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Modelling and Computer Simulation of Granular Media

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Abstract

The purpose of this chapter is twofold; to give an introduction into the physics of granular media, emphasizing modern concepts and research topics, and to review the models most pertinent to the computer simulation of these phenomena. Soft-particle molecular dynamics, event-driven molecular dynamics, the contact dynamics of Moreau and Jean, and the bottom-to-top-restructuring model are discussed in detail. Their range of applicability is carefully assessed, artefacts are pointed out, and key results obtained with the respective methods are presented.

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References

  1. H.M. Jaeger and S.R. Nagel, Science 255, 1523 (1992)

    Google Scholar 

  2. S.R. Nagel, Rev. Mod. Phys. 64, 321 (1992)

    Article  ADS  Google Scholar 

  3. A. Hansen and D. Bideau (eds.), Disorder and Granular Media (North-Holland, Amsterdam 1992)

    Google Scholar 

  4. J. Rajchenbach, E. Clément, J. Duran, and T. Mazozi, in: Scale Invariance, Interfaces, and Non-equilibrium Dynamics, eds. A. McKane, M. Droz, J. Vannimenus, D.E. Wolf (Plenum, New York 1995), p. 313

    Google Scholar 

  5. H.J. Herrmann, Phys. Bl. 51, 1083 (1995)

    ADS  Google Scholar 

  6. G. Hagen, Monatsberichte (Preuß. Akad. d. Wiss., Berlin 1852), p. 35

    Google Scholar 

  7. H.A. Janssen, Zeitschrift VDI 39, 1045 (1895)

    Google Scholar 

  8. F. Radjai: Dynamique des rotations et frottement collectif dans les systèmes granulaires, PhD-thesis, (Université de Paris-Sud XI, Orsay 1995)

    Google Scholar 

  9. P.A. Thompson and G.S. Grest, Phys. Rev. Lett. 67, 1751 (1991)

    Article  ADS  Google Scholar 

  10. L.D. Landau and E.M. Lifshitz, Lehrbuch der Theoretischen Physik Vol. X: Physikalische Kinetik (Akademie-Verlag, Berlin 1983) p. 27

    Google Scholar 

  11. S. Ogawa, in: Proc. US-Japan Seminar on Continuum-Mechanical and Statistical Approaches in the Mechanics of Granular Materials, eds. S.C. Cowin and M. Satake, (Gakujutsu Bunken Pukyukai, Tokio 1978)

    Google Scholar 

  12. I. Goldhirsch, p. 251

    Google Scholar 

  13. I. Goldhirsch, G. Zanetti, Phys. Rev. Lett. 70, 1619 (1993)

    Article  ADS  Google Scholar 

  14. D.E. Wolf, M. Schreckenberg, and A. Bachern (eds.), Traffic and Granular Flow (World Scientific, Singapore 1996)

    Google Scholar 

  15. J. Schäfer and D.E. Wolf, p. 311

    Google Scholar 

  16. P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  17. J.M. Carlson and J.S. Langer, Phys. Rev. Lett. 62, 2632 (1989)

    Article  ADS  Google Scholar 

  18. P. Bak and K. Chen, Sci. Am. 264, 46 (1991)

    Article  Google Scholar 

  19. P. Bak and M. Paczuski, Phys. World 6, 39 (1993)

    Google Scholar 

  20. G. Grinstein, in: Scale Invariance, Interfaces, and Non-equilibrium Dynamics, eds. A. McKane, M. Droz, J. Vannimenus, D.E. Wolf (Plenum, New York 1995), p. 261

    Google Scholar 

  21. V. Frette, K. Christensen, A. Malthe-Sørenssen, J. Feder, T. Jøssang, and P. Meakin, Nature 379, 49 (1996)

    Article  ADS  Google Scholar 

  22. A.N. Kolmogorov, Doklady Akad. Nauk. SSSR 31, 99 (1941)

    Google Scholar 

  23. T. Ishii and M. Matsushita, J. Phys. Soc. Japan 61, 3474 (1992)

    Article  ADS  Google Scholar 

  24. D.R. Wilkinson and S.F. Edwards, Proc. R. Soc. Lond. A 381, 33 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  25. P. Meakin, Physica A 163, 733 (1990)

