Bifurcations in granular media: macro- and micro-mechanics approaches

Félix Darve; Luc Sibille; Ali Daouadji; François Nicot

doi:10.1016/j.crme.2007.08.005

Soils, granular media, civil engineering

Bifurcations in granular media: macro- and micro-mechanics approaches

Félix Darve ¹ ; Luc Sibille ¹; Ali Daouadji ²; François Nicot ³

¹ Laboratoire sols solides structures, UJF–INPG–CNRS, 38041 Grenoble, France
² Laboratoire de physique et mécanique des matériaux, UPV-M, CNRS, Metz, France
³ Cemagref, Unité de Recherche Erosion torrentielle neige et avalanches, Grenoble, France

Comptes Rendus. Mécanique, Joseph Boussinesq, a Scientist of bygone days and present times, Volume 335 (2007) no. 9-10, pp. 496-515.

Abstract
Résumé

Various failure modes related to different kinds of bifurcations occur in nonassociated elastoplastic materials such as geomaterials. After presenting experimental evidence, we study this question by means of phenomenological constitutive relations and direct numerical simulations based on the discrete element method. The second-order work criterion related to diffuse failure modes is particularly considered within the framework of continuum and discrete mechanics. The equations of the bifurcation domain boundary and unstable stress direction cones are established. Diffuse failure is simulated numerically by perturbing bifurcation states.

Différents modes de rupture reliés à différents types de bifurcations apparaissent dans des matériaux élasto-plastiques non-associés tels que les géomatériaux. Après avoir présenté quelques résultats expérimentaux typiques, cette question est abordée au moyen de relations constitutives phénoménologiques et de simulations numériques directes basées sur la méthode des éléments discrets. Le critère du travail du second ordre lié aux modes de rupture diffuse est particulièrement étudié dans le cadre de la mécanique des milieux continus et des milieux discrets. Les équations des limites du domaine de bifurcation et des cônes de directions de contrainte instables sont établies. La rupture diffuse est simulée numériquement par des perturbations des états de bifurcation.

Received: 2006-10-02
Accepted: 2007-01-11
Published online: 2007-09-01

DOI: 10.1016/j.crme.2007.08.005

Keywords: Rupture, Granular media, Bifurcation, Micromechanics, Second order work, Instability, Discrete element method
Mots-clés : Rupture, Milieux granulaires, Bifurcation, Micromécanique, Travail du second ordre, Instabilité, Méthode des éléments discrets

Author's affiliations:

Félix Darve ¹; Luc Sibille ¹; Ali Daouadji ²; François Nicot ³

¹ Laboratoire sols solides structures, UJF–INPG–CNRS, 38041 Grenoble, France
² Laboratoire de physique et mécanique des matériaux, UPV-M, CNRS, Metz, France
³ Cemagref, Unité de Recherche Erosion torrentielle neige et avalanches, Grenoble, France

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     title = {Bifurcations in granular media: macro- and micro-mechanics approaches},
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Félix Darve; Luc Sibille; Ali Daouadji; François Nicot. Bifurcations in granular media: macro- and micro-mechanics approaches. Comptes Rendus. Mécanique, Joseph Boussinesq, a Scientist of bygone days and present times, Volume 335 (2007) no. 9-10, pp. 496-515. doi : 10.1016/j.crme.2007.08.005. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.08.005/

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