Advertisement

Computational Particle Mechanics

, Volume 5, Issue 1, pp 13–33 | Cite as

General advancing front packing algorithm for the discrete element method

  • Carlos A. Recarey Morfa
  • Irvin Pablo Pérez MoralesEmail author
  • Márcio Muniz de Farias
  • Eugenio Oñate Ibañez de Navarra
  • Roberto Roselló Valera
  • Harold Díaz-Guzmán Casañas
Article

Abstract

A generic formulation of a new method for packing particles is presented. It is based on a constructive advancing front method, and uses Monte Carlo techniques for the generation of particle dimensions. The method can be used to obtain virtual dense packings of particles with several geometrical shapes. It employs continuous, discrete, and empirical statistical distributions in order to generate the dimensions of particles. The packing algorithm is very flexible and allows alternatives for: 1—the direction of the advancing front (inwards or outwards), 2—the selection of the local advancing front, 3—the method for placing a mobile particle in contact with others, and 4—the overlap checks. The algorithm also allows obtaining highly porous media when it is slightly modified. The use of the algorithm to generate real particle packings from grain size distribution curves, in order to carry out engineering applications, is illustrated. Finally, basic applications of the algorithm, which prove its effectiveness in the generation of a large number of particles, are carried out.

Keywords

Particle packing Discrete element method Advancing front Particle in contact 

Notes

Acknowledgements

The authors are deeply grateful to the valuable funding, resources, and support of the following institutions: Coordination for the Improvement of Higher Education Personnel - CAPES; Brazilian Ministry of Education, CAPES-MES Project No. 208/13; Brazilian National Research Council, Process No. 163622/2013-2; International Center for Numerical Methods in Engineering, CIMNE, Barcelona, Spain.

