Computational Particle Mechanics

, Volume 6, Issue 1, pp 97–131 | Cite as

3D numerical simulations of granular materials using DEM models considering rolling phenomena

  • Alex Alves BandeiraEmail author
  • Tarek Ismail Zohdi


This work presents a review of the formulation for computer simulation based on the discrete element method to analyze granular materials and a validation of the method using different types of tridimensional examples. The individual particulate dynamics under the combined action of particle collisions, particle–surface contact and adhesive interactions is simulated and aggregated to obtain global system behavior. The formulations to compute the forces and momentums developed at the particles are explained in details. The environment and gravity forces are considered as well as the contact forces that occur due the contact between particles and walls, like normal contact forces, frictional contact forces, damping and adhesive bond. The rolling phenomenon is also taken into account and is presented using a standard formulation. A numerical algorithm adapted from Zohdi is also presented. A few tridimensional examples of classical physics are selected to validate the formulations and the numerical program developed and to provide an illustration of the applicability of the numerical integration scheme. For this purpose, each analytical formulation is demonstrated to compare and analyze the numerical results with the analytical one. At the end of this article, a few tridimensional examples of granular materials are simulated. This article contributes to the study of granular materials including the rotation phenomenon using particle methods.


Particle method DEM Explicit solution Rolling Granular materials 



The authors wish to express sincere appreciation to the independent public foundation Capes (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Ministry of Education of Brazil, Brasília-DF, Brazil), which mission is to foster research and the scientific and technological development. This work was supported by Capes, under the Grants BEX2565/15-3. The authors would like to thank the CRML (Computational Materials Research Laboratory, University of California at Berkeley, USA).


This study was funded by the independent public foundation Capes (“Coordenação de Aperfeiçoamento de Pessoal de Nível Superior”, Ministry of Education of Brazil, Brasília-DF, Brazil) (Grant Number BEX 2565/15-3).

Compliance with ethical standards

Conflict of interest

Regarding the conflict of interest, the author Alex Alves Bandeira has received research grants from Capes to stay one year in University of California, at Berkeley, to developed his post-doc. The author Tarek Ismail Zohdi, coordinator of the CRML (Computational Materials Research Laboratory, University of California, at Berkeley, USA), was his supervisor in this research and kindly welcomed the first author in his Laboratory. The authors declare that they have no conflict of interest. The only requirement of the Capes foundation is to mention its collaboration in the acknowledgments in the publication, as shown in Acknowledgements.


