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Tytuł artykułu

Estimation of energy dissipation during multiparticle contacts in 1D simulations of a granular material

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Języki publikacji
EN
Abstrakty
EN
In this paper we investigate numerically, in one dimension, the dynamics of a granular material taking into account particle collisions. Multiparticle contacts occur when a particle contacts with neighbouring particles in such a way that those contacts have a direct influence on each other. Multiparticle contacts are responsible for the transfer and dissipation of energy in granulr materials. We investigeted two discrete deterministic approaches - molecular dynamics and event driven methods - in order to estimate the energy dissipation in multiparticle contacts. The molecular dynamics method leads to low energy dissipation, whereas the event driven method may lead to high energy dissipation. The paper analyses the extent to which the repulsive force, used in the molecular dynamics technique, affects the numerical values of the energy dissipation. We propose the expression describing the force formulated under fractional calculus. We then illustrate and discuss how to controlthe energy dissipation between the contacting surfaces.
Rocznik
Strony
21--40
Opis fizyczny
Bibliogr. 24 poz., rys., wykr.
Twórcy
  • Institute of Mathematics and Computer Science, Częstochowa University of Technology, Dąbrowskiego 73, 42-200 Częstochowa, Poland
Bibliografia
  • [1] ALLEN M. P. AND TIDESLEY D. J.: Computer Simulation of Liquids, Oxford Univ.
  • [2] BAGLEY R. L., TORVIK P. J.: A theoretical basis for the application of fractional Press, New York 1989. calculus to viscoelasticity, J. of Rheology, 27(1983), 201-210.
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  • [6] EVERSQUE P. AND RAJCHENBACH Letters, 62(1) (1989), 44-46. J.: Instability in a sand heap,
  • [7] GIDASPOW D.: Multiphase Flow and Fluidization. Continuum and Kinetic Theory Descriptions, Academic Press, San Diego, 1994.
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  • [9] JENKINS J. T., MANCINI F.: Balance laws and constitutive relations for plane flows of a dense, binary mixture of smooth, nearly elastic, circular disks, J. of Appl. Mech., 57 (1987), 27-34.
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  • [11] KUWABARA G., KONO K.: Restitution coefficient in a collision between two spheres, Japanese J. of Appl. Phys., 26 Part 1 (1987), 1230-1233.
  • [12] LESZCZYNSKI J.S.: A numerical model for solution of ordinary differential equations of fractional order, Lecture Notes in Computer Science, 2328(2002), 695-702.
  • [13] LESZCZYNSKI J. S.: The calculation of a normal force between multiparticle contacts using fractional operators, Ed. by K.J. Bathe, in: Computational Fluid and Solid Mechanics 2003, Elsevier Science 2003, 2043-2047.
  • [14] LESZCZYNSKI J. S.: Computer simulations of multiparticle-contacts dynamics, Lecture Notes in Computer Science, 2657(2003), 105-114.
  • [15] LESZCZYNSKI J. S.: A discrete model of a two-particle contact applied to cohesive granular materials, Granular Matter 5(2) (2003), 91-98.
  • [16) LUBACHEVSKY B. How to simulate billards and similar systems, J. of Compuational Phys., 94(2) (1991), 255-283,
  • [17] LUDING S., CLEMENT E., BLUMEN A., RAJCHENBACH J. AND DURAN J.: Anoma lous energy dissipation in molecular dynamics simulations of grains, Phys. Rev. E, 50(1994), 4113-4122.
  • [18] MCNAMARA S. AND YOUNG W. R.: Inelastic collapse and clumping in a one di mensional granular medium, Physics Fluids A, 4(1992), 496-504.
  • [19] OLDHAM K. B., SPANIER J.: The Fractional Calculus. Theory and Applications of Differentiation and Integration to Arbitrary Order, Academic Press, New York 1974
  • [20] POURNIN L., LIEBLING TH.M.: Molecular dynamics foree models for better control of energy dissipation in numerical simulations of dense granular media, Phys. Rev. E, 65 (2001), 011302-1-011302-7.
  • [21]) RAPAPORT D. C.: The Art of Molecular Dynamics Simulation, Cambridge Uni Press, Cambridge 1995. SAMKO S.C., KILBAS A. A. AND MARICHEV O. L Fractional Integrals and Deriva tives. Theory and Applications, Gordon and Breach, Amsterdam 1993.
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Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BGPK-0638-2834
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