Computational Particle Mechanics

, Volume 5, Issue 3, pp 319–334 | Cite as

Systemic characterization and evaluation of particle packings as initial sets for discrete element simulations

  • Carlos Recarey Morfa
  • Lucía Argüelles Cortés
  • Márcio Muniz de Farias
  • Irvin Pablo Pérez MoralesEmail author
  • Roberto Roselló Valera
  • Eugenio Oñate


A methodology that comprises several characterization properties for particle packings is proposed in this paper. The methodology takes into account factors such as dimension and shape of particles, space occupation, homogeneity, connectivity and isotropy, among others. This classification and integration of several properties allows to carry out a characterization process to systemically evaluate the particle packings in order to guarantee the quality of the initial meshes in discrete element simulations, in both the micro- and the macroscales. Several new properties were created, and improvements in existing ones are presented. Properties from other disciplines were adapted to be used in the evaluation of particle systems. The methodology allows to easily characterize media at the level of the microscale (continuous geometries—steels, rocks microstructures, etc., and discrete geometries) and the macroscale. A global, systemic and integral system for characterizing and evaluating particle sets, based on fuzzy logic, is presented. Such system allows researchers to have a unique evaluation criterion based on the aim of their research. Examples of applications are shown.



The authors are deeply grateful to the valuable funding, resources and support of the following institutions and people:

\(\bullet \) Brazilian agency for the improvement of higher education personnel (CAPES). Project No. 208/13 and National Post-doctorate Program.

\(\bullet \) International Center for Numerical Methods in Engineering (CIMNE), Barcelona, Spain.

\(\bullet \) Professor Manuel Llanes Abeijón, for his valuable revision of the use of English in the original version of this paper.


