Three-Dimensional Multiscale Bifurcation Analysis of Granular Media

Prunier, Florent; Nicot, François; Darve, Félix; Laouafa, Farid; Lignon, Sylvain

doi:10.1061/(asce)em.1943-7889.0000003

Cited by 29 publications

(13 citation statements)

References 26 publications

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“…It is noted that the incrementally non‐linear model can be seen as incrementally piecewise linear with an infinite number of tensorial zones. Thus, with some numerical developments, an approximation of the bifurcation limit has been calculated 51. Finally, Figure 18 shows some instability cones as calculated by both models for stress–strain states located beyond the bifurcation limit.…”

Section: Macro‐ and Micro‐modelling Of Soil Failurementioning

confidence: 98%

Diffuse failure in geomaterials: Experiments, theory and modelling

Daouadji

Darve

Gali

et al. 2010

Num Anal Meth Geomechanics

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International audienceThis paper presents a synthesis of the works performed by various teams from France, Italy and Canada around the question of second-order work criterion. Because of the non-associative character of geomaterials plastic strains, it is now recognized that a whole bifurcation domain exists in the stress space with various possible modes of failure. In a first part these failure modes are observed in lab experimental tests and in discrete element modelling. Then a theoretical study of second-order work allows to establish a link with the kinetic energy, giving a basis to explain the transition from a prefailure (quasi)static regime to a postfailure dynamic regime. Eventually the main features of geomaterials failure are obtained by applying second-order work criterion to five different constitutive rate-independent models-three being phenomenological and two micromechanical. As a whole this paper tries to gather together all the elements for a proper understanding and use of second-order work criterion in geomechanics

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Section: Macro‐ and Micro‐modelling Of Soil Failurementioning

confidence: 98%

Diffuse failure in geomaterials: Experiments, theory and modelling

Daouadji

Darve

Gali

et al. 2010

Num Anal Meth Geomechanics

Self Cite

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“…In the classical elasto‐plastic theory, the material flow rule on the plastic limit surface refers to the eigenvector associated with the vanishing of an eigenvalue of the constitutive matrix since its determinant becomes zero. As such, the material flow rule at plastic limit conditions properly characterizes the ultimate failure mechanism 21, 23. In Section 5, the eigenvector related to the first vanishing eigenvalue of the symmetric part of the stiffness matrix is determined and plotted as a displacement field over the finite element mesh.…”

Section: Introductionmentioning

confidence: 99%

Effect of Hydrogen on O₂ Adsorption and Dissociation on a TiO₂ Anatase (001) Surface

Liu¹,

Wang²,

Pan³

et al. 2013

ChemPhysChem

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The effect of hydrogen on the adsorption and dissociation of the oxygen molecule on a TiO2 anatase (001) surface is studied by first-principles calculations coupled with the nudged elastic band (NEB) method. Hydrogen adatoms on the surface can increase the absolute value of the adsorption energy of the oxygen molecule. A single H adatom on an anatase (001) surface can lower dramatically the dissociation barrier of the oxygen molecule. The adsorption energy of an O2 molecule is high enough to break the O=O bond. The system energy is lowered after dissociation. If two H adatoms are together on the surface, an oxygen molecule can be also strongly adsorbed, and the adsorption energy is high enough to break the O=O bond. However, the system energy increases after dissociation. Because dissociation of the oxygen molecule on a hydrogenated anatase (001) surface is more efficient, and the oxygen adatoms on the anatase surface can be used to oxidize other adsorbed toxic small gas molecules, hydrogenated anatase is a promising catalyst candidate.

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“…For the directions on the cone boundary, the second‐order work is nil. These directions therefore belong to the isotropic cone of K s and can be characterized by the ratios 24: where λ 2 and λ 3 satisfy the equation of the isotropic cone f (λ 2 , λ 3 )=0.…”

Section: An Attempt At Generalizationmentioning

confidence: 99%

Bifurcation and generalized mixed loading conditions in geomaterials

Nicot¹,

Challamel

Lerbet

et al. 2010

Num Anal Meth Geomechanics

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International audienceThe concept of bifurcation has been widely discussed, based, for example, on homogeneous tests in soil mechanics. Essentially two-dimensional (axisymmetric) conditions have been considered. This paper aims at deriving a bifurcation criterion in geomechanics, independently of the problem's dimension. This criterion is related to the vanishing of the determinant of the symmetric part of the material's (or the discrete system's) constitutive (or stiffness) matrix. The derivation is essentially based on the notion of loading parameters (controlling the loading). Basically, a bifurcation occurs when the existence of a unique solution to the quasistatic problem, involving a given set of loading parameters, is lost. Interestingly, the criterion is shown to be independent of the choice of loading parameters. As a possible extension, the context of structure mechanics is considered, and the close connection between both soil and structure analysis is discussed

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Three-Dimensional Multiscale Bifurcation Analysis of Granular Media

Cited by 29 publications

References 26 publications

Diffuse failure in geomaterials: Experiments, theory and modelling

Diffuse failure in geomaterials: Experiments, theory and modelling

Effect of Hydrogen on O₂ Adsorption and Dissociation on a TiO₂ Anatase (001) Surface

Bifurcation and generalized mixed loading conditions in geomaterials

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Three-Dimensional Multiscale Bifurcation Analysis of Granular Media

Cited by 29 publications

References 26 publications

Diffuse failure in geomaterials: Experiments, theory and modelling

Diffuse failure in geomaterials: Experiments, theory and modelling

Effect of Hydrogen on O2 Adsorption and Dissociation on a TiO2 Anatase (001) Surface

Bifurcation and generalized mixed loading conditions in geomaterials

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Product

Resources

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Effect of Hydrogen on O₂ Adsorption and Dissociation on a TiO₂ Anatase (001) Surface