Granular Matter

, 21:80 | Cite as

Two-dimensional particle shapes modelling for DEM simulations in engineering: a review

  • Jalal KafashanEmail author
  • Joanna Wiącek
  • Noorhazlinda Abd Rahman
  • Jieqing Gan
Original Paper


The Discrete Element Method/Modelling (DEM) is a well-elaborated method for modelling the dynamical behaviour of particulate systems. The term “DEM” refers to a family of numerical methods for computing the motion of a large number of particles such as molecules, grains, and rocks. Despite it was originally pioneered for rock mechanics, DEM is being developed for wide-range of applications in most engineering domains. The representation of particle shape geometry in DEM is crucial, which has a direct impact on the computational performance of the methods and on the dynamical behaviour of particulate systems. Most applications are limited in time of simulation to simple particle shapes due to the increase in computation with increasing complexity of geometry. Currently, many methods for particle shape representation are proposed due to irregular shape of the real particles. This paper reviews the research and methods of particle shapes modelling for 2D-DEM over the last three decades. This includes classification of particle shapes models in the different categories, applicable to numerous engineering disciplines that use DEM.


Computational simulation Discrete element method Mechanics of particulate solids Mechanics of particulate materials Particle technology Shape modelling 



The first author is immensely grateful to Prof. Ramon and Dr. Tijskens from Division of Mechatronics of KULeuven University and Department of Mathematics–Computer Science of UAntwerpen, Belgium, respectively for their valuable and general comments on the initial version of manuscript. The author express his thanks to Prof. Graham Mustoe, Colorado School of Mines; Dr. Kejun Dong, Institute for Infrastructure Engineering of Western Sydney University; Prof. Thorsten Pöschel, Institute for Multiscale Simulation; Prof. Álvaro Ramírez-Gómez, Technical University of Madrid; Prof. Tang-Tat Ng, University of New Mexico; Prof. Aibing Yu, Monash University of Australia; Prof. Hou Meiying, Laboratory of Soft Matter Physics (LSMP) of China; Prof. Bernhard Peters, University of Luxembourg; Prof. Mojtaba Ghadiri, University of Leeds; and Prof. Hans Herrmann, Institute for Building Materials of ETH Zürich, respectively for their modesty in responding and for sending the requested papers. Last but not least, we would also like to thank all the persons at Granular Matter-Springer who facilitated to complete this review paper in its printed format.

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest related to this manuscript.


  1. 1.
    Pope, G.G.: A discrete element method for the analysis of plane elasto-plastic stress problems. Aeronaut. Q. 17(1), 83–104 (1966)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Cundall, P.A.: A computer model for simulating progressive large scale movements in blocky rock systems. In: Proceedings of the Symposium of the International Society of Rock Mechanics, vol. 1, Paper No. II-8. Nancy, France (1971)Google Scholar
  3. 3.
    Jean, M., Moreau, J. J.: Unilaterality and dry friction in the dynamics of rigid body collections. In: Proceedings of Contact Mechanics International Symposium, pp. 31–48. Presses, Polytechniques et Universitaires Romandes, Lausanne, Switzerland (1992)Google Scholar
  4. 4.
    Moreau, J.J.: Numerical investigation of shear zones in granular materials. In: Wolf, D.E., Grassberger, P. (eds.) Friction Arching Contact Dynamics, pp. 233–247. World Scientific, Singapore (1997)Google Scholar
  5. 5.
    Radjai, F., Richefeu, V.: Contact dynamics as a nonsmooth discrete element method. Mech. Mater. 41, 715–728 (2009)CrossRefGoogle Scholar
  6. 6.
    McCammon, J.A., Gelin, B.R., Karplus, M.: Dynamics of folded proteins. Nature 267(5612), 585–590 (1977)ADSCrossRefGoogle Scholar
  7. 7.
