Transition dynamics and magic-number-like behavior of frictional granular clusters

Tordesillas, Antoinette; Walker, David M.; Froyland, Gary; Zhang, Jie; Behringer, Robert

doi:10.1103/physreve.86.011306

Cited by 49 publications

(60 citation statements)

References 58 publications

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“…Although significant attention has been paid to force transmission in granular systems, little is known about the regulation of internal forces that leads to this dual pattern of heterogeneity, in particular, its dependence on the strength of the contacts as well as the local and global topology of the contact network of the material (e.g., Ref. [11,[21][22][23][24][25][26]). This gap in knowledge has become one of the most pressing issues in the science of granular materials, no doubt pushed to the forefront by the rapid advances in imaging techniques [21,[27][28][29][30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Network flow model of force transmission in unbonded and bonded granular media

et al. 2015

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An established aspect of force transmission in quasistatic deformation of granular media is the existence of a dual network of strongly versus weakly loaded particles. Despite significant interest, the regulation of strong and weak forces through the contact network remains poorly understood. We examine this aspect of force transmission using data on microstructural fabric from: (I) three-dimensional discrete element models of grain agglomerates of bonded subspheres constructed from in situ synchrotron microtomography images of silica sand grains under unconfined compression and (II) two-dimensional assemblies of unbonded photoelastic circular disks submitted to biaxial compression under constant volume. We model force transmission as a network flow and solve the maximum flow-minimum cost (MFMC) problem, the solution to which yields a percolating subnetwork of contacts that transmits the "maximum flow" (i.e., the highest units of force) at "least cost" (i.e., the dissipated energy from such transmission). We find the MFMC describes a two-tier hierarchical architecture. At the local level, it encapsulates intraconnections between particles in individual force chains and in their conjoined 3-cycles, with the most common configuration having at least one force chain contact experiencing frustrated rotation. At the global level, the MFMC encapsulates interconnections between force chains. The MFMC can be used to predict most of the force chain particles without need for any information on contact forces, thereby suggesting the network flow framework may have potential broad utility in the modeling of force transmission in unbonded and bonded granular media.

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Section: Introductionmentioning

confidence: 99%

Network flow model of force transmission in unbonded and bonded granular media

et al. 2015

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“…8(c) and 8(d), which may result in a rich array of dynamics with varying degrees of influence on macroscopic behavior during the different regimes of the loading history. It is possible to distill all of these possible configurational rearrangements to a smaller subset by ranking their prevalence in simulation and experiment using the relative probabilities of particle cluster conformations and conformational transitions established from recent advances in Markov transition dynamics [46]. In combination with this study we can now identify which sets of possible transitions are most prevalent for particles within a given community thus expanding but focusing the approach of [17] to include those cluster transitions and rearrangements essential to capturing the jamming-unjamming-jamming behavior observed in shear bands.…”

Section: Relevance To Continuum Modelingmentioning

confidence: 99%

Taxonomy of granular rheology from grain property networks

Walker

Tordesillas

2012

Phys. Rev. E

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We construct complex networks from symbolic time series of particle properties within a dense quasistatically deforming granular assembly subjected to biaxial compression. The structure of the resulting networks embodies the evolving structural rearrangements in the granular material, in both contact forces and contact topologies. These rearrangements are usefully summarized through standard network statistics as well as building block motifs and community structures. Dense granular media respond to applied compression and shear by a process of self-organization to form two cooperatively evolving structures comprising the major load-bearing columnlike force chains, and the lateral trusslike three-cycle triangle topologies. We construct networks summarizing their individual evolution based on relationships between symbolic time series indicating a particle's chronological force chain and three-cycle membership histories. We test which particle membership histories are similar with respect to each other through the information theory-based measure of Hamming distance. The complex networks summarize the essential structural rearrangements, while the community structures within the networks partition the material into distinct zones of deformation, including interlacing subregions of failure inside the shear band. The taxonomy of granular rheology at the mesoscopic scale distills the inelastic structural rearrangements throughout loading history down to its core elements, and should lay bare an objective and physics-based formalism for thermodynamic internal variables and associated evolution laws.

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“…However, the granular materials are usually polydisperse. Formation of shear bands in polydisperse assemblies was studied in [24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Rotations and pattern formation in granular materials under loading

Pasternak

Dyskin

Esin

et al. 2015

Philosophical Magazine

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Shear band formation and evolution is a predominant mechanism of deformation patterning in granular materials. Independent rotations of separate particles can affect the pattern formation by adding the effect of rotational degrees of freedom to the mechanism of instability. We conducted 2D physical modelling where the particles are represented by smooth steel discs. We use the digital image correlation in order to recover both displacement and independent rotation fields in the model. We performed model calibration and determine the values of mechanical parameters needed for a DEM numerical modelling. Both mono-and polydisperse particle assemblies are used. During the loading, the deformation pattern undergoes stages of shear band formation followed by its dissolution due to recompaction and particle rearrangement with the subsequent formation of multiple shear bands merging into a single one and the final dissolution. We show that while the average (over the assembly) values of the angles of disc rotations are insignificantly different from zero, the particle rotations exhibit clustering at the mesoscale (sizes larger than the particles but smaller than the whole assembly): monodisperse assemblies produce vertical columns of particles rotating the same direction; polydisperse assemblies 2D form clusters of particles with alternating rotations. Thus, particle rotations produce a structure on their own, a structure different form the ones formed by particle displacements and force chains. This can give a rise to moment chains. These emerging mesoscopic structures -not observable at the macroscale -indicate hidden aspects of 'Cosserat behaviour' of the particles.

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Transition dynamics and magic-number-like behavior of frictional granular clusters

Cited by 49 publications

References 58 publications

Network flow model of force transmission in unbonded and bonded granular media

Network flow model of force transmission in unbonded and bonded granular media

Taxonomy of granular rheology from grain property networks

Rotations and pattern formation in granular materials under loading

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