The dynamics of multiparticle collisions in motion of a granular material

• Authors: Jacek Leszczyński
• Languages of publication: EN

Abstracts

EN

We consider the complex problem of how to calculate particle motions taking into account multiparticle collisions. Multiparticle contacts occur when a particle collides with neighbouring particles, so that those contacts have a direct influence on each other. We will focus on the molecular dynamics method. Particularly, we will analyse what happens in cohesive materials during multiparticle contacts. We investigated the expression of repulsive force formulated under fractional calculus which is able to control dynamically the transfer and dissipation of energy in granular media. Such approach allows to perform simulations of arbitrary multiparticle collisions and also granular cohesion dynamics.

Keywords

EN

granular matter; multiparticle collisions; cohesion; fractional derivative; 45.70.-n ; 83.10.Pp ; 83.10.Rs ; 45.50.Tn ; 2.70.Ns ; 45.10.Hj

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2003
• Volume: 1
• Issue: 4
• Pages: 596-605

Dates

published

1 - 12 - 2003

online

1 - 12 - 2003

Contributors

author

Jacek Leszczyński

• Institute of Mathematics and Computer Science, Czestochowa University of Technology, Dąbrowskiego 73, 42-200, Czestochowa, Poland

References

• [1] M.P. Allen and D.J. Tidesley (Eds.) Computer Simulations of Liquids, Oxford Univ. Press, New York, 1989.
• [2] P.A. Cundall and O.D.L. Strack (Eds.): “A discrete numerical model for granular assemblies”, Geotechnique, Vol. 29, (1979), pp. 47–65. [Crossref]
• [3] D. Gidaspow (Ed.): Multiphase Flow and Fluidization. Continuum and Kinetic Theory Descriptions, Academic Press. San Diego, 1994.
• [4] G. Kuwabara, K. Kono: “Restitution coefficient in a collision between two spheres”, Jap. J. Appl. Phys., Vol. 26 Part 1. (1987), pp. 1230–1233. http://dx.doi.org/10.1143/JJAP.26.1230[Crossref]
• [5] J.S. Leszczynski: “A numerical method for solution of ordinary differential equations of fractional order”, Lecture Notes in Computer Science, Vol. 2328, (2002), pp. 695–702. http://dx.doi.org/10.1007/3-540-48086-2_77[Crossref]
• [6] J.S. Leszczynski: “A discrete model of a two-particle contact applied to cohesive granular materials”, Granular Matter, Vol. 5(2), (2003), pp. 91–98. http://dx.doi.org/10.1007/s10035-003-0129-7[Crossref]
• [7] J.S. Leszczynski: “Computer simulations of multiparticle-contacts dynamics”, Lecture Notes in Computer Science, Vol. 2657, (2003), pp. 105–114.
• [8] J.S. Leszczynski: “The calculation of a normal force between multiparticle contacts using fractional operators” inComputational Fluid and Solid Mechanics 2003, K.J. Bathe (Ed.), Elsevier Science, 2003, pp. 2043–2047.
• [9] S. Luding, E. Cl'ement, A. Blumen, J. Rajchenbach and J. Duran: “Anomalous energy dissipation in molecular dynamics simulations of grains”, Phys. Rev. E, Vol. 50, (1994), pp. 4113–4122. http://dx.doi.org/10.1103/PhysRevE.50.4113[Crossref]
• [10] S. McNamara and W.R. Young: “Inelastic collapse and clumping in a one dimensional medium”, Phys. Fluids Vol. A 4, (1992), pp. 496–504. http://dx.doi.org/10.1063/1.858323[Crossref]
• [11] K.B. Oldham, J. Spanier (Eds.): The Fractional Calculus. Theory and Applications of Differentiation and Integration to Arbitrary Order, Academic Press, New York, 1974.
• [12] L. Pournin, Th.M. Liebling: “Molecular dynamics force models for better control of energy dissipation in numerical simulations of dense granular media”, Phys. Rev. E, Vol. 65, (2001), pp. 011302-1–011302-7. http://dx.doi.org/10.1103/PhysRevE.65.011302[Crossref]
• [13] D.C. Rappaport (Ed.): The Art of Molecular Dynamics Simulation. Cambridge Univ. Press. Cambridge, 1995.
• [14] O.R. Walton, R.L. Braun: “Viscosity, granular-temperature and stress calculations for shearing assemblies of inelastic frictional disks”, J. Rheol., Vol. 30, (1986), pp. 949–980. http://dx.doi.org/10.1122/1.549893[Crossref]

Identifiers

DOI

10.2478/BF02475905