Green's Function Probe of a Static Granular Piling

Reydellet, G.; Clément, Éric

doi:10.1103/physrevlett.86.3308

Cited by 88 publications

(127 citation statements)

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“…The scalar q-model [5] reproduces reasonably well the observed force distribution, but yields diffusive propagation of forces, in conflict with experiments [11,12]. Continuum elastic and elasto-plastic theories [6] predict responses in qualitative agreement with experiments [7][8][9][10], but they provide a description only at the average macroscopic level. More ad-hoc "stressonly" models [2] include structural randomness, but its consequences on the distribution of forces are unclear.…”

mentioning

confidence: 86%

“…On the bottom of the pile, only the middle peak persists. The response of different system sizes exhibits self-similarity.Force transmissions in (static) granular packings have attracted a lot of attention in recent years [1][2][3][4][5][6][7][8][9][10][11][12][13]. Granular packings are assemblies of macroscopic particles that interact only via mechanical repulsion effected through physical contacts.…”

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confidence: 99%

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Response of a hexagonal granular packing under a localized external force: exact results

Ostojic¹,

Panja²

2005

J. Stat. Mech.

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Abstract. -We study the response of a two-dimensional hexagonal packing of rigid, frictionless spherical grains due to a vertically downward point force on a single grain at the top layer. We use a statistical approach, where each configuration of the contact forces is equally likely. We show that this problem is equivalent to a correlated q-model. We find that the response displays two peaks which lie precisely on the downward lattice directions emanating from the point of application of the force. With increasing depth, the magnitude of the peaks decreases, and a central peak develops. On the bottom of the pile, only the middle peak persists. The response of different system sizes exhibits self-similarity.Force transmissions in (static) granular packings have attracted a lot of attention in recent years [1][2][3][4][5][6][7][8][9][10][11][12][13]. Granular packings are assemblies of macroscopic particles that interact only via mechanical repulsion effected through physical contacts. Experimental and numerical studies of these systems have identified two main characteristics. First, large fluctuations are found to occur in the magnitudes of inter-grain forces, implying that the probability distribution of the force magnitudes is rather broad [4]. Secondly, the average propagation of forcesstudied via the response to a single external force -is strongly dependent on the underlying contact geometry [3,[11][12][13].The available theoretical models capture either one or the other of these two aspects. The scalar q-model [5] reproduces reasonably well the observed force distribution, but yields diffusive propagation of forces, in conflict with experiments [11,12]. Continuum elastic and elasto-plastic theories [6] predict responses in qualitative agreement with experiments [7-10], but they provide a description only at the average macroscopic level. More ad-hoc "stressonly" models [2] include structural randomness, but its consequences on the distribution of forces are unclear. In other words, an approach that produces both realistic fluctuations and propagation of forces in granular materials from the same set of fundamental principles is still called for.A simple conjecture, which could provide such a fundamental principle for all problems of granular statics, has been put forward by Edwards years ago [14,15]. The idea is to consider all "jammed" configurations equally probable. A priori, there is no justification for such an c EDP Sciences

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mentioning

confidence: 86%

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confidence: 99%

Response of a hexagonal granular packing under a localized external force: exact results

Ostojic¹,

Panja²

2005

J. Stat. Mech.

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“…Ordered 3D packings exhibit multiple force peaks for shallow systems [24] and less structure for deeper ones. Somewhat larger (in terms of number of particles), disordered 3D systems [20,21] exhibit a single peak in the force distribution measured at the floor, whose width is proportional to the depth of the system.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, the response of granular slabs resting on a horizontal floor to a 'point force' applied at the center of the top of the system has been studied experimentally [19][20][21][22][23][24][25]. In [19,22,23], the intergrain force distribution has been measured in two-dimensional (2D) systems as a function of vertical and horizontal distance from the point of application of the force.…”

Section: Introductionmentioning

confidence: 99%

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Small and large scale granular statics

Goldenberg

Goldhirsch

2004

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Recent experimental results on the static or quasistatic response of granular materials have been interpreted to suggest the inapplicability of the traditional engineering approaches, which are based on elasto-plastic models (which are elliptic in nature). Propagating (hyperbolic) or diffusive (parabolic) models have been proposed to replace the 'old' models. Since several recent experiments were performed on small systems, one should not really be surprised that (continuum) elasticity, a macroscopic theory, is not directly applicable, and should be replaced by a grain-scale ("microscopic") description. Such a description concerns the interparticle forces, while a macroscopic description is given in terms of the stress field. These descriptions are related, but not equivalent, and the distinction is important in interpreting the experimental results. There are indications that at least some large scale properties of granular assemblies can be described by elasticity, although not necessarily its isotropic version. The purely repulsive interparticle forces (in non-cohesive materials) may lead to modifications of the contact network upon the application of external forces, which may strongly affect the anisotropy of the system. This effect is expected to be small (in non-isostatic systems) for small applied forces and for pre-stressed systems (in particular for disordered systems). Otherwise, it may be accounted for using a nonlinear, incrementally elastic model, with stress-history dependent elastic moduli. Although many features of the experiments may be reproduced using models of frictionless particles, results demonstrating the importance of accounting for friction are presented.

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