How to model orthotropic materials by the discrete element method (DEM): random sphere packing or regular cubic arrangement?

  • Rémi CurtiEmail author
  • Stéphane Girardon
  • Guillaume Pot
  • Philippe Lorong


The discrete element method (DEM) is used for continuous material modeling. The method is based on discretizing mass material into small elements, usually spheres, which are linked to their neighbors through bonds. If DEM has shown today its ability to model isotropic materials, it is not yet the case of anisotropic media. This study highlights the obstacles encountered when modeling orthotropic materials. In the present application, the elements used are spheres and bonds are Euler–Bernoulli beams developed by André et al. (Comput Methods Appl Mech Eng 213–216:113–125, 2012. Two different modeling approaches are considered: cubic regular arrangements, where discrete elements are placed on a regular Cartesian lattice, and random sphere-packed arrangements, where elements are randomly packed. As the second approach is by definition favoring the domain’s isotropy, a new method to affect orientation-dependent Young’s modulus of bonds is proposed to create orthotropy. Domains created by both approaches are loaded in compression in-axis (along the material orthotropic directions) and off-axis to determine their effective Young’s modulus according to the loading direction. Results are compared to the Hankinson model which is especially used to represent high orthotropic behavior such as encountered in wood or synthetic fiber materials. For this class of materials, it is shown that, contrary to cubic regular arrangements, the random sphere-packed arrangements exhibit difficulties to reach highly orthotropic behavior (in-axis tests). Conversely, this last arrangements display results closer to continuous orthotropic material during off-axis tests.


Discrete element method Orthotropic behavior Elements packing Elasticity 



The authors would like to acknowledge GranOO staff members, especially Jean-Luc Charles and Damien André for the training they provided.


These works were conducted thanks to the support of the region Bourgogne Franche-Comté and were funded by the ANR-10-EQPX-16 XYLOFOREST-XYLOMAT and the French MESRI.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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© OWZ 2018

Authors and Affiliations

  1. 1.LaBoMaP, EA 3633Arts et MétiersClunyFrance
  2. 2.PIMM, UMR CNRS 8006Arts et MétiersParisFrance

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