A micro-mechanical investigation of bifurcation in granular materials

By François Nicot, Félix Darve. 2007

94 citations recorded by the source corpus.

In this paper, the notion of loss of sustainability of a mechanical state in a granular assembly is investigated. The vanishing of the second-order work, defined on the macroscopic scale from tensorial variables, is shown to play a fundamental role in detecting the occurrence of this type of bifurcation. Then a link is established between the macroscopic second-order work on the specimen scale and a discrete local expression that introduces microscopic variables defined on each contact scale. This relation opens up a micro-mechanical interpretation allowing one to examine which micro-structural features are responsible for the vanishing of the macroscopic second-order work. Finally, it is established that both geometrical and material micro-structural origins may combine to induce the occurrence of bifurcation on a specimen scale.

Subfields: Civil and Structural Engineering, Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/ed10b03e9cc6ce65f2f0a46dd6946b6f8f4157dc

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Citations in the corpus

Bifurcation modeling in geomaterials: From the second‐order work criterion to spectral analyses (2009, unknown): “Figure 3 shows the 3D bifurcation domain obtained with Darve’s two constitutive models [25] and dense sand.”
Bifurcation in granular materials: An attempt for a unified framework (2009, unknown): “Greater detail can be found in (Nicot and Darve, 2007; Nicot et al., 2007).”
Failure in rate-independent granular materials as a bifurcation toward a dynamic regime (2012, unknown): “…the energy conservation law in continuum mechanics (Mandel, 1966) expressed with a Lagrangian formalism and differentiated with respect to time (Nicot and Darve, 2007; Nicot et al., 2007), it is possible to obtain the kinetic energy as a function of the integrals of the discrete second-order…”
Controllability, uniqueness and existence of the incremental response: A mathematical criterion for elastoplastic constitutive laws (2011, background): “This criterion can be shown to be a powerful tool to envisage the onset of diffuse instabilities and can be associated with the loss of existence and uniqueness of the incremental response (Darve et al., 2004; Nicot and Darve, 2007).”
Diffuse failure in geomaterials: Experiments, theory and modelling (2011, unknown): “This approach corresponds to the loss of sustainability [27].”