  1. 1.
    Cundall PA (1971) A computer model for simulating progressive large-scale movements in Blocky rock system. In: Proceedings of international symposium on rock fractures, Nancy, France, vol 2, pp 128–132Google Scholar
  2. 2.
    Cundall PA, Strack O (1979) A discrete numerical mode for granular assemblies. Geotechnique 29(1):47–65CrossRefGoogle Scholar
  3. 3.
    Deresiewicz H (1958) Mechanics of granular matter. Adv Appl Mech 5:233–306MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Wakabayashi T (1950) Photo-elastic method for determination of stress in powered mass. J Phys Soc Jpn 5:383–385CrossRefGoogle Scholar
  5. 5.
    Dantu P (1957) Contribuition à l’étude mécanique et géométrique des milieux pul-vérulents. In: Proceedings of the 4th international conference on soil mechanics and foundation engineering, London, vol 1, pp 144–148Google Scholar
  6. 6.
    Josseling De, de Jong G, Verruijt A (1969) Etude photo-élastique d’un empilement de disques. Cashiers du Groupe Français de Rheologie 2:73–86Google Scholar
  7. 7.
    Serrano AA, Rodríguez Ortiz JM (1973) A contribution to the mechanics of heterogeneous granular media. In: Symposium on plasticity and soil mechanics, Cambridge, England, pp 215–228Google Scholar
  8. 8.
    Schwartz SR, Richardson DC, Michel P (2012) An implementation of the soft-sphere discrete element method in a high-performance parallel gravity tree-code. Granul Matter 14:363–380CrossRefGoogle Scholar
  9. 9.
    Sànchez D (2015) Asteroid evolution: role of geotechnical properties. In: International Astronomical Union, Cambridge University Press, Cambridge, pp 111–121Google Scholar
  10. 10.
    Hong DC, McLennan JA (1992) Molecular dynamics simulations of hard sphere granular particles. Phys A 187:159–171CrossRefGoogle Scholar
  11. 11.
    Huilin L, Yunhua Z, Ding J, Gidaspow D, Wei L (2007) Investigation of mixing/segregation of mixture particles in gas-solid fluidized beds. Chem Eng Sci 62:301–317CrossRefGoogle Scholar
  12. 12.
    Kosinski P, Hoffmann AC (2009) Extension of the hard-sphere particle-wall collision model to account for particle deposition. Phys Rev 79(6):061302: 1–061302: 11Google Scholar
  13. 13.
    Mitarai N, Nakanishi H (2003) Hard-sphere limit of soft-sphere model for granular materials: stiffness dependence of steady granular flow. Phys Rev 67(2):021301: 1–021301: 8Google Scholar
  14. 14.
    Cleary PW, Sawley ML (2002) DEM modelling of industrial granular flows: 3D case studies and the effect of particle shape on hopper discharge. Appl Math Model 26:89–111CrossRefzbMATHGoogle Scholar
  15. 15.
    Tsuji Y, Tanaka T, Ishida T (1992) Lagrangian numerical simulation of plug flow of cohesionless particles in a horizontal pipe. Powder Technol 71:239–250CrossRefGoogle Scholar
  16. 16.
    Sànchez DPSDJ (2011) Simulating asteroid rubble piles with a self-gravitating soft-sphere distinct element method model. Astrophys J 727:120–134CrossRefGoogle Scholar
  17. 17.
    Tancredi G, Maciel A, Heredia L, Richeri P, Nesmachnow S (2011) Granular physics in low-gravity environments using DEM. In: MNRAS, pp 3368–3380Google Scholar
  18. 18.
    Mehta AJ (2011) Granular physics. Cambridge University Press, Cambridge. ISBN 9780511535314zbMATHGoogle Scholar
  19. 19.
    Vu-Quoc L, Zhang X, Walton OR (2000) A 3-D discrete-element method for dry granular flows of ellipsoidal particles. Comput Methods Appl Mech Eng 187:483–528CrossRefzbMATHGoogle Scholar
  20. 20.
    Martin CL, Bouvard D (2003) Study of the cold compaction of composite powders by the discrete element method. Acta Mater 51:373–386CrossRefGoogle Scholar
  21. 21.
    Oñate E, Labra C, Zarate F, Rojek J, Miquel J (2005) Avances en el Desarrollo de los Métodos de Elementos Discretos y de Elementos Finitos para el Análisis de Problemas de Fractura. Anales de Mecánica de la Fractura 22:27–34Google Scholar
  22. 22.
    Zohdi TI, Wriggers P (2001) Modeling and simulation of the decohesion of particulate aggregates in a binding matrix. Eng Comput 18:79–95. ISSN 0264-4401Google Scholar
  23. 23.
    Zohdi TI (2013) Rapid simulation of laser processing of discrete particulate materials. Arch Comput Methods Eng 20(4):309–325CrossRefGoogle Scholar
  24. 24.
    Ghaboussi J, Barbosa R (1990) Tree-dimensional discrete element method for granular material. Int J Numer Anal Meth Geomech 14:451–472CrossRefGoogle Scholar
  25. 25.
    Donzé FV, Richefeu V, Magnier SA (2009) Advances in discrete element method applied to soil, rock and concrete. Mech Electron J Geotech Eng 8:1–44Google Scholar
  26. 26.
    Fortin J, Millet O, De Saxce G (2005) Numerical simulation of granular materials by an improved discrete element method. Int J Numer Meth Eng 62:639–663MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Kruggel-Emden H, Simsek E, Rickelt S, Wirtz S, Scherer V (2007) Review and extension of normal force models for the discrete element method. Powder Technol 171:157–173CrossRefGoogle Scholar
  28. 28.
    Obermayr M, Dressler K, Vrettos C, Eberhard P (2011) Prediction of draft force in cohesionless soil with the discrete element method. J Terrramech 48:347–358CrossRefGoogle Scholar
  29. 29.
    El Shamy U, Aldebhamid Y (2014) Modeling granular soils liquefaction using coupled lattice Boltzmann method and discrete element method. Soil Dyn Earthq Eng 67:119–132CrossRefGoogle Scholar
