From force distribution to average coordination number in frictional granular matter

Wang, Ping; Ci, Song; Briscoe, Christopher; Wang, Kun; Makse, Hernán A.

doi:10.1016/j.physa.2010.05.053

Cited by 14 publications

(14 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…5A for 2-D frictional spheres packing. We observe a monotonic decrease with increasing µ from 2D = 4 at µ = 0, a well-known behavior of frictional packings, previously found in numerous studies, both experimentally and numerically [26,35,[37][38][39][40][41][42][43][44]. Notice that the critical contact number we obtain at infinite friction is slightly above the Maxwell argument D + 1; also a typical feature [37,40,42].…”

Section: A Force Distribution For Frictionless Spheres Packingssupporting

confidence: 80%

Cavity method for force transmission in jammed disordered packings of hard particles

Lin

Mari

et al. 2014

Soft Matter

Self Cite

View full text Add to dashboard Cite

The force distribution of jammed disordered packings has always been considered a central object in the physics of granular materials. However, many of its features are poorly understood. In particular, analytic relations to other key macroscopic properties of jammed matter, such as the contact network and its coordination number, are still lacking. Here we develop a mean-field theory for this problem, based on the consideration of the contact network as a random graph where the force transmission becomes a constraint satisfaction problem. We can thus use the cavity method developed in the past few decades within the statistical physics of spin glasses and hard computer science problems. This method allows us to compute the force distribution P(f) for random packings of hard particles of any shape, with or without friction. We find a new signature of jamming in the small force behavior P(f) ∼ f(θ), whose exponent has attracted recent active interest: we find a finite value for P(f = 0), along with θ = 0. Furthermore, we relate the force distribution to a lower bound of the average coordination number z[combining macron](μ) of jammed packings of frictional spheres with coefficient μ. This bridges the gap between the two known isostatic limits z[combining macron]c (μ = 0) = 2D (in dimension D) and z[combining macron]c(μ → ∞) = D + 1 by extending the naive Maxwell's counting argument to frictional spheres. The theoretical framework describes different types of systems, such as non-spherical objects in arbitrary dimensions, providing a common mean-field scenario to investigate force transmission, contact networks and coordination numbers of jammed disordered packings.

show abstract

Section: A Force Distribution For Frictionless Spheres Packingssupporting

confidence: 80%

Cavity method for force transmission in jammed disordered packings of hard particles

Lin

Mari

et al. 2014

Soft Matter

Self Cite

View full text Add to dashboard Cite

show abstract

“…A direct consequence of this is the strong local heterogeneity of the stress distribution within the medium [7]. Since Dantu [8] and De Josselin de Jong [9], we already know that the distribution of the contact forces, resulting from an externally applied load, is very inhomogeneous [10,11], as shown in experiments by photoelastic visualization [9,11,12] and via simulations [10,13]. The contact network determines most salient mechanical properties of a dense granular medium such as its ability to bear load, its nonlinear elastic response, and flow behavior.…”

Section: Introductionmentioning

confidence: 99%

Evolution of grain contacts in a granular sample under creep and stress relaxation

Miksic

Alava

2013

Phys. Rev. E

View full text Add to dashboard Cite

This article deals with the characterization, using an acoustic technique, of the mechanical behavior of a dry dense granular medium under quasistatic loading. Ultrasound propagation through the contact-force network supporting the external load offers a noninvasive probe of the viscoelastic properties of such heterogeneous media. First the response of a glass bead packing is studied in an oedometric configuration during creep and relaxation tests. Quasilogarithmic increases of sound velocities are found in both mechanical tests. A model based on the mechanics of microcontacts between rough grains adequately reproduces our experimental results, especially for the evolution of elastic modulus. Another main experimental finding is that collective grain rearrangements within the packing also play a crucial role at the early stage of creep and relaxation.

show abstract

“…Several computational studies have measured the contact number as a function of µ for packings of frictional disks and spheres using 'fast' compression algorithms that generate amorphous configurations [7][8][9]. In particular, these studies find z = z 0 min = 4 and z ∞ min = 3 in the µ → 0 and ∞ limits, respectively, for bidisperse disks [10,11].…”

mentioning

confidence: 99%

“…The calculations presented in this Letter provide a framework for addressing several important open questions related to frictional packings. For example, why does the crossover from the low-to high-friction limits in the average contact number and packing fraction occur near µ * ≈ 10 −2 for disks [10,11] compared to 10 −1 for spheres [8,10] for fast compression algorithms. In addition, using the methods described above, we will be able to determine how the crossover from low-to highfriction behavior depends on the compression rate and degree of thermalization.…”

mentioning

confidence: 99%

Statistics of Frictional Families

et al. 2014

View full text Add to dashboard Cite

We develop a theoretical description for mechanically stable frictional packings in terms of the difference between the total number of contacts required for isostatic packings of frictionless disks and the number of contacts in frictional packings, m=Nc0 - Nc. The saddle order m represents the number of unconstrained degrees of freedom that a static packing would possess if friction were removed. Using a novel numerical method that allows us to enumerate disk packings for each m, we show that the probability to obtain a packing with saddle order m at a given static friction coefficient μ, Pm(μ), can be expressed as a power series in μ. Using this form for Pm(μ), we quantitatively describe the dependence of the average contact number on the friction coefficient for static disk packings obtained from direct simulations of the Cundall-Strack model for all μ and N.

show abstract

From force distribution to average coordination number in frictional granular matter

Cited by 14 publications

References 30 publications

Cavity method for force transmission in jammed disordered packings of hard particles

Cavity method for force transmission in jammed disordered packings of hard particles

Evolution of grain contacts in a granular sample under creep and stress relaxation

Statistics of Frictional Families

Contact Info

Product

Resources

About