  1. 1.
    Stoyan D, Kendall WS, Mecke J (1995) Stochastic geometry and its applications. Wiley, ChichesterzbMATHGoogle Scholar
  2. 2.
    O’Sullivan C (2011) Particulate discrete element modelling: a geomechanics perspective, vol 4. Applied geotechnics. Spon Press, LondonGoogle Scholar
  3. 3.
    He D, Ekere NN, Cai L (2001) New statistic techniques for structure evaluation of particle packing. Mater Sci Eng A 298:209–215CrossRefGoogle Scholar
  4. 4.
    Stoyan D (2002) Random systems of hard particles: models and statistics. Chin J Stereol Image Anal 7(1):1–13Google Scholar
  5. 5.
    Craig RF (2004) Soil mechanics. Taylor & Francis, LondonGoogle Scholar
  6. 6.
    Bezrukov A, Stoyan D, Bargiel M (2001) Spatial statistics for simulated packings of spheres. Image Anal Steorol 20:203–206CrossRefGoogle Scholar
  7. 7.
    Bagi K (2005) An algorithm to generate random dense arrangements for discrete element simulations of granular assemblies. Granul Matter 7:31–43. CrossRefzbMATHGoogle Scholar
  8. 8.
    Torquato S, Stillinger FH (2002) Controlling the Short-range order and packing densities of many-particle systems. J Phys Chem B 106(33):8354–8359. CrossRefGoogle Scholar
  9. 9.
    Torquato S, Truskett TM, Debenedetti PG (2000) Is random close packing of spheres well defined? Phys Rev Lett 84(10):2064–2067Google Scholar
  10. 10.
    Reboul N, Vincens E, Cambou B (2008) A statistical analysis of void size distribution in a simulated narrowly graded packing of spheres. Granul Matter 10:457–468. CrossRefzbMATHGoogle Scholar
  11. 11.
    Atkinson J (2007) The mechanics of soils and foundations. Taylor and Francis, LondonGoogle Scholar
  12. 12.
    Rothenburg L, Bathurst RJ (1989) Analytical study of induced anisotropy in idealized granular materials. Géotechnique 39(4):601–614. CrossRefGoogle Scholar
  13. 13.
    Kuhn MR (1999) Structured deformation in granular materials. Mech Mater 31(6):407–429. CrossRefGoogle Scholar
  14. 14.
    Kuhn MR (2003) Heterogeneity and patterning in the quasi-static behavior of granular materials. Granul Matter 4(4):155–166. CrossRefzbMATHGoogle Scholar
  15. 15.
    Thornton C (2000) Numerical simulations of deviatoric shear deformation of granular media. Géotechnique 50(1):43–53. CrossRefGoogle Scholar
  16. 16.
    Jiang MJ, Konrad JM, Leroueil S (2003) An efficient technique for generating homogeneous specimens for DEM studies. Comput Geotech 30(7):579–597. CrossRefGoogle Scholar
  17. 17.
    Field W (1963) Towards the statical definition of a granular mass. In: Paper presented at the 4th Australia and New Zealand conference on soil mechanicsGoogle Scholar
  18. 18.
    Mitchell J (1993) Fundamentals of soil behavior, 2nd edn. Wiley, New YorkGoogle Scholar
  19. 19.
    Kuwano R, Jardine RJ (2002) On the applicability of cross-anisotropic elasticity to granular materials at very small strains. Géotechnique 52(10):727–749. CrossRefGoogle Scholar
  20. 20.
    Oda M, Nemat-Nasser S, Konishi J (1985) Stress-induced anisotropy in granular masses. Soils Found 25(3):85–97CrossRefGoogle Scholar
  21. 21.
    Li X, Li X-S (2009) Micro–macro quantification of the internal structure of granular materials. J Eng Mech 135(7):641–656. CrossRefGoogle Scholar
  22. 22.
    Hill R (1963) Elastic properties of reinforced solids: some theoretical principles. J Mech Phys Solids 11(5):357–372. CrossRefzbMATHGoogle Scholar
  23. 23.
    Cui L, O’Sullivan C (2003) Analysis of a triangulation based approach for specimen generation for discrete element simulations. Granul Matter 5(3):135–145. CrossRefzbMATHGoogle Scholar
  24. 24.
    Cui L, O’Sullivan C (2006) Exploring the macro- and micro-scale response of an idealised granular material in the direct shear apparatus. Géotechnique 56(7):455–468. CrossRefGoogle Scholar
  25. 25.
    Oda M, Konishi J, Nemat-Nasser S (1980) Some experimentally based fundamental results on the mechanical behaviour of granular materials. Géotechnique 30(4):479–495. CrossRefGoogle Scholar
  26. 26.
    Rothenburg L, Kruyt NP (2004) Critical state and evolution of coordination number in simulated granular materials. Int J Solids Struct 41(21):5763–5774. CrossRefzbMATHGoogle Scholar
  27. 27.
    Hasan A, Alshibli KA (2010) Experimental assessment of 3D particle-to-particle interaction within sheared sand using synchrotron microtomography. Géotechnique 60(5):369–379. CrossRefGoogle Scholar
  28. 28.
    O’Hern CS, Silbert LE, Liu AJ, Nagel SR (2003) Jamming at zero temperature and zero applied stress: the epitome of disorder. Phys Rev E 68(1):011306CrossRefGoogle Scholar
