Key features of Granular plasticity

Antony, S. Joseph; Hoyle, W.; Ding, Youdong; Radjaï, Farhang; Troadec, H.; Roux, Stéphane

doi:10.1039/9781847550996-00157

Cited by 35 publications

(40 citation statements)

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“…18) and K (2) to discuss stability properties of packings. The corrections to the degree of force indeterminacy due to free mechanism motions, as expressed by relations (19) or (20), will also be used.…”

Section: Rigidity and Stiffness Matricesmentioning

confidence: 99%

“…Discrete numerical simulation [18] proved a valuable tool to investigate the internal state of packings, as it is able to reproduce mechanical behaviors, and to identify relevant variables other than Φ, such as coordination number and fabric (or distribution of contact orientations) [19,20,21,22,23]. In the case of sphere packings, simulations have been used to characterize the geometry of gravity-deposited systems [24,25] or oedometrically compressed ones [26], to investigate the quasistatic, hysteretic stress-strain dependence in solid packings [27,28], and their pressure-dependent elastic moduli in a com-pression experiment [29,30].…”

Section: Introduction a Context And Motivationsmentioning

confidence: 99%

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Internal states of model isotropic granular packings. I. Assembling process, geometry, and contact networks

2007

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This is the first paper of a series of three, in which we report on numerical simulation studies of geometric and mechanical properties of static assemblies of spherical beads under an isotropic pressure. The influence of various assembling processes on packing microstructures is investigated. It is accurately checked that frictionless systems assemble in the unique random close packing (RCP) state in the low pressure limit if the compression process is fast enough, higher solid fractions corresponding to more ordered configurations with traces of crystallization. Specific properties directly related to isostaticity of the force-carrying structure in the rigid limit are discussed. With frictional grains, different preparation procedures result in quite different inner structures that cannot be classified by the sole density. If partly or completely lubricated they will assemble like frictionless ones, approaching the RCP solid fraction ΦRCP ≃ 0.639 with a high coordination number: z * ≃ 6 on the force-carrying backbone. If compressed with a realistic coefficient of friction µ = 0.3 packings stabilize in a loose state with Φ ≃ 0.593 and z * ≃ 4.5. And, more surprisingly, an idealized "vibration" procedure, which maintains an agitated, collisional régime up to high densities results in equally small values of z * while Φ is close to the maximum value ΦRCP. Low coordination packings have a large proportion (>10%) of rattlers -grains carrying no force -the effect of which should be accounted for on studying position correlations, and also contain a small proportion of localized "floppy modes" associated with divalent grains. Low pressure states of frictional packings retain a finite level of force indeterminacy even when assembled with the slowest compression rates simulated, except in the case when the friction coefficient tends to infinity. Different microstructures are characterized in terms of near neighbor correlations on various scales, and some comparisons with available laboratory data are reported, although values of contact coordination numbers apparently remain experimentally inaccessible.

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Section: Rigidity and Stiffness Matricesmentioning

confidence: 99%

Section: Introduction a Context And Motivationsmentioning

confidence: 99%

Internal states of model isotropic granular packings. I. Assembling process, geometry, and contact networks

2007

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“…IV B 2. In this respect, assemblies of frictionless grains differ from systems with intergranular friction, in which one given contact network may support stresses within a finite range in the thermodynamic limit, for arbitrary large stiffness levels κ [61] (whence vertical parts in stress versus strain plots, as obtained in simulations with models of rigid grains [51,62,63]). This property of frictional grain assemblies excludes the possibility of a one-to-one relation between stresses and fabric.…”

Section: Constitutive Relationsmentioning

confidence: 99%

Solidlike behavior and anisotropy in rigid frictionless bead assemblies

Peyneau

Roux

2008

Phys. Rev. E

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We investigate the structure and mechanical behavior of assemblies of frictionless, nearly rigid equal-sized beads, in the quasistatic limit, by numerical simulation. Three different loading paths are explored: triaxial compression, triaxial extension and simple shear. Generalizing recent result, we show that the material, despite rather strong finite sample size effects, is able to sustain a finite deviator stress in the macroscopic limit, along all three paths, without dilatancy. The shape of the yield surface in principal stress space differs somewhat from the Mohr-Coulomb prediction, and is more adequately described by the Lade-Duncan or Matsuoka-Nakai criteria. We study geometric characteristics and force networks under varying stress levels within the supported range. Although the scalar state variables stay equal to the values observed in systems under isotropic pressure, the material, once subjected to a deviator stress, possesses some fabric and force distribution anisotropies. Each kind of anisotropy can be described, in good approximation, by a single parameter. Within the supported stress range, along each one of the three investigated stress paths, among those three quantities: deviator stress to mean stress ratio, fabric anisotropy parameter, force anisotropy parameter, any one determines the values of the two others. The pair correlation function also exhibits short range anisotropy, up to a distance between bead surfaces of the order of 10% of the diameter. The tensor of elastic moduli is shown to possess a nearly singular, uniaxial structure related to stress anisotropy. Possible stress-strain relations in monotonic loading paths are also discussed.

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“…The shear strength of dry granular materials is generally attributed to the buildup of an anisotropic structure during shear due to friction between the particles and as a result of steric effects depending on particle shape [37,38,39]. Several methods have been used to quantify the fabric (structural) anisotropy of granular materials [13,40,41].…”

Section: B Fabric Anisotropymentioning

confidence: 99%

Force transmission in a packing of pentagonal particles

et al. 2007

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We perform a detailed analysis of the contact force network in a dense confined packing of pentagonal particles simulated by means of the contact dynamics method. The effect of particle shape is evidenced by comparing the data from pentagon packing and from a packing with identical characteristics except for the circular shape of the particles. A counterintuitive finding of this work is that, under steady shearing, the pentagon packing develops a lower structural anisotropy than the disk packing. We show that this weakness is compensated by a higher force anisotropy, leading to enhanced shear strength of the pentagon packing. We revisit "strong" and "weak" force networks in the pentagon packing, but our simulation data provide also evidence for a large class of "very weak" forces carried mainly by vertex-to-edge contacts. The strong force chains are mostly composed of edge-to-edge contacts with a marked zig-zag aspect and a decreasing exponential probability distribution as in a disk packing.

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Key features of Granular plasticity

Cited by 35 publications

References 0 publications

Internal states of model isotropic granular packings. I. Assembling process, geometry, and contact networks

Internal states of model isotropic granular packings. I. Assembling process, geometry, and contact networks

Solidlike behavior and anisotropy in rigid frictionless bead assemblies

Force transmission in a packing of pentagonal particles

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