    Warshel, A., Levitt, M.: Theoretical studies of enzymic reactions: dielectric, electrostatic and steric stabilization of the carbonium ion in the reaction of lysozyme. J. Mol. Biol. 103(2), 227–249 (1976)CrossRefGoogle Scholar
  8. 8.
    Andrade, J.E., Lim, K.W., Avila, C.F., Vlahinić, I.: Granular element method for computational particle mechanics. Comput. Methods Appl. Mech. Eng. 241–244, 262–274 (2012)ADSzbMATHCrossRefGoogle Scholar
  9. 9.
    Andrade, J.E., Avila, C.F.: Granular element method (GEM): linking inter-particle forces with macroscopic loading. Granular Matter 14, 51–61 (2012)CrossRefGoogle Scholar
  10. 10.
    Kafashan, J., Tijskens, B., Ramon, H.: Shape modelling of fruit by image processing. Commun. Agric. Appl. Biol. Sci. 70(2), 161–164 (2005)Google Scholar
  11. 11.
    Sadrnia, H., Rajabipour, A., Jafari, A., Javadi, A., Mostofi, Y., Kafashan, J., Dintwa, E., De Baerdemaeker, J.: Stress distribution in watermelon (cv. ‘Crimson sweet’) under axial compression. Commun Agric Appl Biol Sci. 72(1), 281–284 (2007)Google Scholar
  12. 12.
    Kafashan, J., Van Liedekerke, P., Ramon, H., Tijskens, B.: An Approach to represent realistic particles of bulk assembly in three-dimensional-DEM simulations and applications. Commun. Agric. Appl. Biol. Sci. 76(1), 33–36 (2011)Google Scholar
  13. 13.
    Kafashan, J., Van Liedekerke, P., Ramon, H., Tijskens, B.: A multi-ring model to simulate particle-based systems in biomaterials transport. In: 38th International Symposium on “Actual Tasks on Agricultural Engineering”, Opatija, Croatia, pp. 211–218 (2010). ISSN 1333-2651Google Scholar
  14. 14.
    Cundall, P.A., Strack, O.D.L.: A discrete numerical model for granular assemblies. Geotechnique 29, 47–65 (1979)CrossRefGoogle Scholar
  15. 15.
    Kafashan, J., Van Liedekerke, P., Ramon, H., Tijskens, B.: Particulate Materials Simulations and Applications in Engineering Domains. Multidisciplinary Academic Symposium, UCL, London, UK (2009)Google Scholar
  16. 16.
    Kafashan, J.: Computational Simulations: Alternative Solution in Sensing and Monitoring of Biomaterials. J. Biosens. Bioelectron. (2013). CrossRefGoogle Scholar
  17. 17.
    Recareyabc, C., Péreza, I., Rosellóa, R., Munizb, M., Hernándezb, E., Giraldob, R., Oñatecd, E.: Advances in particle packing algorithms for generating the medium in the discrete element method. Comput. Methods Appl. Mech. Eng. 345, 336–362 (2018)ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    Seelen, L.J.H., Padding, J.T., Kuipers, J.A.M.: A granular discrete element method for arbitrary convex particle shapes: method and packing generation. Chem. Eng. Sci. 189, 84–101 (2018)CrossRefGoogle Scholar
  19. 19.
    Dehestani, M., Asadi, A., Mousavi, S.S.: On discrete element method for rebar-concrete interaction. Constr. Build. Mater. 151, 220–227 (2017)CrossRefGoogle Scholar
  20. 20.
    Majidi, B., Rolfe, P., Fafard, M., Ziegler, D.P., Alamdari, H.: Numerical modeling of compaction and flow of coke/pitch mixtures using discrete element method. Constr. Build. Mater. 169, 315–324 (2018)CrossRefGoogle Scholar
  21. 21.
    André, D., Iordanoff, I., Charles, J., Néauport, J.: Discrete element method to simulate continuous material by using the cohesive beam model. Comput. Methods Appl. Mech. Eng. 213–216, 113–125 (2012)ADSzbMATHCrossRefGoogle Scholar
  22. 22.
