Jamming phase diagram for frictional particles

Ciamarra, Massimo Pica; Pastore, Raffaele; Nicodemi, Mario; Coniglio, Antonio

doi:10.1103/physreve.84.041308

Cited by 95 publications

(121 citation statements)

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“…Both the average coordination number and the largest rigid cluster size jump at the transition, yet there exists a diverging lengthscale [1][2][3][4]. Frictional jamming is more puzzling: The hysteresis observed in the stress-strain rate curves of stresscontrolled flow simulations [5][6][7][8] and experiments [9] has lead to an interpretation as a first-order transition. Yet, signs of second-order criticality appear when treating the fraction of contacts at the Coulomb threshold as an additional parameter [10][11][12].…”

mentioning

confidence: 99%

“…2). Experimental [9] and simulated frictional systems [5][6][7][8] report a hysteresis loop in the stress-strain relations, through a protocol that includes either a strain rate ramp or constant stress driving. As a function of density, φ = 0.8225 − 0.84, we see a transition through jamming, as evidenced by the pressure distribution shifting from a peak at 10 −4 (in units of overlap) to a peak at 10 −2 ( Fig.…”

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Rigid Cluster Decomposition Reveals Criticality in Frictional Jamming

Henkes¹,

Quint²,

Fily³

et al. 2016

Phys. Rev. Lett.

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We study the nature of the frictional jamming transition within the framework of rigidity percolation theory. Slowly sheared frictional packings are decomposed into rigid clusters and floppy regions with a generalization of the pebble game including frictional contacts. We discover a second-order transition controlled by the emergence of a system-spanning rigid cluster accompanied by a critical cluster size distribution. Rigid clusters also correlate with common measures of rigidity. We contrast this result with frictionless jamming, where the rigid cluster size distribution is noncritical.The interplay of constraints, forces, and driving gives rise to the jamming transition in granular media. It is now wellestablished that the frictionless jamming transition has characteristics of both second-and first-order transitions. Both the average coordination number and the largest rigid cluster size jump at the transition, yet there exists a diverging lengthscale [1][2][3][4]. Frictional jamming is more puzzling: The hysteresis observed in the stress-strain rate curves of stresscontrolled flow simulations [5][6][7][8] and experiments [9] has lead to an interpretation as a first-order transition. Yet, signs of second-order criticality appear when treating the fraction of contacts at the Coulomb threshold as an additional parameter [10][11][12].To elucidate the frictional jamming transition from a microscopic viewpoint, we extend concepts and tools from rigidity percolation, i.e., the onset of mechanical rigidity in disordered spring networks [13][14][15][16], to frictional packings. The former is driven by the emergence of a system-spanning rigid cluster that can be mapped out (in 2d) using the pebble game [17], an improved constraint counting method that goes beyond meanfield by identifying redundant constraints. We, for the first time, implement a generalized pebble game for 2d frictional systems and use it to identify rigid clusters in very slowly sheared packings. As we show below, this allows us to identify a second-order rigidity transition and to link stresses and nonaffine motions to the microscopic structure of frictionally jammed packings.Generalized isostaticity: To establish context, we first review the application of Maxwell constraint counting to jamming [18]. For N particles in d dimensions and a mean number of contacts per particle z, interparticle forces yield dzN/2 constraints. Since each particle has 1 2 d(d + 1) translational and rotational degrees of freedom, there are 1 2 (N − 1)d(d + 1) total degrees of freedom (subtracting out global degrees of freedom). When these match the force constraints, we arrive at the isostatic criterion, or dzN/2 = 1 2 (N − 1)d(d + 1). In the limit N → ∞, z iso = d + 1 for frictional granular materials. For frictionless packings, we ignore rotations and obtain the familiar z iso = 2d.Despite being mean field, i.e. neglecting spatial correla- tions, isostaticity works seemingly well to locate the jamming transition in static frictionless systems [1]. For frictional syste...

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confidence: 99%

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confidence: 99%

Rigid Cluster Decomposition Reveals Criticality in Frictional Jamming

Henkes¹,

Quint²,

Fily³

et al. 2016

Phys. Rev. Lett.

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“…At larger strainrates jamming is usually associated with shear thinning [11][12][13][14] or possibly with shear-banding when attractive forces are present [19]. When inter-particle friction is important hysteretic behavior [15,16,18] as well as continuous and discontinuous shear thickening [17,[20][21][22]24] have been observed.…”

Section: Introductionmentioning

confidence: 99%

Rheology near jamming: The influence of lubrication forces

Maiti

Heussinger

2014

Phys. Rev. E

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We study, by computer simulations, the role of different dissipation forces on the rheological properties of highly-dense particle-laden flows. In particular, we are interested in the close-packing limit (jamming) and the question if "universal" observables can be identified that do not depend on the details of the dissipation model. To this end, we define a simplified lubrication force and systematically vary the range hc of this interaction. For fixed hc a cross-over is seen from a Newtonian flow regime at small strain rates to inertia-dominated flow at larger strain rates. The same cross-over is observed as a function of the lubrication range hc. At the same time, but only at high densities close to jamming, single-particle velocities as well as local density distributions are unaffected by changes in the lubrication range -they are candidates for "universal" behavior. At densities away from jamming, this invariance is lost: short-range lubrication forces lead to pronounced particle clustering, while longer-ranged lubrication does not. These findings highlight the importance of "geometric" packing constraints for particle motion -independent of the specific dissipation model. With the free volume vanishing at random-close packing, particle motion is more and more constrained by the ever smaller amount of free space. On the other side, macroscopic rheological observables, as well as higher-order correlation functions retain the variability of the underlying dissipation model.

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“…However, the notion of an a-thermal jamming "point" was recently challenged by report on shear-jamming regime [21,38,149,220] slightly below the traditional (isotropic) jamming point, whereby application of shear strains can jam these states. This suggests the existence of a broad range of φ J , even for a given material [12,32,117,134,148,[151][152][153][154][155]198].…”

Section: Jamming In Granular Materialsmentioning

confidence: 99%

“…Some of these mechanisms include inhomogeneity in systems, such as reflected by force-networks [162,181,185], over-population of weak/soft/slow mechanical oscillation modes [182], diverging correlation lengths and relaxation time-scales [23,113,150,209], but also some universal behavior [32]. Other phenomena occur like shear-strain localization [153,158,200], anisotropic evolution of structure and stress [21,38,55,84,150,158,162,182,185,209], clustering, shear-band formation, size segregation [168], arching [82], density waves, acoustic effects and pattern formation such as sand ripples and dunes [7] and oscillating mass flow rates [137].…”

Section: Need To Study Granular Materialsmentioning

confidence: 99%

Micro-macro and jamming transition of polydisperse granular materials

Kumar¹

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Jamming phase diagram for frictional particles

Cited by 95 publications

References 48 publications

Rigid Cluster Decomposition Reveals Criticality in Frictional Jamming

Rigid Cluster Decomposition Reveals Criticality in Frictional Jamming

Rheology near jamming: The influence of lubrication forces

Micro-macro and jamming transition of polydisperse granular materials

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