Discrete Element Methods: Basics and Applications in Engineering

  • Peter WriggersEmail author
  • B. Avci
Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 599)


A computational approach is presented in this contribution that allows a direct numerical simulation of 3D particulate movements. The given approach is based on the Discrete Element Method (DEM) The particle properties are constitutively described by specific models that act at contact points. The equations of motion will be solved by appropriate time marching algorithms. Additionally coupling schemes with the Finite Element Method (FEM) are discussed for the numerical treatment of particle-solid and particle-fluid interaction. The presented approach will be verified by computational results and compared with those of the literature. Finally, the method is applied for the simulation of different engineering applications using computers with parallel architecture.


  1. Alder, B. J., & Wainwright, T. E. (1957). Phase transition for a hard sphere system. Journal of Chemical Physics, 27(5), 1208–1209.CrossRefGoogle Scholar
  2. Allen, M. P., & Tildesley, D. J. (1987). Computer simulation of liquids. New York: Oxford University Press.zbMATHGoogle Scholar
  3. Avci, B., & Wriggers, P. (2012). A dem-fem coupling approach for the direct numerical simulation of 3d particulate flows. Journal of Applied Mechanics, 79, 01901.CrossRefGoogle Scholar
  4. Brilliantov N. V., Albers N., Spahn F., & Pöschel T. (2007). Collision dynamics of granular particles with adhesion. Physical Review E, 76(5, Part 1).Google Scholar
  5. Brilliantov N. V., Spahn F., Hertzsch J. M., & Pöschel T. (1996). Model for collisions in granular gases. Physical Review E, 53(5, Part B), 5382–5392.Google Scholar
  6. Choi, J., Kudrolli, A., & Bazant, M. Z. (2005). Velocity profile of granular flows inside silos and hoppers. Journal of Physics: Condensed Matter, 17, 2533–2548.Google Scholar
  7. Choi, J., Kudrolli, A., Rosales, R. R., & Bazant, M. Z. (2004). Diffusion and mixing in gravity-driven dense granular flows. Physical Review Letters, 92, 174301.CrossRefGoogle Scholar
  8. Cundall, P. A., & Strack, O. D. L. (1979). Discrete numerical model for granular assemblies. Geotechnique, 29(1), 47–65.CrossRefGoogle Scholar
  9. Dhia, H. B., & Rateau, G. (2005). The arlequin method as a flexible engineering design tool. International Journal of Numerical Methods in Engineering, 62, 1442–1462.CrossRefGoogle Scholar
  10. Dominik, C., & Tielens, A. G. G. M. (1995). Resistance to rolling in the adhesive contact of 2 elastic spheres. Philosophical Magazine A—Physics of Condensed Matter Structure Defects and Mechanical Properties, 72(3), 783–803.Google Scholar
  11. Gingold, R. A., & Monaghan, J. J. (1977). Smoothed particle hydrodynamics: Theory and application to non-spherical stars. Monthly Notices of the Royal Astronomical Society, 181(3), 375–389.CrossRefGoogle Scholar
  12. Gómez-Gesteira, M., Crespo, A. J., Rogers, B. D., Dalrymple, R. A., Dominguez, J. M., & Barreiro, A. (2012a). Sphysics-development of a free-surface fluid solver-part 2: Efficiency and test cases. Computers & Geosciences, 48, 300–307.Google Scholar
  13. Gomez-Gesteira, M., Rogers, B. D., Crespo, A. J., Dalrymple, R. A., Narayanaswamy, M., & Dominguez, J. M. (2012b). Sphysics-development of a free-surface fluid solver-part 1: Theory and formulations. Computers & Geosciences, 48, 289–299.Google Scholar
  14. Hertz, H. (1882). Über die Berührung fester elastischer Körper. Journal für die reine und angewandte Mathematik, 92, 156–171.zbMATHGoogle Scholar
  15. Ishibashi, I., Perry, C., & Agarwal, T. K. (1994). Experimental determinations of contact friction for spherical glass particles. Soils and Foundations, 34, 79–84.CrossRefGoogle Scholar
  16. Iwashita, K., & Oda, M. (1998). Rolling resistance at contacts in simulation of shear band development by dem. Journal of Engineering Mechanics-ASCE, 124(3), 285–292.CrossRefGoogle Scholar
  17. Johnson, A. A., & Tezduyar, T. E. (1997). 3d simulation of fluid-particle interactions with the number of particles reaching 100. Computer Methods in Applied Mechanics and Engineering, 145(3–4), 301–321.CrossRefGoogle Scholar
