granular medium layer containing particles with polydisperse size distribution are performed using the discrete element method (DEM). The wave is generated by a piston subjected to an impulse load. It is shown that in the free surface layer, rotation wave structures are formed. Their location, time of occurrence and duration are determined using correlation analysis. These wave structures are revealed when the friction between the grains (particles) is incorporated and, moreover, the gravitation field resulting in the non-uniform distribution of the inter-particle force field is taken into account. The absence of the rotation wave formation is also shown when the inhomogeneity caused by the gravitational field is destroyed by vertical loading.

Key words: granular medium, nonlinear waves, rotation wave structure

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References
  1. H. M. Jaeger, S. R. Nagel, Science 255, 1523 (1992);
    Crossref
  2. H. M. Jaeger, S. R. Nagel, Rev. Mod. Phys. 68, 1259 (1996);
    Crossref
  3. A. Mehta, Granular Physics (Cambridge University Press, Cambridge, 2007).
  4. B. Andreotti, Y. Forterre, O. Pouliquen, Granular Media: between Fluid and Solid (Cambridge University Press, Cambridge, 2013).
  5. V. A. Danylenko, S. V. Mykulyak, V. O. Polyakovskyi, V. V. Kulich, I. I. Oleynik, Phys. Rev. E. 96, 012906 (2017);
    Crossref
  6. S. V. Mykulyak, V. O. Polyakovskyi, S. I. Skurativskyi, Pure Appl. Geophys. 176, 4309 (2019);
    Crossref
  7. C. H. Liu, S. R. Nagel, Phys. Rev. Lett. 68, 301 (1992);
    Crossref
  8. C. H. Liu, S. R. Nagel, Phys. Rev. B 48, 15646 (1993);
    Crossref
  9. C. H. Liu, S. R. Nagel, J. Phys.: Condens. Matter 6, A433 (1994);
    Crossref
  10. X. Jia, C. Caroli, B. Velicky, Phys. Rev. Lett. 82, 1863 (1999);
    Crossref
  11. E. T. Owens, K. E. Daniels, Europhys. Lett. 94, 54005 (2011);
    Crossref
  12. S. R. Hostler, C. E. Brennen, Phys. Rev. E 72, 031303 (2005);
    Crossref
  13. J. Anfosso, V. Gibiat, Europhys. Lett. 67, 376 (2004);
    Crossref
  14. X. Jia, Phys. Rev. Lett. 93, 154303 (2004);
    Crossref
  15. E. Somfai, J. N. Roux, J. H. Snoeijer, M. van Hecke, W. van Saarloos, Phys. Rev. E 72, 021301 (2005);
    Crossref
  16. V. N. Nikolaevskiy, Geomechanics and Fluidodynamics: With Applications to Reservoir Engineering. Ser.: Theory and Applications of Transport in Porous Media 8 (Springer, Netherlands, 1996).
  17. B. Velický, C. Caroli, Phys. Rev. E 65, 021307 (2002);
    Crossref
  18. H. A. Makse, N. Gland, D. L. Johnson, L. Schwartz, Phys. Rev. E 70, 061302 (2004);
    Crossref
  19. O. Mouraille, W. A. Mulder, S. Luding, J. Stat. Mech. 7, P07023 (2006);
    Crossref
  20. O. Mouraille, S. Luding, Ultrasonics 48, 498 (2008);
    Crossref
  21. V. F. Nesterenko, Dynamics of Heterogeneous Materials (Springer-Verlag, New York, 2001);
    Crossref
  22. S. Sen, M. Manciu, R.S. Sinkovits, A. J. Hurd, Granul. Matter 3 (2001) 33-39;
    Crossref
  23. S. Job, F. Melo, A. Sokolow, S. Sen, Granul. Matter 10, 13 (2007);
    Crossref
  24. A. P. Awasthi, K. J. Smith, P. H. Geubelle, J. Lambros, Mech. Materials 54, 100 (2012);
    Crossref
  25. A. Leonard, F. Fraternali, C. Daraio, Exp. Mech. 53, 327 (2013);
    Crossref
  26. M. Manjunath, A. Awasthi, P. Geubelle, Physica D 266, 42 (2014);
    Crossref
  27. A. Awasthi, Z. Wang, N. Broadhurst, P. Geubelle, Granular Matter 17, 21 (2015);
    Crossref
  28. P. Evesque, J. Rajchenbach, Phys. Rev. Lett. 62, 44 (1989);
    Crossref
  29. C. Laroche, S. Douady, S. Fauve, J. Phys. France 50, 699 (1989);
    Crossref
  30. J. Knight et al., Phys. Rev. E 54, 5726 (1996);
    Crossref
  31. C. R. Wassgren Jr., Ph.D. thesis (California Institute of Technology, 1997).
  32. S. V. Mykulyak, Phys. Mesomech. 17, 157 (2014);
    Crossref
  33. L. D. Landau, E. M. Lifshitz, Elasticity Theory (Pergamon Press, Oxford, 1975).
  34. H.J. Herrmann, S. Luding, Continuum Mech. Thermodyn. 10, 189 (1998);
    Crossref
  35. W. C. Swope, H. C. Andersen, P. H. Berens, K. R. Wilson, J. Chem. Phys. 76, 637 (1982);
    Crossref
  36. Q. Spreiter and M. Walter, J. Comput. Phys.152, 102 (1999);
    Crossref