    Cai, R., Xu, L., Zheng, J., Zhao, Y.: Modified cell-linked list method using dynamic mesh for discrete element method. Powder Technol. 340, 321–330 (2018)CrossRefGoogle Scholar
  23. 23.
    Garner, S., Strong, J., Zavaliangos, A.: Study of the die compaction of powders to high relative densities using the discrete element method. Powder Technol. 330, 357–370 (2018)CrossRefGoogle Scholar
  24. 24.
    Kumar, R., Patel, C.M., Jana, A.K., Gopireddy, S.R.: Prediction of hopper discharge rate using combined discrete element method and artificial neural network. Adv. Powder Technol. 29, 2822–2834 (2018)CrossRefGoogle Scholar
  25. 25.
    Gupta, V., Sun, X., Xu, W., Sarv, H., Farzan, H.: A discrete element method-based approach to predict the breakage of coal. Adv. Powder Technol. 28, 2665–2677 (2017)CrossRefGoogle Scholar
  26. 26.
    Truszkowska, A., Yu, Q., Greaney, P.A., Evans, T.M., Kruzic, J.J.: A discrete element method representation of an anisotropic elastic continuum. J. Mech. Phys. Solids 121, 363–386 (2018)ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    Leclerc, W., Haddad, H., Guessasma, M.: On the suitability of a Discrete Element Method to simulate cracks initiation and propagation in heterogeneous media. Int. J. Solids Struct. 108, 98–114 (2017)CrossRefGoogle Scholar
  28. 28.
    Sinaie, S., Heidarpour, A., Zhao, X.L.: A micro-mechanical parametric study on the strength degradation of concrete due to temperature exposure using the discrete element method. Int. J. Solids Struct. 88–89, 165–177 (2016)CrossRefGoogle Scholar
  29. 29.
    Gotoh, H., Harada, E., Andoh, E.: Simulation of pedestrian contra-flow by multi-agent DEM model with self-evasive action model. Saf. Sci. 50, 326–332 (2012)CrossRefGoogle Scholar
  30. 30.
    Harada, E., Gotoh, H., Rahman, N.B.A.: A switching action model for DEM-based multi-agent crowded behavior simulator. Saf. Sci. 79, 105–115 (2015)CrossRefGoogle Scholar
  31. 31.
    Kawaguchi, T.: Discrete particle simulation for high-density crowd. Transport. Res. Proc. 2, 418–423 (2014)CrossRefGoogle Scholar
  32. 32.
    Peng, L., Ma, J., Lo, S.: Discrete element crowd model for pedestrian evacuation through an exit. Chin. Physics B 25(3), 034501 (2016)ADSCrossRefGoogle Scholar
  33. 33.
    Walton, O.R.: Particle-dynamics calculations of shear flow. In: Jenkins, J.T., Satake, M. (eds.) Mechanics of Granular Materials: New Models and Constitutive Relations. Studies in Applied Mechanics, vol. 7, pp. 327–338 (1983)CrossRefGoogle Scholar
  34. 34.
    Williams, J.R., Pentland, A.: Superquadrics and model dynamics for discrete elements in interactive design. Eng. Comput. 9, 115–128 (1992)CrossRefGoogle Scholar
  35. 35.
    Hogue, C.: Shape representation and contact detection for discrete element simulations of arbitrary geometries. Eng. Comput. 15(2–3), 374–390 (1998)zbMATHCrossRefGoogle Scholar
  36. 36.
    Ting, J.M., Khwaja, M., Meachum, L., Rowell, J.D.: An ellipse-based discrete element model for granular materials. Int. J. Numer. Anal. Meth. Geomech. 17, 603–623 (1993)zbMATHCrossRefGoogle Scholar
  37. 37.
    Ashmawy, A.K., Sukumaran, B., Hoang, A.V.: Evaluating the influence of particle shape on liquefaction behavior using discrete element method. In: Proceedings of the Thirteenth International Offshore and Polar Engineering Conference (ISOPE 2003) Honolulu, Hawaii, May 2003 (2003)Google Scholar
  38. 38.
