The stress transmission universality classes of periodic granular arrays

Ball, Robin C.; Grinev, D. V.

doi:10.1016/s0378-4371(00)00580-x

Cited by 16 publications

(4 citation statements)

References 17 publications

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“…We consider here only the elastic part of the pressure since it dominates over the kinetic and dissipative parts at the low strain rates we consider. The elastic part of the stress tensor is given by [36],…”

Section: Modelmentioning

confidence: 99%

Compression- and shear-driven jamming of U-shaped particles in two dimensions

Marschall

Teitel

2015

Granular Matter

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We carry out numerical simulations of soft, U-shaped, frictionless particles in d = 2 dimensions in order to explore the effects of complex particle shape on the jamming transition. We consider both cases of uniform compression-driven and shear-driven jamming as packing fraction φ and compression or shear rate is varied. Upon slow compression, jamming is found to occur when the isostatic condition is satisfied. Under driven steady state shearing, jamming occurs at a higher packing fraction φJ than observed in compression. A growing relaxation time and translational correlation length is found as φ increases towards φJ . We consider the orientational ordering and rotation of particles induced by the shear flow. Both nematic and tetratic ordering are found, but these decrease as φ increases to φJ . At the jamming transition, the nematic ordering further decreases, while the tetratic ordering increases, but the orientational correlation lengths remain small throughout. The average angular velocity of the particles is found to increase as φ increases, saturating to a plateau just below φJ , but then increasing again as φ increases above φJ .[The final publication is available at Springer via http://dx.

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Section: Modelmentioning

confidence: 99%

Compression- and shear-driven jamming of U-shaped particles in two dimensions

Marschall

Teitel

2015

Granular Matter

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“…Particles are considered to be perfectly hard, perfectly rough and each particle α has a coordination number z α = d+1 [7]. Theory which confirms this observation has been proposed for periodic arrays of particles with perfect and zero friction [8]. What is the statistical distribution of contact forces in a packing of particles?…”

Section: The Statically Determinate Problemmentioning

confidence: 91%

The toy-model of the Boltzmann type equation for the contact force distribution in disordered packings of particles

Grinev

2022

Preprint

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The packing of hard-core particles in contact with their neighbors is considered as the simplest model of disordered particulate media. We formulate the statically determinate problem which allows analytical investigation of the statistical distribution of contact force magnitude. The simplest Boltzmann type equation for the probability of contact force distribution is formulated and studied. An experimentally observed exponential distribution is derived.

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“… 20 Generically, z c = d ( d + 1) and d + 1 for d -dimensional systems of frictionless and frictional non-spherical elements, respectively. 21 Analysis of stress transmission in these materials explains the ubiquity of non-uniform stress states exhibited by particulate media. 22 – 25 A first-principles continuum stress theory for two-dimensional isostatic granular media has been developed, based on a parameterisation of the inter-element forces into ‘loop forces’, where loops are the elementary voids, or cells, enclosed by individual elements.…”

Section: Introductionmentioning

confidence: 99%