    Article  ADS  Google Scholar 

  26. G. Baumann, LM. Jánosi, and D.E. Wolf, Phys. Rev. E 51, 1879 (1995)

    Article  ADS  Google Scholar 

  27. D. Bideau, I. Ippolito, L. Samson, G.G. Batrouni, S. Dippel, A. Aguirre, A. Calvo, and C. Henrique, in (eds.), Traffic and Granular Flow (World Scientific, Singapore 1996) , p. 279

    Google Scholar 

  28. S. Dippel, L. Samson, and G.G. Batrouni, p. 353

    Google Scholar 

  29. E. Clément, J. Rajchenbach, and J. Duran, Europhys. Lett. 30, 7 (1995)

    Article  ADS  Google Scholar 

  30. F. Cantelaube and D. Bideau, Europhys. Lett. 30, 133 (1995)

    Article  ADS  Google Scholar 

  31. A. Rosato, F. Prinz, K.J. Strandburg, and R. Swendsen, Phys. Rev. Lett. 58, 1038 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  32. R. Jullien, P. Meakin, and A. Pavlovitch, Phys. Rev. Lett. 70, 2195 (1993)

    Article  ADS  Google Scholar 

  33. S. Dippel and S. Luding, J.Phys. I France 5, 1527 (1995)

    Article  Google Scholar 

  34. J.B. Knight, H.M. Jaeger, and S.R. Nagel, Phys. Rev. Lett. 70, 3728 (1993)

    Article  ADS  Google Scholar 

  35. J. Duran, T. Mazoni, E. Clément, and J. Rajchenbach, Phys. Rev. E 50, 5138 (1994)

    Article  ADS  Google Scholar 

  36. T. Pöschel and H.J. Herrmann, Europhys. Letters 29, 123 (1995)

    Article  ADS  Google Scholar 

  37. J. Duran, J. Rajchenbach, and E. Clément, Phys. Rev. Lett. 70, 2431 (1993)

    Article  ADS  Google Scholar 

  38. O. Zik, D. Levine, S.G. Lipson, S. Shtrikman, and J. Stavans, Phys. Rev. Lett. 73, 644 (1994)

    Article  ADS  Google Scholar 

  39. F. Melo, P. Umbanhowar, and H.L. Swinney, Phys. Rev. Lett. 72, 172 (1994)

    Article  ADS  Google Scholar 

  40. P.A. Cundall and O.D.L. Strack, Géotechnique 29, 47 (1979)

    Article  Google Scholar 

  41. P.K. Haff and B.T. Werner, Powder Technol. 48, 239 (1986)

    Article  Google Scholar 

  42. M.P. Allen and D.J. Tildesley, Computer Simulation of Liquids (Clarendon Press, Oxford 1987)

    MATH  Google Scholar 

  43. H.J. Herrmann, in: Lectures in Computational Physics, eds. P.L. Garrido and J. Marro (Springer, Heidelberg 1995)

    Google Scholar 

  44. G. Ristow, in: Annual Reviews of Computational Physics I, ed. D. Stauffer (World Scientific, Singapore 1994)

    Google Scholar 

  45. K.L. Johnson, Contact Mechanics (Cambridge University Press, Cambridge 1989)

    Google Scholar 

  46. L.D. Landau and E.M. Lifshitz, Lehrbuch der Theoretischen Physik Vol.VII: Elastizitätstheorie (Akademie-Verlag, Berlin 1989)