    Wang, L., Park, J.Y., Fu, Y.: Representation of real particles for DEM simulation using X-ray tomography (equalant ellipsoid, sphere). Constr. Build. Mater. 21(2), 338–346 (2007)CrossRefGoogle Scholar
  39. 39.
    Masala, S., Chan, D., Lu, H., Chalaturnyk, R.: A Java-based graphical user interface for a 2-D discrete element program, Discrete Element Methods. In: Numerical Modeling of Discontinua: Proceedings of the Third International Conference September 23–25, 2002, Santa Fe, New Mexico, USA, pp. 125–130 (2002)Google Scholar
  40. 40.
    Helbing, D.: Collective phenomena and states in traffic and self-driven many-particle systems. Comput. Mater. Sci. 30, 180–187 (2004)CrossRefGoogle Scholar
  41. 41.
    Han, K., Feng, Y.T., Owen, D.R.J.: Polygon-based contact resolution for superquadrics. Int. J. Numer. Meth. Eng. 66, 485–501 (2006)zbMATHCrossRefGoogle Scholar
  42. 42.
    Lin, P., Lo, S.M., Yuen, K.K., Huang, H.C., Liang, J.: A granular dynamic method for modelling the egress pattern at an exit. Fire Saf. J. 42(5), 377–383 (2007)CrossRefGoogle Scholar
  43. 43.
    Singh, H., Arter, R., Dodd, L., Langston, P., Lester, E., Drury, J.: Modelling subgroup behaviour in crowd dynamics DEM simulation. Appl. Math. Model. 33(12), 4408–4423 (2009)zbMATHCrossRefGoogle Scholar
  44. 44.
    Abd Rahman, N., Harada, E., Gotoh, H., Yoshizawa, Y.: Evacuation process during tsunami disaster at the Langkawi international airport, Malaysia by DEM-based multi-agent model. In: Conference: Proceedings of International Sessions in Coastal Engineering, JSCE, At University of Fukuoka, Japan, vol. 4 (2013)Google Scholar
  45. 45.
    Zhu, H., Nicot, F., Darve, F.: Meso-structure evolution in a 2D granular material during biaxial loading. Granular Matter 18, 3 (2016)CrossRefGoogle Scholar
  46. 46.
    Kozicki, J., Tejchman, J.: Investigations of quasi-static vortex structures in 2D sand specimen under passive earth pressure conditions based on DEM and Helmholtz–Hodge vector field decomposition. Granular Matter 19, 19–31 (2017)CrossRefGoogle Scholar
  47. 47.
    Oh, H., Park, J.: Main factor causing “faster-is-slower” phenomenon during evacuation: rodent experiment and simulation. Sci. Rep. 7, 1–14 (2017)ADSCrossRefGoogle Scholar
  48. 48.
    Zhao, L., Liu, X., Mao, J., Xu, D., Munjiza, A., Avital, E.: A novel discrete element method based on the distance potential for arbitrary 2D convex elements. Int. J. Numer. Methods Eng. 115(2), 1–30 (2018)MathSciNetCrossRefGoogle Scholar
  49. 49.
    Kang, C., Chan, D.: Numerical simulation of 2D granular flow entrainment using DEM. Granular Matter 20(1), 13 (2018)CrossRefGoogle Scholar
  50. 50.
    Rahman, N.A.: Crowd Behavior Simulation of Pedestrians during Evacuation Process DEM-Based Approach. Springer, Netherland (2018)Google Scholar
  51. 51.
    Jensen, R.P., Edil, T.B., Bosscher, P.J., Plesha, M.E., Kahla, N.B.: Effect of particle shape on interface behavior of DEM-simulated granular materials. Int. J. Geomech. 1(1), 1–19 (2001)CrossRefGoogle Scholar
  52. 52.
