KINEROS2/AGWA: Model Use, Calibration, and Validation

Goodrich, David C.; Burns, I. Shea; Unkrich, Carl L.; Semmens, Darius J.; Guertin, D. Phillip; Hernández, Mariano; Yatheendradas, Soni; Kennedy, Jeffrey R.; Levick, Lainie R.

doi:10.13031/2013.42264

Cited by 113 publications

(106 citation statements)

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“…Note that the "linear" regime observed here should not be confused with the linear response and should rather be seen as a saturation of the nonlinearities. For very small strain, (γ ≃ 10 −6 ), such as those probed in numerical studies [3,42], and much smaller than the lowest strain probed here (γ ≃ 10 −3 ), one expects to recover a linear response for all ∆φ > 0 [24]. For strains of experimental relevance, very recent numerical studies have reported a crossover from the linear response at small strains to a shear softening regime, with a exponent β ≃ 0.5 [43,44], compatible with the present results.…”

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confidence: 64%

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Shear Modulus and Dilatancy Softening in Granular Packings above Jamming

2014

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We investigate experimentally the mechanical response to shear of a monolayer of bi-disperse frictional grains across the jamming transition. We inflate an intruder inside the packing and use photo-elasticity and tracking techniques to measure the induced shear strain and stresses at the grain scale. We quantify experimentally the constitutive relations for strain amplitudes as low as 10 −3 and for a range of packing fractions within 2% variation around the jamming transition. At the transition strong nonlinear effects set in : both the shear modulus and the dilatancy shear-soften at small strain until a critical strain is reached where effective linearity is recovered. The scaling of the critical strain and the associated critical stresses on the distance to jamming are extracted. We check that the constitutive laws, together with mechanical equilibrium, correctly predict to the observed stress and strain profiles. These profiles exhibit a spatial crossover between an effective linear regime close to the inflater and the truly nonlinear regime away from it. The crossover length diverges at the jamming transition. Introduction. -Understanding the mechanical properties of dense packings of athermal particles, such as grains, foams and emulsions, remains a conceptual and practical challenge. When decreasing the packing fraction φ, these intrinsically out-of-equilibrium systems lose their rigidity at the so-called jamming transition, φ = φ J , when the confining pressure approaches zero and the particles deformations vanish [1][2][3][4]. In the case of frictionless spheres [2,3], the loss of mechanical stability coincides with the onset of isostaticity : the average number of contacts z decreases to its isostatic value, for which the number of geometrical and mechanical equilibrium constraints exactly match the number of degrees of freedom. Approaching the transition, the material becomes more and more fragile [5], and its linear response, dominated by floppy modes [6], exhibits critical scaling [2][3][4]7].

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confidence: 64%

“…Also, the relevance of the linear response very close to the transition remains a matter of debate [22][23][24]. At finite shear strain amplitude γ, non-linear effects become dominant [9,25,26] and the mechanical response of the system is no longer relevantly described exclusively by ∆z.…”

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confidence: 99%

Shear Modulus and Dilatancy Softening in Granular Packings above Jamming

2014

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“…For small N, these networks become macroscopically floppy upon the removal of a single bond, but this effect disappears as N increases, and we expect that their networks are similar to our SR networks, with K → 0. Another recent conditional cutting protocol allows for the independent tuning of the ratio of bulk and shear moduli [40]. We hope that our work will inspire work to analyze such network topologies, leading to better understanding which other families of networks can be constructed, with distinct properties of the .…”

