Advertisement

Applications of the discrete element method in mechanical engineering

  • Florian FleissnerEmail author
  • Timo Gaugele
  • Peter Eberhard
Article

Abstract

Compared to other fields of engineering, in mechanical engineering, the Discrete Element Method (DEM) is not yet a well known method. Nevertheless, there is a variety of simulation problems where the method has obvious advantages due to its meshless nature. For problems where several free bodies can collide and break after having been largely deformed, the DEM is the method of choice. Neighborhood search and collision detection between bodies as well as the separation of large solids into smaller particles are naturally incorporated in the method. The main DEM algorithm consists of a relatively simple loop that basically contains the three substeps contact detection, force computation and integration. However, there exists a large variety of different algorithms to choose the substeps to compose the optimal method for a given problem. In this contribution, we describe the dynamics of particle systems together with appropriate numerical integration schemes and give an overview over different types of particle interactions that can be composed to adapt the method to fit to a given simulation problem. Surface triangulations are used to model complicated, non-convex bodies in contact with particle systems. The capabilities of the method are finally demonstrated by means of application examples.

Keywords

Discrete element method Numerical integration Quaternions Surface triangulation Multibody system coupling 

References

  1. 1.
    Cundall, P.A.: A computer model for simulation of progressive, large-scale movements in blocky rock systems. In: Proceedings of the Symposium of the International Society of Rock Mechanics, Nancy (1971) Google Scholar
  2. 2.
    Cundall, P.A., Strack, O.D.L.: A discrete numerical model for granular assemblies. Geotechnique 29, 47–56 (1979) CrossRefGoogle Scholar
  3. 3.
    Shabana, A.A.: Computational Dynamics. Wiley, New York (2001) Google Scholar
  4. 4.
    Omelyan, I.P.: On the numerical integration of motion for rigid polyatomics: the modified quaternion approach. Comput. Phys. 12(1), 97–103 (1998) CrossRefGoogle Scholar
  5. 5.
    Roberson, R.E., Schwertassek, R.: Dynamics of Multibody Systems. Springer, Berlin (1988) zbMATHGoogle Scholar
  6. 6.
    Hairer, E., Wanner, G.: Stiff differential equations solved by Radau methods. J. Comput. Appl. Math. 111, 93–111 (1999) zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Hairer, E., Wanner, G.: Solving Ordinary Differential Equations. II: Stiff and Differential-Algebraic Problems. Springer, Berlin (1991) zbMATHGoogle Scholar
  8. 8.
    Petzold, L.R.: A description of DASSL: a differential/algebraic system solver. In: Stepleman, R. (ed.) Scientific Computing: Application of Mathematics and Computing to the Physical Sciences, vol. 2, pp. 65–68 (1983) Google Scholar
  9. 9.
    Verlet, L.: Computer experiments on classical fluids. Phys. Rev. 159, 98–103 (1967) CrossRefGoogle Scholar
  10. 10.
    Allen, M.P., Tildesley, D.J.: Computer Simulations of Liquids. Clarendon, Oxford (1989) Google Scholar
  11. 11.
    Geradin, M., Rixon, D.: Mechanical Vibrations. Theory and Application to Structural Dynamics. Wiley, Chichester (1997) Google Scholar
  12. 12.
    Zohdi, T.I.: Charge-induced clustering in multifield particulate flows. Int. J. Numer. Methods Eng. 62, 870–898 (2004) CrossRefMathSciNetGoogle Scholar
  13. 13.
    Lankarani, H.M., Nikravesh, P.E.: A contact force model with hysteresis damping for impact analysis of multibody systems. J. Mech. Des. 112, 369–376 (1990) CrossRefGoogle Scholar
  14. 14.
    Muth, B., Eberhard, P.: Collisions between particles of complex shape. In: Garcia-Rojo, R., Herrmann, H.J., McNamara, S. (eds.) Powders and Grains, pp. 1379–1383 (2005) Google Scholar
  15. 15.
    Muth, B., Eberhard, P.: Investigation of large systems consisting of many spatial polyhedral bodies. In: van Campen, D.H., Lzurko, M.D., van den Oever, W.P.J.M. (eds.) Proceedings of the ENOC-2005, Fifth EUROMECH Nonlinear Dynamics Conference, pp. 1644–1650 (2005) Google Scholar
  16. 16.
    Brendel, L., Dippel, S.: Lasting Contacts in Molecular Dynamics Simulations, p. 313ff. Kluwer Academic, Dordrecht (1998) Google Scholar
  17. 17.
    Herrmann, H., D’Adetta, G.A., Kun, F., Ramm, E.: Two-dimensional dynamic simulation of fracture and fragmentation of solids. Comput. Assis. Mech. Eng. Sci. 6, 385–402 (1999) zbMATHGoogle Scholar
  18. 18.
    Potapov, A.V., Hopkins, M.A., Campbell, C.S.: A two-dimensional dynamic simulation of solid fracture. Int. J. Mod. Phys. C 6(3), 371–398 (1995) CrossRefGoogle Scholar
  19. 19.
    D’Addetta, G.A., Ramm, E.: A microstructure-based simulation environment on the basis of an interface enhanced particle model. Granul. Matter 8, 159–174 (2006) CrossRefGoogle Scholar
  20. 20.
    Liu, K., Gao, L., Tanimura, S.: Application of discrete element method in impact problems. JSME Int. J. Ser. A 47(2), 138–145 (2004) CrossRefGoogle Scholar
  21. 21.
    Courant, R., Friedrichs, K., Lewy, H.: On the partial difference equations of mathematical physics. IBM J. 11, 215–234 (1967) zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  • Florian Fleissner
    • 1
    Email author
  • Timo Gaugele
    • 1
  • Peter Eberhard
    • 1
  1. 1.Institute of Engineering and Computational MechanicsUniversity of StuttgartStuttgartGermany

Personalised recommendations