    Jensen, R.P.: DEM simulation of particle damage in granular media-structure interfaces. Int. J. Geomech. 1(1), 21–39 (2001)CrossRefGoogle Scholar
  53. 53.
    Cleary, P.W., Sawley, M.L.: DEM modelling of industrial granular flows: 3D case studies and the effect of particle shape on hopper discharge. Appl. Math. Model. 26(2), 89–111 (2002)zbMATHCrossRefGoogle Scholar
  54. 54.
    Langston, P.A., Awamleh, M.A., Fraige, F.Y., Asmar, B.N.: Distinct element modelling of non-spherical frictionless particle flow. Chem. Eng. Sci. 59, 425–435 (2004)CrossRefGoogle Scholar
  55. 55.
    Li, J., Langston, P.A., Webb, C., Dyakowski, T.: Flow of sphero-disc particles in rectangular hoppers-a DEM and experimental comparison in 3D. Chem. Eng. Sci. 59(24), 5917–5929 (2004)CrossRefGoogle Scholar
  56. 56.
    Cleary, P.W.: The effect of particle shape on simple shear flows. Powder Technol. 179(3), 144–163 (1983)CrossRefGoogle Scholar
  57. 57.
    Zhang, Q., Xu, W., Liu, Q., Liu, Q., Meng, Q.: A novel non-overlapping approach to accurately represent 2D arbitrary particles for DEM modelling. J. Cent. South Univ. 24, 190–202 (2017)CrossRefGoogle Scholar
  58. 58.
    Jia, X., Gan, M., Williams, R.A., Rhodes, D.: Validation of a digital packing algorithm in predicting powder packing densities. Powder Technol. 174, 10–13 (2007)CrossRefGoogle Scholar
  59. 59.
    Cundall, P.A., Strack, O.D.L.: Modelling of microscopic mechanisms in granular material. In: Jenkinsand, J.T., Satake, M. (eds.) Mechanics of Granular Materials: New Models and Constitutive Relations, pp. 137–149. Elsevier, Amsterdam (1983)CrossRefGoogle Scholar
  60. 60.
    Ng, T.T., Dobry, R.: Numerical simulation of monotonic and cyclic loading of granular soils. J. Geotech. Eng. 120(2), 388–403 (1994)CrossRefGoogle Scholar
  61. 61.
    Xu, B.H., Yu, A.B.: Numerical simulation of the gas-solid flow in a fluidized bed by combining discrete particle method with computational fluid dynamics. Chem. Eng. Sci. 52, 2785–2809 (1997)CrossRefGoogle Scholar
  62. 62.
    Jensen, R.P., Bosscher, B.J., Plesha, M.E., Edil, T.B.: DEM simulation of granular media-structure interface: effects of surface roughness and particle shape. Int. J. Numer. Anal. Meth. Geomech. 23(6), 531–547 (1999)zbMATHCrossRefGoogle Scholar
  63. 63.
    Hossain, Z., Indraratna, B., Darve, F., Thakur, P.K.: DEM analysis of angular ballast breakage under cyclic loading. Geomech. Geoeng. 2(3), 175–181 (2007)CrossRefGoogle Scholar
  64. 64.
    Barr, A.: Superquadrics and angle-preserving transformations. IEEE Comput. Graphics Appl. 1, 11–23 (1981)CrossRefGoogle Scholar
  65. 65.
    Lin, X., Ng, T.T.: Contact detection algorithms for three-dimensional ellipsoids in discrete element modelling. Int. J. Numer. Anal. Meth. Geomech. 19, 653–659 (1995)zbMATHCrossRefGoogle Scholar
  66. 66.
    Rothenburg, L., Bathurst, R.J.: Micromechanical features of granular assemblies with planar elliptical particles. Géotechnique 42(1), 79–95 (1992)CrossRefGoogle Scholar
  67. 67.
