Advertisement

Computational Particle Mechanics

, Volume 5, Issue 1, pp 35–47 | Cite as

A contact detection algorithm for deformable tetrahedral geometries based on a novel approach for general simplices used in the discrete element method

  • Sven Stühler
  • Florian Fleissner
  • Peter Eberhard
Article

Abstract

We present an extended particle model for the discrete element method that on the one hand is tetrahedral in shape and on the other hand is capable to describe deformations. The deformations of the tetrahedral particles require a framework to interrelate the particle strains and resulting stresses. Hence, adaptations from the finite element method were used. This allows to link the two methods and to adequately describe material and simulation parameters separately in each scope. Due to the complexity arising of the non-spherical tetrahedral geometry, all possible contact combinations of vertices, edges, and surfaces must be considered by the used contact detection algorithm. The deformations of the particles make the contact evaluation even more challenging. Therefore, a robust contact detection algorithm based on an optimization approach that exploits temporal coherence is presented. This algorithm is suitable for general \(\mathbb {R}^{\text {n}}\) simplices. An evaluation of the robustness of this algorithm is performed using a numerical example. In order to create complex geometries, bonds between these deformable particles are introduced. This coupling via the tetrahedra faces allows the simulation bonding of deformable bodies composed of several particles. Numerical examples are presented and validated with results that are obtained by the same simulation setup modeled with the finite element method. The intention of using these bonds is to be able to model fracture and material failure. Therefore, the bonds between the particles are not lasting and feature a release mechanism based on a predefined criterion.

Keywords

Discrete element method Tetrahedral particles Deformable particles Contact detection Non-spherical particles Bonded particles 

Notes

Compliance with ethical standards

Conflicts of interest

The authors declare that they have no conflict of interest.

