Abstract.
We analyze the dynamics of a 3D granular packing composed of particles of irregular polyhedral shape confined inside a rectangular box with a retaining wall subjected to horizontal harmonic forcing. The simulations are performed by means of the contact dynamics method for a broad set of loading parameters. We explore the vibrational dynamics of the packing, the evolution of solid fraction and the scaling of dynamics with the loading parameters. We show that the motion of the retaining wall is strongly anharmonic as a result of jamming and grain rearrangements. It is found that the mean particle displacement scales with inverse square of frequency, the inverse of the force amplitude and the square of gravity. The short-time compaction rate grows in proportion to frequency up to a characteristic frequency, corresponding to collective particle rearrangements between equilibrium states, and then it declines in inverse proportion to frequency.
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References
I.S. Aranson, Rev. Mod. Phys. 78, 641 (2006).
J.B. Knight, H.M. Jaeger, S.R. Nagel, Phys. Rev. Lett. 70, 3728 (1993).
K.M. Aoki, T. Akiyama, Phys. Rev. Lett. 52, 3288 (1996).
E. Clement, L. Vanel, J. Rajchenbach, J. Duran, Phys. Rev. E 53, 2972 (1996).
K. Liffman, G. Metcalfe, P. Cleary, Phys. Rev. Lett. 79, 4574 (1997).
O. Sano, Phys. Rev. E. 72, 051307 (2005).
P. Ribière, P. Richard, R. Delannay, D. Bideau, Phys. Rev. E 71, 011304 (2005).
M. Pica Ciamarra, M. Nicodemi, A. Coniglio, Phys. Rev. E 75, 021303 (2007).
H.M. Jaeger, S.R. Nagel, R.P. Behringer, Rev. Mod. Phys. 68, 1259 (1996).
C.E. Brennen, S. Ghosh, C.R. Wassgren, Vertical oscillation of a bed of granular material, in Powders and Grains 93, edited by C. Thornton (Balkema, Rotterdam, 1993) pp. 247-252.
S. Luding, Phys. Rev. E 52, 4442 (1995).
R.C. Weathers, M.L. Hunt, C.E. Brennen, A.T. Lee, C.R. Wassgren, Effects of Horizontal Vibration on Hopper Flows of Granular Material, in Symposium of Mechanics of Deformation and Flow of Particulate Materials, edited by C.S. Chang, A. Misra, R.Y. Liang, M. Babic (ASCE, New York, 1997) pp. 349-360.
C. Josserand, A.V. Tkachenko, D.M. Mueth, H.M. Jaeger, Phys. Rev. Lett. 85, 3632 (2000).
C.R. Wassgren, M.L. Hunt, P.J. Freese, J. Palamara, C.E. Brennen, Phys. Fluids 14, 3439 (2002).
A. Kudrolli, Rep. Prog. Phys. 67, 209 (2004).
E. Ben-Naim, J.B. Knight, E.R. Nowak, J. Chem. Phys. 100, 6778 (1996).
K.M. Aoki, T. Akiyama, Y. Maki, T. Watanabe, Phys. Rev. E 54, 874 (1996).
M.L. Hunt, R.C. Weathers, A.T. Lee, C.E. Brennen, Phys. Fluids 11, 68 (1999).
F. Alonso-Marroquin, H.J. Herrmann, Phys. Rev. Lett. 92, 054301 (2004).
S. Luding, M. Nicolas, O. Pouliquen, A minimal model for slow dynamics: Compaction of granular media under vibration or shear, in Compaction of Soils, Granulates and Powders, edited by D. Kolymbas, W. Fellin (Balkema, Rotterdam, 2004) pp. 241-249.
N. Vandewalle, G. Lumay, O. Gerasimov, F. Ludewig, Eur. Phys. J. E 22, 241 (2007).
E. Azéma, F. Radjai, R. Peyroux, F. Dubois, G. Saussine, Phys. Rev. E 74, 031302 (2006).
R.N. Swamy, H. Stavrides1, Mater. Struct. 9, 243 (2000).
K.H. Khayat, P. Paultre, S. Tremblay, Mater. J. 98, 371 (2001).
G. Saussine, Contribution à la modélisation de granulats tridimensionnels: application au ballast, PhD dissertation, Univérsité Montpellier 2, France, 2004. http://tel.archives-ouvertes.fr/tel-00077519/en/
X. Oviedo-Marlot, Etude du comportement du ballast par un modèle micromécanique, Phd dissertation, Laboratoire Central des Ponts et Chaussées (LCPC), France, 2001.
M. Jean, J.J. Moreau, Unilaterality and dry friction in the dynamics of rigid body collections, in Proceedings of Contact Mechanics International Symposium (Presses Polytechniques et Universitaires Romandes, Lausanne, Switzerland, 1992) pp. 31-48.
J. Moreau, Second European Solid Mechanics Conference, Genoa, 1994, Vol. 13 (Elsevier, Paris, 1994) pp. 93-114.
F. Radjai, Comput. Phys. Commun. 121-122, 294 (1999).
F. Dubois, M. Jean, LMGC90 une plateforme de développement dédiée à la modélisation des problèmes d'intéraction, in Actes du sixième colloque national en calcul des structures, Vol. 1 (CSMA-AFM-LMS, Giens, 2003) pp. 111-118.
M. Renouf, P. Alart, Comput. Methods Appl. Mech. Engrg. 194, 2019 (2005).
E.G. Nezami, Y.M.A Hashash, D. Zaho, J. Ghaboussi, Comput. Geotech. 31, 575 (2004).
G. Saussine, C. Cholet, P.E. Gautier, F. Dubois, C. Bohatier, J.J. Moreau, Comput. Methods Appl. Mech. Eng. 195, 2841 (2006).
R.M. Nedderman, Statics and Kinematics of Granular Materials (Cambrige University Press, Cambrige, 1992).
F. Radjai, S. Roux, Contact Dynamics Study of 2D Granular Media: Critical States and Relevant Internal Variables, in The Physics of Granular Media, edited by H. Hinrichsen, D.E. Wolf (Wiley, 2004) pp. 165-186.
J.K. Mitchell, K. Soga, Fundamentals of Soil Behavior (Wiley, New York, 2005).
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Azéma, E., Radjaï, F., Peyroux, R. et al. Short-time dynamics of a packing of polyhedral grains under horizontal vibrations. Eur. Phys. J. E 26, 327–335 (2008). https://doi.org/10.1140/epje/i2007-10331-0
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DOI: https://doi.org/10.1140/epje/i2007-10331-0