Topology of the force network in the jamming transition of an isotropically compressed granular packing

Arévalo, Roberto; Zuriguel, Iker; Maza, Diego

doi:10.1103/physreve.81.041302

Cited by 88 publications

(93 citation statements)

References 25 publications

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“…Additionally, they reported that the lengths of these chains satisfy an approximately exponential distribution. Arevalo et al [18] examined polygonal structures that underly a forcechain network, which they determined by selecting all inter-particle forces above some threshold. In their numerical simulations, they observed that triangular structures dominate the network near a critical packing fraction.…”

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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“…The general trend is that the force increases with the number of sides of the polygon. The fact that small polygons in the network allocate smaller forces than big polygons was already observed for the compressed system [25,26].…”

Section: Contact Forcesmentioning

confidence: 85%

“…In Fig. 5 a comparison is made between an isotropically compressed system that is jammed [25] (left column) and the tapped samples studied in this work (right column). From the data for the topological distance and the giant component, a different qualitative behavior is revealed for both types of networks.…”

Section: Force Network Relation To Compressed Systemsmentioning

confidence: 99%

“…At this point, let us note that any static granular system can be considered in terms of nodes (the grains) and edges (the contacts between grains). This approach has been recently applied to address a wide variety of granular phenomena such as porosity [21], force distribution [22], rheology [23], signal propagation [24] and jamming transition [25,26].…”

Section: Introductionmentioning

confidence: 99%

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Tapped granular packings described as complex networks

Arévalo

Pugnaloni

Maza

et al. 2013

Philosophical Magazine

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We characterize the structure of simulated two-dimensional granular packings using concepts from complex networks theory. The packings are generated by a simulated tapping protocol, which allows us to obtain states in mechanical equilibrium in a wide range of densities. We show that our characterization method is able to discriminate non-equivalent states that have the same density. We do this by examining differences in the topological structure of the contact network of the packings. In particular, we find that the polygons of the network are specially sensitive probes for the contact structure. Additionally, we compare the network properties obtained in two different scenarios: the tapped and a compressed system.

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“…The analysis of the topology of the force networks has been shown very fruitful [18,19] in a static granular packing. The process of jamming in the light of the topology of force networks was studied in [20,21]. Again, the role of loops in the network was proven to be relevant at the transition point, with third-order loops behaving as an order parameter.…”

Section: Introductionmentioning

confidence: 99%

Topological analysis of tapped granular media using persistent homology

et al. 2014

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We use the first Betti number of a complex to analyze the morphological structure of granular samples in mechanical equilibrium. We investigate two-dimensional granular packings after a tapping process by means of both simulations and experiments. States with equal packing fraction obtained with different tapping intensities are distinguished after the introduction of a filtration parameter which determines the particles (nodes in the network) that are joined by an edge. This is accomplished by just using the position of the particles obtained experimentally and no other information about the possible contacts, or magnitude of forces.

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Topology of the force network in the jamming transition of an isotropically compressed granular packing

Cited by 88 publications

References 25 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

Tapped granular packings described as complex networks

Topological analysis of tapped granular media using persistent homology

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