Analysis of local behaviour in granular materials

Ngoc-Son Nguyen; Hélène Magoariec; Bernard Cambou

doi:10.1016/j.crme.2014.01.004

Analysis of local behaviour in granular materials
[Analyse du comportement local des matériaux à une échelle mésoscopique]

Ngoc-Son Nguyen ¹ ; Hélène Magoariec ¹ ; Bernard Cambou ¹

¹ LTDS – UMR 5513, École centrale de Lyon, 36, avenue Guy-de-Collongue, 69134 Écully cedex, France

Comptes Rendus. Mécanique, Volume 342 (2014) no. 3, pp. 156-173.

Résumé
Abstract

Une échelle locale, appelée l'échelle mésoscopique, a été introduite récemment dans l'approche multi-échelles pour les matériaux granulaires 2D. Cette échelle est définie au niveau de sous domaines constitués de boucles fermées limitées par des particules en contacts. La contrainte et la déformation ont été définies à cette échelle, et leur relation avec la structure locale a été étudiée. L'objectif de cet article est d'analyser le comportement local des milieux granulaires à cette échelle, c'est-à-dire la relation entre contrainte, déformation et structure. Des analyses sont réalisées sur la simulation numérique, par la méthode des éléments discrets, d'un essai de compression biaxiale d'un échantillon de matériau granulaire 2D. L'échantillon considéré est relativement dense et la sollicitation est suffisamment lente pour que l'échantillon puisse être considéré dans un régime quasi statique. Le nombre de particules dans chaque sous-domaine varie de 3 à 12. Les analyses réalisées montrent que l'évolution de l'état interne de l'échantillon correspond à une évolution de la quantitié des sous-domaines orientés dans des directions différentes. De plus, le comportement des sous-domaines est fortement piloté par leur orientation, plutôt que par leur densité. Les sous-domaines orientés dans la direction de compression se comportent comme un matériau dense, tandis que ceux orientés dans la direction d'extension se comportent comme un matériau lâche.

A local scale, called the meso-scale, has recently been introduced to the multi-scale approach for 2D granular materials. This local scale is defined at the level of meso-domains enclosed by particles in contact. Stress and strain have been defined at this local scale, and their relation with the local structure has been studied. The purpose of this paper is to analyse the behaviour of granular materials at the meso-scale, i.e. the stress–strain–structure relationship at this scale. Analyses are performed on a 2D numerical granular sample subjected to a biaxial compression test and simulated with the Discrete Element Method (DEM). The sample is quite dense and it is loaded at a relatively low strain rate so that the state of the sample can be considered as being quasi-static. The size of sub-domains in the sample varies largely from 3 to 12 particles. It is shown that the evolution of the internal state of the sample corresponds, at the meso-scale, to a clear evolution of the quantity of meso-domains oriented in different directions. In addition, the behaviour of meso-domains is highly governed by their orientation rather than their density, especially for the strongly elongated meso-domains: the meso-domains oriented in the compression (resp. extension) direction behave like a dense (resp. loose) granular material.

Publié le : 2014-03-01

DOI : 10.1016/j.crme.2014.01.004

Keywords: Granular material, Multi-scale approach, Discrete element method, Meso-scale, Local behaviour
Mot clés : Matériaux granulaires, Approche multi-échelles, Méthode des éléments discrets, Échelle mésoscopique, Comportement local

Affiliations des auteurs :

Ngoc-Son Nguyen ¹ ; Hélène Magoariec ¹ ; Bernard Cambou ¹

¹ LTDS – UMR 5513, École centrale de Lyon, 36, avenue Guy-de-Collongue, 69134 Écully cedex, France

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     title = {Analysis of local behaviour in granular materials},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {156--173},
     publisher = {Elsevier},
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     number = {3},
     year = {2014},
     doi = {10.1016/j.crme.2014.01.004},
     language = {en},
}

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Ngoc-Son Nguyen; Hélène Magoariec; Bernard Cambou. Analysis of local behaviour in granular materials. Comptes Rendus. Mécanique, Volume 342 (2014) no. 3, pp. 156-173. doi : 10.1016/j.crme.2014.01.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2014.01.004/

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