References

  1. 1.
    Cundall PA, Strack ODL (1979) A discrete numerical model for granular assemblies. Geotechnique 29(1):47–65CrossRefGoogle Scholar
  2. 2.
    Cundall PA (1988) Computer simulation of dense sphere assemblies. In: Satake M, Jenkins JT (eds) Micro-mechanics of granular materials. Elsevier, Amsterdam, pp 113–123Google Scholar
  3. 3.
    Kuhn MR (2003) A smooth convex three-dimensional particle for the discrete element method. J Eng Mech 129(5):539–547CrossRefGoogle Scholar
  4. 4.
    Ting JM, Khwaja M, Meachum LR, Rowell JD (1993) An ellipse-based discrete element model for granular materials. Int J Numer Anal Methods Geomech 17:603–623CrossRefzbMATHGoogle Scholar
  5. 5.
    Feng YT, Han K, Owen DRJ (2002) An advancing front packing of polygons, ellipses and spheres. In: Cook BK, Jensen RP (eds) Discrete Element Methods. Numerical Modeling of Discontinua, Santa Fe, New Mexico, USA, Setptember 23–25 2002. Geotechnical Special Publication. American Society of Civil Engineers, pp. 93–98Google Scholar
  6. 6.
    Feng YT, Han K, Owen DRJ (2003) Filling domains with disks: an advancing front approach. Int J Numer Methods Eng 56:699–713. doi: 10.1002/nme.583 CrossRefzbMATHGoogle Scholar
  7. 7.
    Bagi K (2005) Methods to generate random dense arrangements of particles. In: Thematic meeting on numerical simulations, ParisGoogle Scholar
  8. 8.
    Valera R, Pérez Morales I, Vanmaercke S, Recarey Morfa C, Argüelles Cortés L, Díaz-Guzmán Casañas H (2015) Modified algorithm for generating high volume fraction sphere packings. Comput Part Mech:1-12. doi: 10.1007/s40571-015-0045-8
  9. 9.
    Wang C-Y, Wang C-F, Sheng J (1999) A packing generation scheme for the granular assemblies with 3d ellipsoidal particles. Int J Numer Anal Methods Geomech 23:815–828CrossRefzbMATHGoogle Scholar
  10. 10.
    Benabbou A, Borouchaki H, Laug P, Lu J (2008) Sphere packing and applications to granular structure modeling. In: Proceedings of the 17th international meshing roundtable. Springer Berlin, pp 1–18. doi: 10.1007/978-3-540-87921-3
  11. 11.
    Benabbou A, Borouchaki H, Laug P, Lu J (2010) Numerical modeling of nanostructured materials. Finite Elem Anal Des 46(1–2):165–180. doi: 10.1016/j.finel.2009.06.030 CrossRefGoogle Scholar
  12. 12.
    Laug P, Borouchaki H, Benabbou A, Lu J (2008) Modélisation géométrique des structures granulaires. C R Méc 336(6):506–511. doi: 10.1016/j.crme.2008.02.011 CrossRefzbMATHGoogle Scholar
  13. 13.
    Han K, Feng YT, Owen DRJ (2005) Sphere packing with a geometric based compression algorithm. Powder Technol 155:33–41CrossRefGoogle Scholar
  14. 14.
    Nandakumar K, Shu Y, Chuang KT (1999) Predicting geometrical properties of random packed beds from computer simulation. AIChE J 45(11):2286–2297CrossRefGoogle Scholar
  15. 15.
    Sutou A, Dai Y (2002) Global optimization approach to unequal sphere packing problems in 3D. J Optim Theory Appl 114(3):671–694MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Cui L, O’Sullivan C (2003) Analysis of a triangulation based approach for specimen generation for discrete element simulations. Granul Matter 5:135–145. doi: 10.1007/s10035-003-0145-7 CrossRefzbMATHGoogle Scholar
  17. 17.
    Donzé FV (2006) Discrete element group for hazard mitigation. Université Joseph Fourier, GrenobleGoogle Scholar
  18. 18.
    Jerier J-F, Richefeu V, Imbault D, Donzé F-V (2010) Packing spherical discrete elements for large scale simulations. Comput Methods Appl Mech Eng 199(25–28):1668–1676CrossRefzbMATHGoogle Scholar
  19. 19.
    Georgalli GA, Reuter MA (2008) A particle packing algorithm for packed beds with size distribution. Granul Matter 10:257–262. doi: 10.1007/s10035-008-0097-z CrossRefzbMATHGoogle Scholar
  20. 20.
    Saucier R (2000) Computer generation of statistical distributions. ARMY RESEARCH LABORATORYGoogle Scholar
  21. 21.
    Munjiza A, Andrews KRF (1998) NBS contact detection algorithm for bodies of similar size. Int J Numer Methods Eng 43:131–149CrossRefzbMATHGoogle Scholar
  22. 22.
    Möller T, Haines E, Hoffman N (1999) Real-time rendering. A. K. Peters, NatickGoogle Scholar
  23. 23.
    Han K, Feng YT, Owen DRJ (2006) Polygon-based contact resolution for superquadrics. Int J Numer Methods Eng 66:485–501. doi: 10.1002/nme.1569 CrossRefzbMATHGoogle Scholar
  24. 24.
    Mirtich B (1998) V-Clip: fast and robust polyhedral collision detection. ACM Trans Graph 17(3):177–208. doi: 10.1145/285857.285860 CrossRefGoogle Scholar
  25. 25.
    Yung-ming C, Wensheng C, Xiurun G Procedure to detect the contact of three-dimensional blocks using penetration edges method. In: Cook BK, Jensen RP (eds) Discrete Element Methods: Numerical Modeling of Discontinua, Santa Fe, New Mexico, USA, Setptember 23–25 2002. Geotechnical Special Publication. American Society of Civil Engineers, pp. 79–85Google Scholar
  26. 26.
    Hogue C (1998) Shape representation and contact detection for discrete element simulations of arbitrary geometries. Eng Comput 15(3):374–390CrossRefzbMATHGoogle Scholar
  27. 27.
    Barbosa RE (1990) Discrete element models for granular materials and rock masses. University of Illinois, Urbana-ChampaignGoogle Scholar
  28. 28.
    Cundall PA (1988) Formulation of a three-dimensional distinct element model–part I: a scheme to detect and represent contacts in a system composed of many polyhedral blocks. Int J Rock Mech Min Sci Geomech Abstr 25:107–116CrossRefGoogle Scholar