    Ting, J.M., Meachum, L., Rowell, J.D.: Effect of particle shape on the strength and deformation mechanisms of ellipse-shaped granular assemblages. Eng. Comput. 12(2), 99–108 (1995)CrossRefGoogle Scholar
  68. 68.
    Zhu, Y., Shukla, A., Sadd, M.H.: The effect of microstructural fabric on dynamic load transfer in two dimensional assemblies of elliptical particles. J. Mech. Phys. Solids 44(8), 1283–1303 (1996)ADSCrossRefGoogle Scholar
  69. 69.
    Ng, T.T.: Numerical simulation of granular soil using elliptical particles. Comput. Geotech. 16(2), 153–169 (1994)CrossRefGoogle Scholar
  70. 70.
    Gan, J.Q., Zhou, Z.Y., Yu, A.B.: CFD–DEM modeling of gas fluidization of fine ellipsoidal particles. AlChE J. 62, 62–77 (2016)CrossRefGoogle Scholar
  71. 71.
    Gan, J.Q., Zhou, Z.Y., Yu, A.B.: Particle scale study of heat transfer in packed and fluidized beds of ellipsoidal particles. Chem. Eng. Sci. 144, 201–215 (2016)CrossRefGoogle Scholar
  72. 72.
    Zhou, Z.Y., Pinson, D., Zou, R.P., Yu, A.B.: Discrete particle simulation of gas fluidization of ellipsoidal particles. Chem. Eng. Sci. 66, 6128–6145 (2011)CrossRefGoogle Scholar
  73. 73.
    Džiugys, A., Peters, B.: An approach to simulate the motion of spherical and non-spherical fuel particles in combustion chambers. Granular Matter 3, 231–266 (2001)CrossRefGoogle Scholar
  74. 74.
    Rothenburg, L., Bathurst, R.J.: Numerical simulation of idealized granular assemblies with plane elliptical particles. Comput. Geotech. 11, 315–329 (1991)CrossRefGoogle Scholar
  75. 75.
    Lin, X., Ng, T.T.: Short communication, Contact detection algorithms for three-dimensional ellipsoids in discrete element modelling. Int. J. Numer. Anal. Meth. Geomech. 19, 653–659 (1995)zbMATHCrossRefGoogle Scholar
  76. 76.
    Williams, J.R., O’Connor, R.: A linear complexity algorithm for DE simulation of arbitrary geometries. Eng. Comput. 12, 185–201 (1995)CrossRefGoogle Scholar
  77. 77.
    Munjiza, A., Owen, D.R.J., Bicanic, N.: A combined finite-discrete element method in transient dynamics of fracturing solids. Eng. Comput. 12, 145–174 (1995)zbMATHCrossRefGoogle Scholar
  78. 78.
    Cleary, P.W., Hoyer, D.: Centrifugal mill charge motion and power draw: comparison of DEM predictions with experiment. Int. J. Miner. Process. 59, 131–148 (2000)CrossRefGoogle Scholar
  79. 79.
    Cundall, P.A.: 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, 107–116 (1988)CrossRefGoogle Scholar
  80. 80.
    Shi, G.H.: Discontinous deformation analysis: a new numerical model for the statics and dynamics of deformable block structures. Eng. Comput. 9, 157–168 (1992)CrossRefGoogle Scholar
  81. 81.
    Feng, Y.T., Owen, D.R.J.: A 2D polygon/polygon contact model: algorithmic aspects. Eng. Comput. 21(2–4), 265–277 (2004)zbMATHCrossRefGoogle Scholar
  82. 82.
    Matuttis, H.G., Luding, S., Herrmann, H.J.: Discrete element simulations of dense packings and heaps made of spherical and non-spherical particles. Powder Technol. 109(1), 278–292 (2000)CrossRefGoogle Scholar
  83. 83.
    Krishnasamy, J., Jakiela, M.J.: A method to resolve ambiguities in corner-corner interactions between polygons in the context of motion simulations. Eng. Comput. 12, 135–144 (1995)CrossRefGoogle Scholar
  84. 84.
