Bimodal Character of Stress Transmission in Granular Packings

Radjaï, Farhang; Wolf, Dietrich E.; Jean, Marcel; Moreau, Jean‐Jacques

doi:10.1103/physrevlett.80.61

Cited by 769 publications

(575 citation statements)

References 10 publications

(11 reference statements)

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“…However, even a linear chain of strong particles would not be stable against buckling without the participation of the particles that lie alongside them [23]. Therefore, it is necessary to develop techniques that do not include a minimum threshold force to be able to consider a particle to be part of a network.…”

Section: Introductionmentioning

confidence: 99%

Extraction of force-chain network architecture in granular materials using community detection

et al. 2015

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Force chains form heterogeneous physical structures that can constrain the mechanical stability and acoustic transmission of granular media. However, despite their relevance for predicting bulk properties of materials, there is no agreement on a quantitative description of force chains. Consequently, it is difficult to compare the force-chain structures in different materials or experimental conditions. To address this challenge, we treat granular materials as spatially-embedded networks in which the nodes (particles) are connected by weighted edges that represent contact forces. We use techniques from community detection, which is a type of clustering, to find sets of closely connected particles. By using a geographical null model that is constrained by the particles' contact network, we extract chain-like structures that are reminiscent of force chains. We propose three diagnostics to measure these chain-like structures, and we demonstrate the utility of these diagnostics for identifying and characterizing classes of force-chain network architectures in various materials. To illustrate our methods, we describe how force-chain architecture depends on pressure for two very different types of packings: (1) ones derived from laboratory experiments and (2) ones derived from idealized, numerically-generated frictionless packings. By resolving individual force chains, we quantify statistical properties of force-chain shape and strength, which are potentially crucial diagnostics of bulk properties (including material stability). These methods facilitate quantitative comparisons between different particulate systems, regardless of whether they are measured experimentally or numerically.

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Section: Introductionmentioning

confidence: 99%

Extraction of force-chain network architecture in granular materials using community detection

et al. 2015

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“…Applying the longitudinal force rule, the new shape is easily found to be a catenary, as realized by Hooke [15], and emphasized by Edwards [8]. On the other hand, a general body force can be supported, in three dimensions, if there are several different orientations of force chain, possibly forming a network or "granular skeleton" [7,11,17,18]. A minimal model for this is:…”

Section: Two Types Of Fragilitymentioning

confidence: 99%

“…1 (b)). Applying a similar argument to the intermediate axis leads to the ansatz that all three directors lie along principal stress axes; this is perhaps the simplest model in 3-d. One version of this argument links force chains with the fabric tensor [11], which is then taken coaxial with the stress [18].…”

Section: Fixed Principal Axis (Fpa) Modelmentioning

confidence: 99%

Jamming and stress propagation in particulate matter

Gates

Wittmer

Bouchaud

et al. 1999

Physica A: Statistical Mechanics and its Applications

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We present simple models of particulate materials whose mechanical integrity arises from a jamming process. We argue that such media are generically "fragile", that is, they are unable to support certain types of incremental loading without plastic rearrangement. In such models, fragility is naturally linked to the marginal stability of force chain networks (granular skeletons) within the material. Fragile matter exhibits novel mechanical responses that may be relevant to both jammed colloids and cohesionless assemblies of poured, rigid grains.

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“…It was found that the forces have a nearly decreasing exponential distribution. Numerical simulations by the CD method provided detailed evidence for force chains, the organization of the force network into strong and weak networks, and the exponential distribution of strong forces [13,14]. Moreover, the force probability density functions (pdf's) from simulations showed that the weak forces (below the average force) in a sheared granular system have a nearly uniform or decreasing power law shape in agreement with refined carbon paper experiments [2,5].…”

Section: Introductionmentioning

confidence: 52%

“…The observed shape of force pdf's is unique in two respects: (1) the exponential part reflects the presence of very large forces in the system often appearing in a correlated manner in the form of force chains; (2) the nonvanishing category of weak forces, with a fraction of more than 60% of contact forces below the average force, means that the stability of force chains is ensured by a large number of vanishingly small forces [14,15]. The large number of contacts transmitting very weak forces is a signature of the arching effect.…”

Section: Dry Granular Mediamentioning

confidence: 99%

Force transmission in dry and wet granular media

et al. 2009

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We compare the probability density functions of normal forces in dry and wet granular systems from 3D simulations by molecular dynamics and contact dynamics methods. While the strong forces are characterized by a decreasing exponential distribution, we show that in the range of weak forces the force distribution in a dry granular packing is sensitive to the anisotropy of the packing and the shape of the particles. By means of a model of capillary cohesion, implemented as a force law expressing the capillary force as a function of water volume and the distance between particles, we find that distributions are exponential for both compressive and tensile forces. The particle pressures are shown to form a bi-percolating structure.

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Bimodal Character of Stress Transmission in Granular Packings

Cited by 769 publications

References 10 publications

Extraction of force-chain network architecture in granular materials using community detection

Extraction of force-chain network architecture in granular materials using community detection

Jamming and stress propagation in particulate matter

Force transmission in dry and wet granular media

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