Section: H Y S I C a L R E V I E W L E T T E R S Week Ending 3 April mentioning

confidence: 94%

Rigidity Loss in Disordered Systems: Three Scenarios

et al. 2015

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We reveal significant qualitative differences in the rigidity transition of three types of disordered network materials: randomly diluted spring networks, jammed sphere packings, and stress-relieved networks that are diluted using a protocol that avoids the appearance of floppy regions. The marginal state of jammed and stress-relieved networks are globally isostatic, while marginal randomly diluted networks show both overconstrained and underconstrained regions. When a single bond is added to or removed from these isostatic systems, jammed networks become globally overconstrained or floppy, whereas the effect on stress-relieved networks is more local and limited. These differences are also reflected in the linear elastic properties and point to the highly effective and unusual role of global self-organization in jammed sphere packings. DOI: 10.1103/PhysRevLett.114.135501 PACS numbers: 62.20.D-, 63.50.Lm, 64.60.ah Disordered elastic networks and sphere packings represent a large class of amorphous athermal materials, ranging from (bio)polymer networks to granular media and foams [1][2][3]. Random networks of springs lose their rigidity when enough springs are cut; this random bond dilution process is known as rigidity percolation (RP) [4][5][6][7][8]. Packings of soft spheres do the same when their confining pressure is lowered towards zero: This is called (un)jamming [9][10][11][12][13]. These rigidity loss scenarios have been studied extensively, in particular, for the simplest cases of networks of harmonic springs [7,8] or soft frictionless harmonic spheres [10][11][12][13]. In that case, the linear elastic properties of packings can be mapped to those of a spring network, where each contact is replaced by the appropriate spring [14][15][16]. Lowering the pressure, the number of bonds in the equivalent network decreases.Given this close correspondence, it is surprising that the nature of the RP and unjamming transitions, and of their respective marginally rigid states, are significantly different. For packings of a large number (N) of soft spheres, extensive studies have shown that (i) the connectivity, i.e., the average number of contacts z per particle, goes to z c ¼ 2D þ Oð1=NÞ at the marginal point, where D is the space dimension [3,[9][10][11][12][13][17][18][19][20], (ii) the system remains homogeneously jammed up to the point of unjamming (with the exception of individual loose particles called rattlers or very rare small particle clusters) [10], and (iii) the shear modulus G vanishes as Δz ≔ z − z c whereas the bulk modulus K remains finite when Δz → 0 [9-14]. In contrast, in the rigidity percolation of generic networks, extensive studies have revealed that for large systems (i) the connectivity z, which gives the average number of springs per node, approaches z c ¼ 3.9612… < 2D for the bond diluted triangular network [7,8], (ii) the largest rigid cluster takes on a heterogeneous, fractal shape, and (iii) both the shear modulus G and bulk modulus K smoothly vanish at the critical point in a way typ...

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“…Note that the "linear" regime observed here should not be confused with the linear response and should rather be seen as a saturation of the nonlinearities. For very small strain ðγ ≃ 10 −6 Þ, such as those probed in numerical studies [3,42], and much smaller than the lowest strain probed here ðγ ≃ 10 −3 Þ, one expects to recover a linear response for all Δϕ > 0 [24]. For strains of experimental relevance, very recent numerical studies have reported a crossover from the linear response at small strains to a shear softening regime, with a exponent β ≃ 0.5 [43,44], compatible with the present results.…”

Section: Prl 113 198001 (2014) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 69%

“…Also, the relevance of the linear response very close to the transition remains a matter of debate [22][23][24]. At finite shear strain amplitude γ, nonlinear effects become dominant [9,25,26] and the mechanical response of the system is no longer relevantly described exclusively by Δz.…”

mentioning

confidence: 99%

Pushing on a Nonlinear Material

Daniels¹

2014

Physics

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We investigate experimentally the mechanical response to shear of a monolayer of bidisperse frictional grains across the jamming transition. We inflate an intruder inside the packing and use photoelasticity and tracking techniques to measure the induced shear strain and stresses at the grain scale. We quantify experimentally the constitutive relations for strain amplitudes as low as 10 −3 and for a range of packing fractions within 2% variation around the jamming transition. At the transition strong nonlinear effects set in: both the shear modulus and the dilatancy shear soften at small strain until a critical strain is reached where effective linearity is recovered. The scaling of the critical strain and the associated critical stresses on the distance to jamming are extracted. We check that the constitutive laws, together with mechanical equilibrium, correctly predict to the observed stress and strain profiles. These profiles exhibit a spatial crossover between an effective linear regime close to the inflater and the truly nonlinear regime away from it. The crossover length diverges at the jamming transition.

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KINEROS2/AGWA: Model Use, Calibration, and Validation

Cited by 113 publications

References 47 publications

Shear Modulus and Dilatancy Softening in Granular Packings above Jamming

Shear Modulus and Dilatancy Softening in Granular Packings above Jamming

Rigidity Loss in Disordered Systems: Three Scenarios

Pushing on a Nonlinear Material

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