  29. 29.
    G. Nezami E, M. A. Hashash Y, Zhao D, Ghaboussi J (2006) Shortest link method for contact detection in discrete element method. Int J Numer Anal Methods Geomech 30(8):783–801. doi: 10.1002/nag.500 CrossRefzbMATHGoogle Scholar
  30. 30.
    Nezami EG, Hashash YMA, Zhao D, Ghaboussi J (2004) A fast contact detection algorithm for 3-D discrete element method. Comput Geotech 31:575–587. doi: 10.1016/j.compgeo.2004.08.002 CrossRefGoogle Scholar
  31. 31.
    Chang S-W, Chen C-S (2008) A non-iterative derivation of the common plane for contact detection of polyhedral blocks. Int J Numer Methods Eng 74:734–753. doi: 10.1002/nme.2174 MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Mohammadi S (2003) Discontinuum mechanics using finite and discrete elements. Wit Press, SouthamptonzbMATHGoogle Scholar
  33. 33.
    Wang C-Y, Liang V-C (1997) A packing generation scheme for the granular assemblies with planar elliptical particles. Int J Numer Anal Methods Geomech 21:347–358CrossRefzbMATHGoogle Scholar
  34. 34.
    Lin X, Ng T-T (1995) Contact detection algorithms for three-dimensional ellipsoids in discrete element modelling. Int J Numer Anal Methods Geomech 19:653–659CrossRefzbMATHGoogle Scholar
  35. 35.
    Wang W, Wang J, Kim M-S (2001) An algebraic condition for the separation of two ellipsoids. Comput Aided Geom Des 18:531–539MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Labra C, Oñate E (2009) High-density sphere packing for discrete element method simulations. Commun Numer Methods Eng 25:837–849. doi: 10.1002/cnm.1193 MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Ferrez J-A (2001) Dynamic triangulations for efficient 3d simulation of granular materials. École Polytechnique Fédérale de Lausanne, LausanneGoogle Scholar
  38. 38.
    Benabbou A, Borouchaki H, Laug P, Lu J (2009) Geometrical modeling of granular structures in two and three dimensions. Application to nanostructures. Int J Numer Methods Eng 80(4):425–454. doi: 10.1002/nme.2644 CrossRefzbMATHGoogle Scholar
  39. 39.
    Löhner R, Oñate E (2004) A general advancing front technique for filling space with arbitrary objects. Int J Numer Methods Eng 61:1977–1991. doi: 10.1002/nme.1068
  40. 40.
    Lubachevsky BD (1991) How to simulate billiards and similar systems. J Comput Phys 94(2):255–283. doi: 10.1016/0021-9991(91)90222-7 MathSciNetCrossRefzbMATHGoogle Scholar
  41. 41.
    Lubachevsky BD, Stillinger FH (1990) Geometric Properties of Random Disk Packings. Journal of Statistical Physics 60(5—-6):561–583MathSciNetCrossRefzbMATHGoogle Scholar
  42. 42.
    Eberly DH (2006) 3D game engine design: a practical approach to real-time computer graphics. CRC Press, Boca RatonGoogle Scholar
  43. 43.
    Pérez Morales I, Roselló Valera R, Pérez Brito Y (2008) Generación o empaquetamiento de medios discretos para el Método de Elementos Distintos. Ing Civil CEDEX 152:119–124Google Scholar
  44. 44.
    Pérez Morales I, Valera RR, Brito YP, Casañas HD-G, Morfa CR (2009) Procedimiento de empaquetmiento de partículas genéricas para el Método de Elementos Discretos. Rev Int Métodos Numéricos para Cálculo y Diseño en Ingeniería 25(2):95–110Google Scholar
  45. 45.
    Pérez Morales I (2006) Método de Elementos Distintos. Universidad Central de Las Villas, Cuba, Santa Clara, Tesis de gradoGoogle Scholar
  46. 46.
    Brito YP (2007) Implementación del empaquetamiento en el Método de Elementos Distintos. Universidad Central de Las Villas, Cuba, Santa Clara, Tesis de GradoGoogle Scholar
  47. 47.
    Pérez Morales I (2012) Método de Elementos Discretos: desarrollo de técnicas novedosas para la modelación con métodos de partículas. Ph. D. Thesis, Universidad Central de Las VillasGoogle Scholar
  48. 48.
    Pérez Morales I, de Farias MM, Valera RR, Morfa CR, Martínez Carvajal HE (2016) Contributions to the generalization of advancing front particle packing algorithms. Int J Numer Methods Eng. doi: 10.1002/nme.5192
  49. 49.
    Morales IP, Valera RR, Morfa CR, de Farias MM (2016) Dense packing of general-shaped particles using a minimization technique. Comput Part Mech 1:1–15. doi: 10.1007/s40571-016-0103-x Google Scholar
  50. 50.
    Ortega JAH (2003) Simulación numérica de procesos de llenado mediante elementos discretos. Universidad Politécnica de Cataluña, CataluñaGoogle Scholar
  51. 51.
    Zarowski CJ (2004) An introduction to numerical analysis for electrical and computer engineers. Wiley, New YorkCrossRefzbMATHGoogle Scholar
  52. 52.
    Choi YK, Li X, Rong F, Wang W, Cameron S (2006) Computing the minimum directional distance between two convex polyhedra. Hong Kong UniversityGoogle Scholar

Copyright information

© OWZ 2016

Authors and Affiliations

  • Carlos A. Recarey Morfa
    • 1
    • 2
  • Irvin Pablo Pérez Morales
    • 1
    Email author
  • Márcio Muniz de Farias
    • 2
  • Eugenio Oñate Ibañez de Navarra
    • 3
  • Roberto Roselló Valera
    • 1
  • Harold Díaz-Guzmán Casañas
    • 1
  1. 1.Center of Computational Mechanics and Numerical Methods in Engineering, CIMNE-UCLV ClassroomCentral University of Las VillasSanta ClaraCuba
  2. 2.Faculty of Technology of University of BrasiliaBrasÍliaBrazil
  3. 3.Politechnical University of CatalonyaBarcelonaSpain

Personalised recommendations