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An algorithm to generate random dense arrangements for discrete element simulations of granular assemblies

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Abstract

A discrete element simulation of a mechanical problem involving granular materials begins with the definition of the geometry of the sample to be analyzed. Since the dynamic sample preparation methods typically used in the practice are very time-consuming, constructive algorithms are becoming increasingly popular. This paper introduces a novel constructive method for the preparation of random, isotropic assemblies of contacting circular discs with a user-defined grain size distribution. The proposed approach is compared with other currently applied sample preparation methods.

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References

  1. Saeid, S., Franke, C. (ed.): Procs International Workshop on the Rock Mechanics of Nuclear Waste Repositories. (Vail, Colorado, June 1999) Alexandria, Virginia: American Rock Mechanics Association (1999)

  2. Konietzky, H. (ed).: Numerical Modeling in Micromechanics via Particle Methods. (Procs 1st International PFC Symposium, Gelsenkirchen, Germay 2002), Rotterdam, Balkema (2002)

  3. Foo, Y.Y., Sheng, Y., Briscoe, B.J.: An experimental and numerical study of the compaction of alumina aggregates. Int. J. Solids and Structures 41(21), 5929–5943 (2004)

    Google Scholar 

  4. Hopkins, M.A., Daly, S.F., Lever, J.H.: Three-dimensional simulation of river ice jams. In: Procs 8th International Specialty Conference on Cold Regions Engineering, Fairbanks, AK, August 1996, pp. 12–17

  5. Hopkins, M.A.: Onshore Ice Pile-up: A Comparison between Experiments and Simulations. J. Cold Regions Science and Technology 26, 205–214 (1997)

    Google Scholar 

  6. Csepella, D., Vida, J., Bagi, K., Bojtár, I.: The interaction between blood flow and vessel wall. In: Bojtár, I. (ed.): Procs. Ist Hungarian Conference on Biomechanics, 11–12 June 2004, Budapest, Hungary, 2004, pp. 59–63

  7. Helbing, D., Farkas, I., Vicsek, T.: Simulating dynamical features of escape panic. Nature 407(28), 487–490 (2000)

    Google Scholar 

  8. Cundall, P.A. – Strack, O.D.L.: A discrete numerical model for granular assemblies. Geotechnique 29(1), 47–65 (1979)

    Google Scholar 

  9. Cundall, P.A.: Computer simulation of dense sphere assemblies. In: Satake, M., Jenkins, J.T. (eds.): Micro-mechanics of Granular Materials, Elsevier (1988), pp. 113–123

  10. Kuhn, M.R.: A smooth convex three-dimensional particle for the Discrete Element Method. J. Eng Mech. 129(5), 539–547 (2003)

    Google Scholar 

  11. Ting, J.M., Khwaja, M., Meachum, L.R., Rowell, J.D.: An Ellipse-based Discrete Element Model for Granular Materials. Int. J. for Numerical and Analytical Methods in Geomechanics 17(9), 603–623 (1993)

    Google Scholar 

  12. Serrano, A.A., Rodriguez-Ortiz, J.M.: A contribution to the mechanics of heterogeneous granular media. In: Procs. Symp. Plasticity and Soil Mechanics 1973, pp. 215–227

  13. Bagi, K.: A quasi-static numerical model for micro-level analysis of granular assemblies. Mechanics of Materials 16(1–2), 101–110 (1993)

    Google Scholar 

  14. Kishino, Y.: Disc model analysis of granular media. In: Satake, M., Jenkins, J.T. (eds.): Micromechanics of Granular Materials, Elsevier 1988, pp. 143–152

  15. Zhuang, X., Didwania, A.K., Goddard, J.D.: Simulation of the quasi-static mechanics and scalar transport properties of ideal granular assemblages. J. Comput. Phys. 121(2), 331–346 (1995)

    Google Scholar 

  16. Bojtár, I.: Numerical analysis of the microstructure of granular media. Építés- és Építészettudomány 1–2, 75–93, in Hungarian (1989)

  17. Bagi, K.: From order to chaos: The mechanical behaviour of regular and irregular assemblies. In: Bagi, K. (ed): Procs. QuaDPM’03 Workshop, 25–28 August 2003, Budapest, Hungary 2003, pp. 33–42