    Pöschel, T., Buchholtz, V.: Molecular dynamics of arbitrarily shaped granular particles. J. Phys. I 5(11), 1431–1455 (1995)Google Scholar
  85. 85.
    Tillemans, H.J., Herrmann, H.J.: Simulating deformations of granular solids under shear. Physica A 217, 261–288 (1995)ADSCrossRefGoogle Scholar
  86. 86.
    Alonso-Marroquín, F., Mühlhaus, H.B., Herrmann, H.J.: Micromechanical investigation of granular ratcheting using a discrete model of polygonal particles. Particuology 6, 390–403 (2008)zbMATHCrossRefGoogle Scholar
  87. 87.
    Barbosa, R., Ghaboussi, J.: Discrete finite element method. Eng. Comput. 9, 253–266 (1992)CrossRefGoogle Scholar
  88. 88.
    Mirghasemi, A.A., Rothenburg, L., Matyas, E.L.: Influence of particle shape on engineering properties of assemblies of two-dimensional polygon-shaped particles. Geotechnique 52(3), 209–217 (2002)CrossRefGoogle Scholar
  89. 89.
    Seyedi Hosseininia, E., Mirghasemi, A.A.: Numerical simulation of breakage of two-dimensional polygon-shaped particles using discrete element method. Powder Technol. 166, 100–112 (2006)CrossRefGoogle Scholar
  90. 90.
    Alonso-Marroquin, F.: Micromechanical investigation of soil deformation: incremental response and granular ratcheting. Ph.D. thesis, University of Stuttgart. Logos Verlag, Berlin (2004)Google Scholar
  91. 91.
    Alonso-Marroquin, F., Herrmann, H.J.: Calculation of the incremental stress-strain relation of a polygonal packing. Phys. Rev. E 66, 021301 (2002)ADSCrossRefGoogle Scholar
  92. 92.
    Alonso-Marroquin, F., Herrmann, H.J., Vardoulakis, I.: Micromechanical investigation of soil plasticity: an investigation using a discrete model of polygonal particles. In Modeling of Cohesive-Frictional Materials, Stuttgart, Germany (2004)Google Scholar
  93. 93.
    Alonso-Marroquin, F., Wang, Y.: An efficient algorithm for granular dynamics simulation with complex-shaped objects. Granular Matter 11, 317–329 (2009)zbMATHCrossRefGoogle Scholar
  94. 94.
    Alonso-Marroquín, F.: Spheropolygons: a new method to simulate conservative and dissipative interactions between 2D complex-shaped rigid bodies. Europhys. Lett. 83, 14001 (2008)ADSCrossRefGoogle Scholar
  95. 95.
    Dobrohotoff, P.B., Azeezullah, S.I., Maggi, F., Alonso-Marroquin, F.: Optimal description of two-dimensional complex-shaped objects using spheropolygons. Granular Matter 14(5), 651–658 (2012)CrossRefGoogle Scholar
  96. 96.
    Potapov, A.V., Campbell, C.S.: A fast model for the simulation of non-round particles. Granular Matter 1, 9–14 (1998)zbMATHCrossRefGoogle Scholar
  97. 97.
    Williams, J.R., O’Connor, R.: Discrete element simulation and the contact problem. Arch. Computat. Methods Eng. 6, 279–304 (1999)MathSciNetCrossRefGoogle Scholar
  98. 98.
    Dong, K., Wang, C., Yu, A.: A novel method based on orientation discretization for discrete element modeling of non-spherical particles. Chem. Eng. Sci. 126, 500–516 (2015)CrossRefGoogle Scholar
  99. 99.
    Szarf, K., Combe, G., Villard, P.: Polygons vs. clumps of discs: a numerical study of the influence of grain shape on the mechanical behaviour of granular materials. Powder Technol. 208, 279–288 (2011)CrossRefGoogle Scholar
  100. 100.
