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Chapitre D'ouvrage Année : 2008

Bifurcation in granular materials: a multiscale approach

Bifurcation dans les matériaux granulaires : une approche multi-échelles

L. Sibille
François Nicot
O. Cazacu
  • Fonction : Coordinateur scientifique

Résumé

This chapterdeals with two basic features of granular materials. First, a certain type of failure, described as a loss of sustainability, is investigated. For nonassociated materials such as granular assemblies a broad domain exists, strictly within the plastic limit, where different failure modes can coexist. The notion of loss of sustainability was recently shown to be a proper mode of bifurcation. Given a mechanical rate-independent system in equilibrium under prescribed control parameters, the mechanical state is reputed unsustainable if and only if the system can reach spontaneously another mechanical state. It was established in a very general manner that such bifurcation modes, characterized by a development of kinetic energy, are detected by the vanishing of the second-order work. Afterward, by specializing the investigation to granular materials, both macroscopic (on the specimen scale) and microscopic (on contact scale) second-order works are shown to be related through a fundamental multiscale relation. This relation, at the basis of our microstructural investigation, indicates that a material cause (related to the plastic behavior of some contacts) together with a geometrical cause (related to the deletion of contacts) are responsible for the vanishing of the macroscopic second-order work. Then, the existence of a regular or a singular flow rule for the plastic strains is queried from a multiscale approach. By considering our micro-directional model, it is shown that a regular flow rule exists only in two-dimensional conditions, and disappears as soon as more general three-dimensional loading conditions are considered. The microstructural origin of this basic feature is discussed, and the strong influence of the loading history on the nature of the plastic flow rule is clearly pointed out.
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Dates et versions

hal-02591261 , version 1 (15-05-2020)

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Citer

F. Prunier, F. Darve, L. Sibille, François Nicot, O. Cazacu. Bifurcation in granular materials: a multiscale approach. Multiscale modeling of heterogeneous materials, Hermès Science Publications, pp.14, 2008, 978-1-8482-1047-9. ⟨hal-02591261⟩
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