  18. Feng, Y.T., Owen, D.R.J.: Filling domains with disks: an advancing front approach. Int. J. Numer. Meth. Engng 56, 699–713 (2003)

    Google Scholar 

  19. Cui, L., O’Sullivan, C.: Analysis of a triangulation based approach for specimen generation for discrete element simulations. Granular Matter 5(3), 135–145 (2003)

    Google Scholar 

  20. Stoyan, D.: Models of random systems of non-intersecting spheres, In: Prague Stochastics’98, JCMF 1998, pp. 543–547

  21. Stoyan, D.: Random systems of hard particles: Models and statistics, Chinese Journal of Stereology and Image Analysis 7(1), 1–13 (2002)

    Google Scholar 

  22. Häggström, O., Meester, R.: Nearest neighbour and hard sphere models in continuum percolation. Random Struct. Algor. 9, 295–315 (1996)

    Google Scholar 

  23. Evans, J.W.: Random and cooperative sequential adsorption. Rev. Mod. Phys. 65, 1281–1304 (1993)

    Google Scholar 

  24. Döge, G.: Perfect simulation for random sequential adsorption of d dimensional spheres with random radii. J. Statist. Comput. Simul. 69, 141–156 (2001)

    Google Scholar 

  25. Particle Flow Code in 2 Dimensions. Itasca, Thresher Square East, 708 South Third Street 310, Minneapolis, Minnesota 55415 USA (2002)

  26. Particle Flow Code in 3 Dimensions. Itasca, Mill Place, 111 Third Avenue South, 450, Minneapolis, Minnesota 55401 USA (2003)

  27. Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., Teller, E.: Equations of state calculations by fast computing machines. J. Chem. Phys. 21, 1087–1092 (1953)

    Google Scholar 

  28. Hastings, W.K.: Monte Carlo sampling methods using Markov chains and their applications. Biometrica 57, 97–109 (1970)

    Google Scholar 

  29. Mase, S., Moller, J., Stoyan, D., Waagepeterse, R.P. Döge, G.: Packing densities and simulated tempering for hard core Gibbs point processes. Ann. Inst. Statist. Math. 53, 661–680 (2001)

    Google Scholar 

  30. Torquato, S.: Random heterogeneous materials. Springer-Verlag, New York (2002), see p. 275

  31. Jodrey, W.S., Tory, E.M.: Simulation of close random packing of spheres. J. Simulation 32, 1–12 (1979)

    Google Scholar 

  32. Jodrey, W.S., Tory, E.M.: Computer simulation of close random packing of equal spheres. Phys. Rev. A 32, 2347–2351 (1985)

    Google Scholar 

  33. Stillinger, F.H., DiMarzio, E.A., Kornegay, R.L.: Systematic approach to explanation of the rigid disc phase transition. J. Chem. Phys. 40, 1564–1576 (1964)

    Google Scholar 

  34. Moscinski, J., Bargiel, M., Rycerz, Z.A., Jacobs, P.W.M.: The force biased algorithm for the irregular close packing of equal hard spheres. Molecular Simulation 3, 201–212 (1989)

    Google Scholar 

  35. Lubachevsky, B.D., Stillinger, F.H.: Geometrik properties of random disk packings. J. Stat. Phys. 60, 561–583 (1990)

    Google Scholar 

  36. Feng, Y.T., Han, K., Owen, D.R.J.: Filling domains with disks. In: Bicanic, N. (ed): Procs. ICADD-4, 6–8 June 2001, Glasgow, University of Glasgow (2001), pp. 239–250

  37. Bagi, K.: Geometrical modeling of granular assemblies. Acta Technica Acad. Sci. Hung. 107(1–2), 1–16 (1995)

    Google Scholar 

  38. Bagi, K.: Stress and strain in granular assemblies. Mechanics of Materials 22, 165–177 (1996)

    Google Scholar 

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Bagi, K. An algorithm to generate random dense arrangements for discrete element simulations of granular assemblies. Granular Matter 7, 31–43 (2005). https://doi.org/10.1007/s10035-004-0187-5

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