  30. 30.
    Casas G, Mukjerjee D, Celigueta MA, Zohdi TI, Eugenio O (2017) A modular, partitioned, discrete element framework for industrial grain distribution systems with rotating machinery. J Comput Part Mech 4:181–198CrossRefGoogle Scholar
  31. 31.
    Kacianauskas R, Maknickas A, Kaceniauskas A, Markauskas D, Balevicius R (2010) Parallel discrete element simulation of poly-dispersed granular material. Adv Eng Softw 41:52–63CrossRefzbMATHGoogle Scholar
  32. 32.
    Elaskar SA, Godoy LA, Gray DD, Stiles JM (2000) A viscoplastic approach to model the flow of granular solids. Int J Solids Struct 37:2185–2214CrossRefzbMATHGoogle Scholar
  33. 33.
    Wada K, Senshu H, Matsui T (2006) Numerical simulation of impact cratering on granular material. Icarus 180(2):528–545CrossRefGoogle Scholar
  34. 34.
    Campello EDMB (2015) A description of rotations for DEM models of particle system. Comput Part Mech 2:109–125CrossRefGoogle Scholar
  35. 35.
    Zohdi TI (2014) Additive particle deposition and selective laser processing—a computational manufacturing framework. Comput Mech 54(1):171–191MathSciNetCrossRefGoogle Scholar
  36. 36.
    Zohdi TI (2014) A direct particle-based computational framework for electrically-enhanced thermo-mechanical sintering of powdered materials. Math Mech Solids 19(1):1–21MathSciNetCrossRefGoogle Scholar
  37. 37.
    Johnson KL (2003) Contact mechanics, 9th edn. Cambridge University Press, CambridgeGoogle Scholar
  38. 38.
    Bandeira AA, Wriggers P, Pimenta PM (2001) Homogenization methods leading to interface laws of contact mechanics—a finite element approach for large 3D deformation using augmented lagrangian method. Int J Numer Method EngGoogle Scholar
  39. 39.
    Wriggers P (2006) Computational contact mechanics, 2nd edn. Springer, BerlinCrossRefzbMATHGoogle Scholar
  40. 40.
    Zohdi TI (2007) Computation of strongly coupled multifield interaction in particle-fluid systems. Comput Methods Appl Mech Eng 196(37):3927–3950MathSciNetCrossRefzbMATHGoogle Scholar
  41. 41.
    Avci B, Wriggers P (2012) A DEM-FEM coupling approach for the direct numerical simulation of 3D particulate flows. J Appl Mech 79:010901: 1–010901: 7CrossRefGoogle Scholar
  42. 42.
    Zohdi TI (2012) Dynamics of charged particulate systems. Springer, BerlinCrossRefzbMATHGoogle Scholar
  43. 43.
    LeVeque RJ (2007) Finite difference methods for ordinary and partial differential equations: stead-state and time-dependent problems. SIAM (Society for Industrial and Applied Mathematics), PhiladelphiaCrossRefzbMATHGoogle Scholar
  44. 44.
    Zohdi TI (2005) Charge-induced clustering in multifield particulate flow. Int J Numer Meth Eng 62(7):870–898MathSciNetCrossRefzbMATHGoogle Scholar
  45. 45.
    Zohdi TI (2013) Numerical simulation of the impact and deposition of charged particulate droplets. J Comput Phys 233(1):509–526MathSciNetCrossRefGoogle Scholar
  46. 46.
    Zohdi TI (2002) An adaptive–recursive staggering strategy for simulating multifield coupled processes in microheterogeneous solids. Int J Numer Meth Eng 53(7):1511–1532MathSciNetCrossRefzbMATHGoogle Scholar
  47. 47.
    Zohdi TI (2010) On the dynamics of charged electromagnetic particulate jets. Arch Comput Methods Eng 17:109–135MathSciNetCrossRefzbMATHGoogle Scholar
  48. 48.
    Wu C-Y, Thornton C, Li L-Y (2009) A semi-analytical model for oblique impacts of elastoplastic spheres. R Soc A 465(2103):937–960CrossRefzbMATHGoogle Scholar
  49. 49.
    Moin P (2010) Fundamentals of engineering numerical analysis, 2nd edn. Cambridge University Press, New YorkCrossRefzbMATHGoogle Scholar
  50. 50.
    Batlle JA, Cardona S (1998) The jamb (self-locking) process in three-dimensional rough collisions. Trans ASME J Appl Mech 65(2):417–423CrossRefGoogle Scholar
  51. 51.
    Batlle JA (1993) On Newton’s and Poisson’s rules of percussive dynamics. J Appl Mech 60(2):376–381CrossRefzbMATHGoogle Scholar
  52. 52.
    Brach RM (1988) Impact dynamics with applications to solid particle erosion. Int J Impact Eng 7(1):37–53CrossRefGoogle Scholar
  53. 53.
    Brach RM (1991) Mechanical impact dynamics: rigid body collisions. NY Wiley Interscience, New YorkGoogle Scholar
  54. 54.
    Thornton C (1997) Coefficient of restitution for collinear collisions of elastic-perfectly plastic spheres. Trans ASME J Appl Mech 64(2):383–386CrossRefzbMATHGoogle Scholar
  55. 55.
    Wu CY, Li LY, Thornton C (2003) Rebound behaviour of spheres for plastic impacts. Int J Impact Eng 28(9):929–946CrossRefGoogle Scholar
  56. 56.
    Cheng W, Brach RM, Dunn PF (2002) Three-dimensional modeling of microsphere contact/impact with smooth, flat surfaces. Aerosol Sci Technol 36(11):1045–1060CrossRefGoogle Scholar
  57. 57.
    Aghamohammadia C, Aghamohammadib A (2011) Slipping and rolling on an inclined plane. Eur J Phys 32:1049–1057CrossRefGoogle Scholar

Copyright information

© OWZ 2018

Authors and Affiliations

  1. 1.Structural Engineering Program, Construction and Structures Department, Polytechnic SchoolFederal University of Bahia – UFBASalvadorBrazil
  2. 2.Computational Materials Research Laboratory, Department of Mechanical EngineeringUniversity of California, BerkeleyBerkeleyUSA

Personalised recommendations