    Google Scholar 

  47. G. Kuwabara and K. Kono, Jap. J. Appl. Phys. 26, 1230 (1987)

    Article  ADS  Google Scholar 

  48. W. Goldsmith, Impact (Edward Arnold, London 1960)

    MATH  Google Scholar 

  49. F.G. Bridges, A. Hatzes, and D.N.C. Lin, Nature 309, 333 (1984)

    Article  ADS  Google Scholar 

  50. R. Sondergaard, K. Chaney, and C.E. Brennen, J. Appl Mech. 57, 694 (1990)

    Article  Google Scholar 

  51. J. Schäfer, S. Dippel, and D.E. Wolf, J. Physique I (1996)

    Google Scholar 

  52. S. Melin, Phys. Rev. E 49, 2353 (1994)

    Article  ADS  Google Scholar 

  53. C.-H. Liu and S.R. Nagel, Phys. Rev. Lett. 68, 2301 (1992)

    Article  ADS  Google Scholar 

  54. S.F. Foerster, M.Y. Louge, H. Chang, and K. Allia, Phys. Fluids 6, 1108 (1994)

    Article  ADS  Google Scholar 

  55. T.G. Drake, J. Geophysical Research 95, 8681 (1990)

    Article  ADS  Google Scholar 

  56. S. Luding, E. Clément, A. Blumen, J. Rajchenbach, and J. Duran, Phys. Rev. E 50, 4113 (1994)

    Article  ADS  Google Scholar 

  57. J. Schäfer, PhD-thesis, (Gerhard-Mercator-Universität, Duisburg 1996)

    Google Scholar 

  58. J. Schäfer and D.E. Wolf, Phys. Rev. E 51, 6154 (1995)

    Article  ADS  Google Scholar 

  59. J.T. Jenkins, J. Appl. Mech. 59, 120 (1992)

    Article  MATH  ADS  Google Scholar 

  60. S. McNamara, W.R. Young, Phys. Rev. E 50, R28 (1994)

    Article  ADS  Google Scholar 

  61. S. Luding, E. Clément, A. Blumen, J. Rajchenbach, and J. Duran, Phys. Rev. E 49, 1634 (1994)

    Article  ADS  Google Scholar 

  62. J.J. Moreau, Eur. J. Mech. A/Solids 13, 93 (1994)

    MATH  MathSciNet  Google Scholar 

  63. M. Jean in: Mechanics of Geometrical Interfaces, eds. A.P.S. Selvadurai and M.J. Boulon (Elsevier, Amsterdam 1995)

    Google Scholar 

  64. F. Radjai, L. Brendel, S. Roux, Non-smoothness, Indeterminacy and Friction in Granular Systems, HLRZ-preprint 80/95

    Google Scholar 

  65. G. Baumann, E. Jobs, and D.E. Wolf, Fractals 1, 767 (1993)

    Article  Google Scholar 

  66. G. Baumann, LM. Jánosi, and D.E. Wolf, Europhys. Lett. 27, 203 (1994)

    Article  ADS  Google Scholar 

  67. G. Baumann, T. Scheffler, I.M. Jánosi, and D.E. Wolf, p. 347

    Google Scholar 

  68. E. Jobs, unpublished

    Google Scholar 

  69. D.E. Wolf and F. Radjai, unpublished

    Google Scholar 

  70. G. Peng and H.J. Herrmann, Phys. Rev. E 48, R1796 (1994)

    Article  ADS  Google Scholar 

  71. A. Károlyi and J. Kertész, p. 359

    Google Scholar 

  72. S. Roux, in: Statistical Models for the Fracture of Disordered Media, eds. H.J. Herrmann and S. Roux, (Elsevier, Amsterdam 1990)

    Google Scholar 

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© 1996 Springer-Verlag Berlin Heidelberg

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Wolf, D.E. (1996). Modelling and Computer Simulation of Granular Media. In: Hoffmann, K.H., Schreiber, M. (eds) Computational Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-85238-1_5

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  • DOI: https://doi.org/10.1007/978-3-642-85238-1_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-85240-4

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