  18. Johnson, K. L., Kendall, K., & Roberts, A. D. (1971). Surface energy and contact of elastic solids. Proceedings of the Royal Society of London Series A-Mathematical and Physical Sciences, 324(1558), 301–313.Google Scholar
  19. Kruggel-Emden, H., Sturm, M., Wirtz, S., & Scherer, V. (2008). Selection of an appropriate time integration scheme for the discrete element method (dem). Computers & Chemical Engineering, 32(10), 2263–2279.Google Scholar
  20. Kuhn, M., & Bagi, K. (2004). Alternative definition of particle rolling in a granular assembly. Journal of Engineering Mechanics-ASCE, 130(7), 826–835.CrossRefGoogle Scholar
  21. Loskofsky, C., Song, F., & Newby, B. Z. (2006). Underwater adhesion measurements using the JKR technique. Journal of Adhesion, 82(7), 713–730.CrossRefGoogle Scholar
  22. Luding, S. (2004). Micro-macro transition for anisotropic, frictional granular packings. International Journal of Solids and Structures, 41(21), 5821–5836.CrossRefGoogle Scholar
  23. Maruzewski, P., Le Touze, D., & Oger, G. (2009). Sph high-performance computing simulations of rigid solids impacting the free-surface of water. Journal of Hydraulic Research, 47, 126–134.Google Scholar
  24. Maugis, D. (1992). Adhesion of spheres—The jkr-dmt transition using a dugdale model. Journal of Colloid and Interface Science, 150(1), 243–269.CrossRefGoogle Scholar
  25. Pöschel, T., & Schwager, T. (2005). Computational Granular Dynamics. Springer.Google Scholar
  26. Quentrec, B., & Brot, C. (1973). New method for searching for neighbors in molecular dynamics computations. Journal of Computational Physics, 13(3), 430–432.CrossRefGoogle Scholar
  27. Sbalzarini, I. F., Walther, J. H., Bergdorf, M., Hieber, S. E., Kotsalis, E. M., & Koumoutsakos, P. (2006). PPM—A highly efficient parallel particle-mesh library for the simulation of continuum systems. Journal of Computational Physics, 215, 566–588.Google Scholar
  28. Springel, V. (2005). The cosmological simulation code gadget-2. Monthly Notices of the Royal Astronomical Society, 364, 1105–1134.CrossRefGoogle Scholar
  29. Ulrich, C., & Rung, T. (2006). Validation and application of a massively-parallel hydrodynamic SPH simulation code. Proceedings of NuTTS ’09.Google Scholar
  30. Verlet, L. (1967). Computer experiments on classical fluids. i. Thermodynamical properties of Lennard-Jones molecules. Physical Review, 159(1), 98–103.CrossRefGoogle Scholar
  31. Walther, J. H., & Sbalzarini, I. F. (2009). Large-scale parallel discrete element simulations of granular flow. Engineering Computations, 26(6, Sp. Iss. SI), 688–697; 4th International Conference on Discrete Element Methods (2007). Australia, Brisbane.Google Scholar
  32. Wellmann, C. (2011) A Two-Scale Model of Granular Materials Using a Coupled Discrete-Finite Element Approach. Dissertation, B11/1, Institute for Continuum Mechanics, Leibniz University Hannover.Google Scholar
  33. Wellmann, C., Lillie, C., & Wriggers, P. (2008). A contact detection algorithm for superellipsoids based on the common-normal concept. Engineering Computations, 25(5–6), 432–442.CrossRefGoogle Scholar
  34. Wellmann, C., & Wriggers, P. (2012). A two-scale model of granular materials. Computer Methods in Applied Mechanics and Engineering, 205–208, 46–58.MathSciNetCrossRefGoogle Scholar
  35. Wriggers, P. (1987). On consistent tangent matrices for frictional contact problems. In G. Pande & J. Middleton (Eds.), Proceedings of NUMETA ’87. M. Nijhoff Publishers, Dordrecht.Google Scholar
  36. Wriggers, P. (2006). Computational Contact Mechanics (2nd ed.). Berlin Heidelberg: Springer.CrossRefGoogle Scholar
  37. Wriggers, P., Van, T. V., & Stein, E. (1990). Finite-element-formulation of large deformation impact- contact-problems with friction. Computers and Structures, 37, 319–333.CrossRefGoogle Scholar
  38. Zhu, H. P., Zhou, Z. Y., Yang, R. Y., & Yu, A. B. (2007). Discrete particle simulation of particulate systems: Theoretical developments. Chemical Engineering Science, 62(13), 3378–3396.CrossRefGoogle Scholar
  39. Zohdi, T. I. (2007). Introduction to the modeling and simulation of particulate flows. SIAM.Google Scholar

Copyright information

© CISM International Centre for Mechanical Sciences, Udine 2020

Authors and Affiliations

  1. 1.Faculty of Mechanical EngineeringInstitut for Continuum Mechanics, Leibniz University HannoverHannoverGermany
  2. 2.CADFEM GmbHHannoverGermany

Personalised recommendations