Comptes Rendus
no. 1
Modeling force transmission in granular materials
[Modélisation de la transmission des forces dans les matériaux granulaires]
Farhang Radjai1, 2 
1 LMGC, UMR 5509 CNRS – University of Montpellier, place Eugène-Bataillon, 34095 Montpellier, France
2 MultiScale Material Science for Energy and Environment, UMI 3466 CNRS–MIT, CEE, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge 02139, USA
Comptes Rendus. Physique, Volume 16 (2015) no. 1, pp. 3-9.

La densité de probabilité des forces de contact dans les matériaux granulaires représente une signature remarquable de la microstructure granulaire et, à ce titre, elle a fait l'objet de nombreuses études et d'efforts de modélisation. Nous allons analyser le rôle fondamental des environnementaux locaux des particules pour la transmission des forces et les effets des contraintes stériques par rapport à l'équilibre des forces. Cette analyse permet de montrer qu'une force de contact met en jeu des forces supérieures et inférieures à cette force dans des proportions qui sont contrôlées par les effets stériques. Cette idée simple conduit à un modèle général qui prédit une expression analytique de la densité des forces avec un seul paramètre libre. Ce paramètre coïncide avec le degré d'homogénéité des forces et peut dépendre de l'anisotropie du réseau des contacts ou des formes et distributions des tailles des particules. Cette expression ajuste bien les données numériques et prédit d'une manière générique la décroissance exponentielle des forces fortes, un petit pic en dessous de la force moyenne et une densité de probabilité non nulle pour les forces très petites.

The probability density function of contact forces in granular materials has been extensively studied and modeled as an outstanding signature of granular microstructure. Arguing that particle environments play a fundamental role in force transmission, we analyze the effects of steric constraints with respect to force balance condition and show that each force may be considered as resulting from a balance between lower and larger forces in proportions that mainly depend on steric effects. This idea leads to a general model that predicts an analytical expression of force density with a single free parameter. This expression fits well our simulation data and generically predicts the exponential fall-off of strong forces, a small peak below the mean force and the non-zero probability of vanishingly small forces.

Publié le :
DOI : 10.1016/j.crhy.2015.01.003
Keywords: Granular matter, Force chains, Arching, Contact dynamics, Molecular dynamics
Mot clés : Matière granulaire, Chaînes de force, Effet de voûte, Exclusions stériques, Dynamique des contacts, Dynamique moléculaire
Farhang Radjai 1, 2

1 LMGC, UMR 5509 CNRS – University of Montpellier, place Eugène-Bataillon, 34095 Montpellier, France
2 MultiScale Material Science for Energy and Environment, UMI 3466 CNRS–MIT, CEE, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge 02139, USA 
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Farhang Radjai. Modeling force transmission in granular materials. Comptes Rendus. Physique, Volume 16 (2015) no. 1, pp. 3-9. doi : 10.1016/j.crhy.2015.01.003. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2015.01.003/

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