  29. 29.
    Satake M (1982) Fabric tensor in granular materials. In: Paper presented at the IUTAM symposium on deformation and failure of granular materialsGoogle Scholar
  30. 30.
    Ng T-T (2004) Macro- and micro-behaviors of granular materials under different sample preparation methods and stress paths. Int J Solids Struct 41(21):5871–5884. CrossRefzbMATHGoogle Scholar
  31. 31.
    Scheidegger A (1965) On the statistics of the orientation of bedding planes, grain axes and similar sedimentological data. US Geol Surv Prof Pap 525:164–167Google Scholar
  32. 32.
    Ken-Ichi K (1984) Distribution of directional data and fabric tensors. Int J Eng Sci 22(2):149–164. MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Oda M (1999) Fabric tensor and its geometrical meaning. In: Oda M, Iwashita K (eds) Mechanics of granular materials. Balkema, Rotterdam, pp 19–27Google Scholar
  34. 34.
    Vanoni V (1975) Sedimentation engineering. American Society of Civil Engineers Printers, New YorkGoogle Scholar
  35. 35.
    Müller G (1967) Sedimentary petrology: methods in sedimentary petrology. E. Schweizerbart’sche Verlagsbuchhandlung, StuttgartGoogle Scholar
  36. 36.
    Trask PD (1930) Mechanical analysis of sediments by centrifuge. Econ Geol 25:581–599CrossRefGoogle Scholar
  37. 37.
    Inman DL (1952) Measures for describing the size distribution of sediments. J Sediment Petrol 22:125–145Google Scholar
  38. 38.
    Folk RL, Ward WC (1957) Brazos River bar, a study in the significance of grain size parameters. J Sediment Petrol 27:3–37CrossRefGoogle Scholar
  39. 39.
    de Mahiques MM (2016) Sediment sorting. In: Kennish MJ (ed) Encyclopedia of estuaries. Springer Netherlands, Dordrecht, pp 560–561.
  40. 40.
    Sowers GB, Sowers GF (1972) Introducción a la mecánica de suelos y cimentaciones. Limusa-Wiley S. A., México D.FGoogle Scholar
  41. 41.
    Saucier R (2000) Computer generation of statistical distributions. Storming Media, 122 pp.
  42. 42.
    Chatfield C (1989) The analysis of time series. An introduction. Chapman and Hall, LondonzbMATHGoogle Scholar
  43. 43.
    Thornton C, Liu L (2000) DEM simulations of uniaxial compression and decompression. In: Kolymbas D, Fellin W (eds) International workshop on compaction of soils, granulates and powders. pp 251–261Google Scholar
  44. 44.
    Kuhn MR (1999) Structured deformation in granular materials. Mech Mater 31:407–429CrossRefGoogle Scholar
  45. 45.
    Rothenburg L, Bathurst R (1989) Analytical study of induced anisotropy in idealized granular materials. Géotechnique 39(4):601–614CrossRefGoogle Scholar
  46. 46.
    Bierwisch C et al (2009) Three-dimensional discrete element models for the granular statics and dynamics of powders in cavity filling. J Mech Phys Solids 57:10–31CrossRefzbMATHGoogle Scholar
  47. 47.
    Kruyt N, Rothenburg L (2009) Plasticity of granular materials: a structural mechanics view. In: Paper presented at the 6th international conference on micromechanics of granular media, Golden, Colorado, 13–7 July 2009Google Scholar
  48. 48.
    Agresti A (2002) Categorical data analysis. Second, 2nd edn. Wiley, New YorkCrossRefzbMATHGoogle Scholar
  49. 49.
    Hollander M, Wolfe DA (1973) Nonparametric statistical methods. John Wiley & Sons, New YorkzbMATHGoogle Scholar
  50. 50.
    Pavan M, Todeschini R (2008) Scientific data ranking methods: theory and applications. Elsevier Science, AmsterdamGoogle Scholar
  51. 51.
    McNeill FM, Thro E (1994) Fuzzy logic: a practical approach. Academic Press, 312 pp.
  52. 52.
    Sivanandam SN, Deepa SN, Sumathi S (2007) Introduction to fuzzy logic using MATLAB. Springer-Verlag, BerlinCrossRefzbMATHGoogle Scholar
  53. 53.
    Han K, Feng YT, Owen DRJ (2005) Sphere packing with a geometric based compression algorithm. Powder Technol 155(1):33–41CrossRefGoogle Scholar
  54. 54.
    Roselló 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. 2(2):161–172.

Copyright information

© OWZ 2017

Authors and Affiliations

  1. 1.Center of Computational Mechanics and Numerical Methods in EngineeringCIMNE-UCLV Classroom, Central University of Las VillasSanta ClaraCuba
  2. 2.Faculty of TechnologyUniversity of BrasiliaBrasiliaBrazil
  3. 3.Faculty of Mathematics, Physics and Computer ScienceCentral University of Las VillasSanta ClaraCuba
  4. 4.Faculty of Technology and Director of InfraLabUniversity of BrasiliaBrasiliaBrazil
  5. 5.Director of the International Center for Numerical Methods in EngineeringPolitechnical University of CatalonyaBarcelonaSpain

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