Jamming for a 2D granular material

This paper focuses on the nature of jamming, as seen in two-dimensional frictional granular systems consisting of photoelastic particles. The photoelastic technique is unique at this time, in its capability to provide detailed particle-scale information on forces and kinematic quantities such as particle displacements and rotations. These experiments first explore isotropic stress states near point J through measurements of the mean contact number per particle, Z, and the pressure, P as functions of the packing fraction, . In this case, the experiments show some but not all aspects of jamming, as expected on the basis of simulations and models that typically assume conservative, hence frictionless, forces between particles. Specifically, there is a rapid growth in Z, at a reasonable which we identify with as c. It is possible to fit Z and P, to power law expressions in - c above c, and to obtain exponents that are in agreement with simulations and models. However, the experiments differ from theory on several points, as typified by the rounding that is observed in Z and P near c. The application of shear to these same 2D granular systems leads to phenomena that are qualitatively different from the standard picture of jamming. In particular, there is a range of packing fractions below c, where the application of shear strain at constant leads to jammed stress-anisotropic states, i.e. they have a non-zero shear stress, τ. The application of shear strain to an initially isotropically compressed (hence jammed) state, does not lead to an unjammed state per se. Rather, shear strain at constant first leads to an increase of both τ and P. Additional strain leads to a succession of jammed states interspersed with relatively localized failures of the force network leading to other stress-anisotropic states that are jammed at typically somewhat lower stress. The locus of jammed states requires a state space that involves not only and τ, but also P. P, τ, and Z are all hysteretic functions of shear strain for fixed . However, we find that both P and τ are roughly linear functions of Z for strains large enough to jam the system. This implies that these shear-jammed states satisfy a Coulomb like-relation, τ = μP. © 2010 The Royal Society of Chemistry.

Stress correlations in granular materials: An entropic formulation

We study the response of dry granular materials to external stress using experiment, simulation, and theory. We derive a Ginzburg-Landau functional that enforces mechanical stability and positivity of contact forces. In this framework, the elastic moduli depend only on the applied stress. A combination of this feature and the positivity constraint leads to stress correlations whose shape and magnitude are extremely sensitive to the nature of the applied stress. The predictions from the theory describe the stress correlations for both simulations and experiments semiquantitatively. © 2009 The American Physical Society.

Spanning the scales of granular materials through microscopic force imaging.

If you walk on sand, it supports your weight. How do the disordered forces between particles in sand organize, to keep you from sinking? This simple question is surprisingly difficult to answer experimentally: measuring forces in three dimensions, between deeply buried grains, is challenging. Here we describe experiments in which we have succeeded in measuring forces inside a granular packing subject to controlled deformations. We connect the measured micro-scale forces to the macro-scale packing force response with an averaging, mean field calculation. This calculation explains how the combination of packing structure and contact deformations produce the observed nontrivial mechanical response of the packing, revealing a surprising microscopic particle deformation enhancement mechanism.

Steady flow dynamics during granular impact.

We study experimentally and computationally the dynamics of granular flow during impacts where intruders strike a collection of disks from above. In the regime where granular force dynamics are much more rapid than the intruder motion, we find that the particle flow near the intruder is proportional to the instantaneous intruder speed; it is essentially constant when normalized by that speed. The granular flow is nearly divergence free and remains in balance with the intruder, despite the latter's rapid deceleration. Simulations indicate that this observation is insensitive to grain properties, which can be explained by the separation of time scales between intergrain force dynamics and intruder dynamics. Assuming there is a comparable separation of time scales, we expect that our results are applicable to a broad class of dynamic or transient granular flows. Our results suggest that descriptions of static-in-time granular flows might be extended or modified to describe these dynamic flows. Additionally, we find that accurate grain-grain interactions are not necessary to correctly capture the granular flow in this regime.

Stress Relaxation for Granular Materials near Jamming under Cyclic Compression.

We have explored isotropically jammed states of semi-2D granular materials through cyclic compression. In each compression cycle, systems of either identical ellipses or bidisperse disks transition between jammed and unjammed states. We determine the evolution of the average pressure P and structure through consecutive jammed states. We observe a transition point ϕ_{m} above which P persists over many cycles; below ϕ_{m}, P relaxes slowly. The relaxation time scale associated with P increases with packing fraction, while the relaxation time scale for collective particle motion remains constant. The collective motion of the ellipses is hindered compared to disks because of the rotational constraints on elliptical particles.

Evaporation-induced evolution of the capillary force between two grains

© 2014, Springer-Verlag Berlin Heidelberg.The evolution of capillary forces during evaporation and the corresponding changes in the geometrical characteristics of liquid (water) bridges between two glass spheres with constant separation are examined experimentally. For comparison, the liquid bridges were also tested for mechanical extension (at constant volume). The obtained results reveal substantial differences between the evolution of capillary force due to evaporation and the evolution due to extension of the liquid bridges. During both evaporation and extension, the change of interparticle capillary forces consists in a force decrease to zero either gradually or via rupture of the bridge. At small separations between the grains (short & wide bridges) during evaporation and at large volumes during extension, there is a slight initial increase of force. During evaporation, the capillary force decreases slowly at the beginning of the process and quickly at the end of the process; during extension, the capillary force decreases quickly at the beginning and slowly at the end of the process. Rupture during evaporation of the bridges occurs most abruptly for bridges with wider separations (tall and thin), sometimes occurring after only 25% of the water volume was evaporated. The evolution (pinning/depinning) of two geometrical characteristics of the bridge, the diameter of the three-phase contact line and the “apparent” contact angle at the solid/liquid/gas interface, seem to control the capillary force evolution. The findings are of relevance to the mechanics of unsaturated granular media in the final phase of drying.

Orientation, Flow, and Clogging in a Two-Dimensional Hopper: Ellipses vs. Disks

Two-dimensional (2D) hopper flow of disks has been extensively studied. Here, we investigate hopper flow of ellipses with aspect ratio $\alpha = 2$, and we contrast that behavior to the flow of disks. We use a quasi-2D hopper containing photoelastic particles to obtain stress/force information. We simultaneously measure the particle motion and stress. We determine several properties, including discharge rates, jamming probabilities, and the number of particles in clogging arches. For both particle types, the size of the opening, $D$, relative to the size of particles, $\ell$ is an important dimensionless measure. The orientation of the ellipses plays an important role in flow rheology and clogging. The alignment of contacting ellipses enhances the probability of forming stable arches. This study offers insight for applications involving the flow of granular materials consisting of ellipsoidal shapes, and possibly other non-spherical shapes.

Universal Quake Statistics: From Compressed Nanocrystals to Earthquakes.

Slowly-compressed single crystals, bulk metallic glasses (BMGs), rocks, granular materials, and the earth all deform via intermittent slips or "quakes". We find that although these systems span 12 decades in length scale, they all show the same scaling behavior for their slip size distributions and other statistical properties. Remarkably, the size distributions follow the same power law multiplied with the same exponential cutoff. The cutoff grows with applied force for materials spanning length scales from nanometers to kilometers. The tuneability of the cutoff with stress reflects "tuned critical" behavior, rather than self-organized criticality (SOC), which would imply stress-independence. A simple mean field model for avalanches of slipping weak spots explains the agreement across scales. It predicts the observed slip-size distributions and the observed stress-dependent cutoff function. The results enable extrapolations from one scale to another, and from one force to another, across different materials and structures, from nanocrystals to earthquakes.