    Alonso-Marroquín, F., Luding, S., Herrmann, H.J., Vardoulakis, I.: Role of anisotropy in the elastoplastic response of a polygonal packing. Phys. Rev. E 71, 051304 (2005)ADSCrossRefGoogle Scholar
  101. 101.
    Potapov, A.V., Campbell, C.S.: Computer simulation of impact-induced particle breakage. Powder Technol. 81, 207–216 (1994)CrossRefGoogle Scholar
  102. 102.
    Nguyen, D.-H., Azéma, É., Sornay, P., Radjaï, F.: Rheology of granular materials composed of crushable particles. Eur. Phys. J. E 41, 50 (2018)CrossRefGoogle Scholar
  103. 103.
    Åström, J.A., Herrmann, H.J.: Fragmentation of grains in a two-dimensional packing. Eur. Phys. J. B Condens. Matter Complex Syst. 5, 551–554 (1998)CrossRefGoogle Scholar
  104. 104.
    Nguyen, D.H., Azéma, E., Sornay, P., Radjai, F.: Bonded-cell model for particle fracture. Phys. Rev. E 91, 022203 (2015)ADSMathSciNetCrossRefGoogle Scholar
  105. 105.
    Itasca: PFC2D (Particle Flow Code in Two Dimensions) version 3.0: Theory and background. Minneapolis: Itasca Consulting Group, Inc. (2002)Google Scholar
  106. 106.
    Alonso-Marroquín, F.: Spheropolygons: a new method to simulate conservative and dissipative interactions between 2D complex-shaped rigid bodies. Europhys. Lett. 83, 14001 (2008)ADSCrossRefGoogle Scholar
  107. 107.
    Sallam, A.M.: Studies on modeling angular soil particles using the discrete element method. Ph.D. dissertation. College of Engineering, University of South Florida, USA (2004)Google Scholar
  108. 108.
    Thomas, P.A., Bray, J.D.: Capturing nonspherical shape of granular media with disk clusters. J. Geotecn. Geoenviron. Eng. ASCE. 125(3), 169–178 (1999)CrossRefGoogle Scholar
  109. 109.
    Langston, P.A., Masling, R., Asmar, B.N.: Crowd dynamics discrete element multi-circle model. Saf. Sci. 44, 395–417 (2006)CrossRefGoogle Scholar
  110. 110.
    Baglietto, G., Parisi, D.R.: Continuous-space automaton model for pedestrian dynamics. Phys. Rev. E 83, 056117 (2011)ADSCrossRefGoogle Scholar
  111. 111.
    Alonso-Marroquin, F., Busch, J., Ramírez-Gómez, Á., Lozano, C.: A Discrete Spheropolygon Model for Calculation of Stress in Crowd Dynamics. Book chapter from book local stability conditions and calibrating procedure for new car-following models used in driving simulators (pp. 179–186). (2015)Google Scholar
  112. 112.
    Kafashan, J., Van Zeebroeck, M., Ramon, H., Tijskens, B.: A novel approach to a realistic discrete element modelling (DEM) in 3D. Commun. Agric. Appl. Biol. Sci. 72(1), 205–208 (2007)Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Jalal Kafashan
    • 1
    • 2
    Email author
  • Joanna Wiącek
    • 3
  • Noorhazlinda Abd Rahman
    • 4
  • Jieqing Gan
    • 5
  1. 1.Department of Mechanical Engineering in Agro-Machinery and Mechanization, Agricultural Engineering Research InstituteAgricultural Research Education and Extension Organization (AREEO)KarajIran
  2. 2.Division of Mechatronics, Biostatistics and Sensors (MeBioS)KU LeuvenLeuvenBelgium
  3. 3.Institute of AgrophysicsPolish Academy of SciencesLublin 27Poland
  4. 4.School of Civil Engineering, Engineering CampusUniversiti Sains MalaysiaNibong TebalMalaysia
  5. 5.Laboratory for Simulation and Modelling of Particulate Systems, Department of Chemical EngineeringMonash UniversityClaytonAustralia

Personalised recommendations