Numerical study of the force network ensemble

Eerd, van Art Rianne; Tighe, BP; Vlugt, Tjh Thijs

doi:10.1080/08927020903015361

Cited by 8 publications

(23 citation statements)

References 48 publications

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“…Because the resulting curves are smoother, we plot the cumulative distribution C z (p) := p 0 dp P (p |z). Figure 4 plots log C z (p) versus (z − d) log p for a frictionless system; the linearity of the curves for small p confirms equation (25).…”

Section: Microscopic Quantitiesmentioning

confidence: 54%

Stress fluctuations in granular force networks

Tighe¹,

Vlugt²

2011

J. Stat. Mech.

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The heterogeneous force networks in static granular media are distinguished from other network structures in that they must satisfy constraints of mechanical equilibrium on every vertex/grain. Here we study the statistics of ensembles of hyperstatic frictionless force networks, which are composed of more forces than can be determined uniquely from force balance. Hyperstatic force networks possess degrees of freedom that rearrange one balanced network into another. We calculate the equation of state and demonstrate that the number of rearrangements governs the macroscopic statistical properties of the ensemble, in particular the macroscopic fluctuations of stress, which scale with distance to the isostatic point. We then show that a maximum entropy postulate allows one to quantitatively capture many features of the microscopic statistics. All predictions are tested against highly accurate Monte Carlo numerical simulations employing umbrella sampling.

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Section: Microscopic Quantitiesmentioning

confidence: 54%

Stress fluctuations in granular force networks

Tighe¹,

Vlugt²

2011

J. Stat. Mech.

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“…The force network among particles in a static or dynamic state can be analyzed in terms of the force probability distribution, which can give us some hints regarding the general behavior of granular systems [28,47]. Many studies have been devoted to determining the shape of the probability density distribution of the normal contact forces between particles P (f ) and its variation under different conditions [48][49][50][51] in addition to the long-range correlations in the forces [28]. Efforts have also been made to investigate the signature change in P (f ) when systems go through jamming transitions [51][52][53].…”

Section: Force Statisticsmentioning

confidence: 99%

Regime transitions of granular flow in a shear cell: A micromechanical study

et al. 2013

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The regime transitions of granular flow in a model shear cell are investigated numerically with a stress-controlled boundary condition. The correlations between the elastically and kinetically scaled stresses and the packing fraction are examined, and two packing fractions (0.58 and 0.50) are identified for the quasistatic to intermediate and intermediate to inertial regime transitions. The profiles and structures of contact networks and force chains among particles in different flow regimes are investigated. It is shown that the connectivity (coordination number) among particles and the homogeneity in the shear flow increase as the system goes through the inertial, intermediate, and then quasistatic regimes, and there is only little variation in the internal structure after the system has entered the quasistatic regime. Short-range force chains start to appear in the inertial regime, which also depend on the magnitude of the shear rate. The percolation of system-spanning force chains through the whole system is a characteristic of the onset of the quasistatic regime, which happens at a packing fraction that is close to the glass transition, i.e., about random loose packing (0.58) but far below the isotropic quasistatic (athermal) jamming packing fraction of random close packing (0.64). The tails of the probability density distribution P(f) of the scaled normal contact forces for the flows in different regimes are quantified by a stretched exponential P(f)=exp(-cf^{n}) with a remarkable finding that n ∼ 1.1 may be a potential demarcation point separating the quasistatic regime and the inertial or intermediate regimes.

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“…All previous simulations of the force network ensemble have been of a microcanonical variety [12,13,15,19,20,25,26]. The microcanonical frictionless triangular lattice has been well-studied in the force network ensemble, and local stress statistics have been determined extremely accurately by employing umbrella sampling [15,25].…”

Section: B Microcanonical Ensemblementioning

confidence: 99%

Force balance in canonical ensembles of static granular packings

Tighe¹,

Vlugt²

2010

J. Stat. Mech.

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We investigate the role of local force balance in the transition from a microcanonical ensemble of static granular packings, characterized by an invariant stress, to a canonical ensemble. Packings in two dimensions admit a reciprocal tiling, and a collective effect of force balance is that the area of this tiling is also invariant in a microcanonical ensemble. We present analytical relations between stress, tiling area and tiling area fluctuations, and show that a canonical ensemble can be characterized by an intensive thermodynamic parameter conjugate to one or the other. We test the equivalence of different ensembles through the first canonical simulations of the force network ensemble, a model system.

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Numerical study of the force network ensemble

Cited by 8 publications

References 48 publications

Stress fluctuations in granular force networks

Stress fluctuations in granular force networks

Regime transitions of granular flow in a shear cell: A micromechanical study

Force balance in canonical ensembles of static granular packings

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