References

  1. 1.
    Abaqus (2014) ABAQUS Documentation. Dassault Systèmes, USAGoogle Scholar
  2. 2.
    Alonso-Marroquín F, Wang Y (2009) An efficient algorithm for granular dynamics simulations with complex-shaped objects. Granul Matter 11(5):317–329CrossRefzbMATHGoogle Scholar
  3. 3.
    Bagherzadeh KhA, Mirghasemi A, Mohammadi S (2011) Numerical simulation of particle breakage of angular particles using combined DEM and FEM. Powder Technol 205(1–3):15–29CrossRefGoogle Scholar
  4. 4.
    Bathe KJ (1996) Finite element procedures. Prentice Hall, New JerseyzbMATHGoogle Scholar
  5. 5.
    Boon CW, Houlsby GT, Utili S (2012) A new algorithm for contact detection between convex polygonal and polyhedral particles in the discrete element method. Comput Geotech 44:73–82CrossRefGoogle Scholar
  6. 6.
    Boon CW, Houlsby GT, Utili S (2013) A new contact detection algorithm for three-dimensional non-spherical particles. Powder Technol 248:94–102CrossRefGoogle Scholar
  7. 7.
    Cleary PW (2010) DEM prediction of industrial and geophysical particle flows. Particuology 8(2):106–118CrossRefGoogle Scholar
  8. 8.
    Cundall PA (1988) 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(3):107–116CrossRefGoogle Scholar
  9. 9.
    Ergenzinger C, Seifried R, Eberhard P (2011) A discrete element model to describe failure of strong rock in uniaxial compression. Granul Matter 13(4):341–364CrossRefGoogle Scholar
  10. 10.
    Favier JF, Abbaspour-Fard M, Kremmer M, Raji AO (1999) Shape representation of axi-symmetrical, non-spherical particles in discrete element simulation using multi-element model particles. Eng Comput 16(4):467–480CrossRefzbMATHGoogle Scholar
  11. 11.
    Fleissner F (2010) Parallel object oriented simulation with Lagrangian particle methods. Doctoral thesis, Schriften aus dem Institut für Technische und Numerische Mechanik der Universität Stuttgart, vol 16. Shaker Verlag, AachenGoogle Scholar
  12. 12.
    Gethin DT, Lewis RW, Ransing RS (2003) A discrete deformable element approach for the compaction of powder systems. Model Simul Mater Sci Eng 11:101–114CrossRefGoogle Scholar
  13. 13.
    Höhner D, Wirtz S, Kruggel-Emden H, Scherer V (2011) Comparison of the multi-sphere and polyhedral approach to simulate non-spherical particles within the discrete element method: Influence on temporal force evolution for multiple contacts. Powder Technol 208(3):643–656CrossRefGoogle Scholar
  14. 14.
    Houlsby GT (2009) Potential particles: a method for modelling non-circular particles in DEM. Comput Geotech 36(6):953–959CrossRefGoogle Scholar
  15. 15.
    Jensen RP, Bosscher PJ, Plesha ME, Edil TB (1999) DEM simulation of granular media-structure interface: effects of surface roughness and particle shape. Int J Numer Anal Methods in Geomech 23(6):531–547CrossRefzbMATHGoogle Scholar
  16. 16.
    Lu M, McDowell GR (2007) The importance of modelling ballast particle shape in the discrete element method. Granul Matter 9(1):69–80Google Scholar
  17. 17.
    Markauskas D, Kačianauskas R, Džiugys A, Navakas R (2010) Investigation of adequacy of multi-sphere approximation of elliptical particles for DEM simulations. Granul Matter 12(1):107–123CrossRefzbMATHGoogle Scholar
  18. 18.
    Mas Ivars D, Potyondy DO, Pierce M, Cundall PA (2008) The smooth-joint contact model. In: Joint Conference 8th. World Congress on computational mechanics (WCCM8) and 5th. European Congress on computational methods in applied sciences and engineering (ECCOMAS 2008)Google Scholar
  19. 19.
    Munjiza A (2004) The combined finite-discrete element method. Wiley, ChichesterCrossRefzbMATHGoogle Scholar
  20. 20.
    Nezami EG, Hashash YMA, Zhao D, Ghaboussi J (2004) A fast contact detection algorithm for 3-d discrete element method. Comput Geotech 31(7):575–587CrossRefGoogle Scholar
  21. 21.
    Nezami EG, Hashash YMA, Zhao D, Ghaboussi J (2006) Shortest link method for contact detection in discrete element method. Int J Numer Anal Methods Geomech 30:783–801CrossRefzbMATHGoogle Scholar
  22. 22.
    Obermayr M, Dressler K, Vrettos C, Eberhard P (2013) A bonded-particle model for cemented sand. Comput Geotech 49:299–313CrossRefGoogle Scholar
  23. 23.
    Pournin L, Liebling TM (2005) A generalization of distinct element method to tridimensional particles with complex shapes. In: García-Rojo R, Herrmann H, McNamara S (eds) Powders and grains 2005. A.A. Balkema Publishers, Rotterdam, pp 1375–1378Google Scholar
  24. 24.
    Rémond S, Gallias JL, Mizrahi A (2008) Simulation of the packing of granular mixtures of non-convex particles and voids characterization. Granul Matter 10(3):157–170CrossRefzbMATHGoogle Scholar
  25. 25.
    Shabana AA (2013) Dynamics of multibody systems, 4th edn. Cambridge University Press, New YorkCrossRefzbMATHGoogle Scholar
  26. 26.
    Stühler S, Fleissner F, Seifried R, Eberhard P (2013) A discrete element approach for wave propagation in thin rods. PAMM 13(1):31–32CrossRefGoogle Scholar
  27. 27.
    Tonon F (2004) Explicit exact formulas for the 3-d tetrahedron inertia tensor in terms of its vertex coordinates. J Math Stat 1(1):8–11MathSciNetzbMATHGoogle Scholar
  28. 28.
    Wellmann C, Lillie C, Wriggers P (2008) A contact detection algorithm for superellipsoids based on the common-normal concept. Eng Comput 25(5):432–442CrossRefzbMATHGoogle Scholar
  29. 29.
    Williams JR, Pentland AP (1992) Superquadrics and modal dynamics for discrete elements in interactive design. Eng Comput 9(2):115–127CrossRefGoogle Scholar
  30. 30.
    Zienkiewicz OC, Taylor RL, Fox DD (2013) The finite element method for solid and structural mechanics, 7th edn. Butterworth-Heinemann, OxfordzbMATHGoogle Scholar

Copyright information

© OWZ 2016

Authors and Affiliations

  • Sven Stühler
    • 1
  • Florian Fleissner
    • 1
  • Peter Eberhard
    • 1
  1. 1.Institute of Engineering and Computational MechanicsUniversity of StuttgartStuttgartGermany

Personalised recommendations