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


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.


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


Compliance with ethical standards

Conflicts of interest

The authors declare that they have no conflict of interest.


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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

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