Recent simulations have predicted that near jamming for collections of spherical particles, there will be a discontinuous increase in the mean contact number Z at a critical volume fraction c . Above c , Z and the pressure P are predicted to increase as power laws in ÿ c . In experiments using photoelastic disks we corroborate a rapid increase in Z at c and power-law behavior above c for Z and P. Specifically we find a power-law increase as a function of ÿ c for Z ÿ Z c with an exponent around 0.5, and for P with an exponent around 1.1. These exponents are in good agreement with simulations. We also find reasonable agreement with a recent mean-field theory for frictionless particles. DOI: 10.1103/PhysRevLett.98.058001 PACS numbers: 45.70.ÿn, 64.60.ÿi, 83.80.Fg A solid, in contrast to a fluid, is characterized by mechanical stability that implies a finite resistance to shear and isotropic deformation. While such stability can originate from long-range crystalline order, there is no general agreement on how mechanical stability arises for disordered systems, such as molecular and colloidal glasses, gels, foams, and granular packings [1]. For a granular system, in particular, a key question concerns how stability occurs when the packing fraction increases from below to above a critical value c for which there are just enough contacts per particle Z to satisfy the conditions of mechanical stability. In recent simulations on frictionless systems it was found that Z exhibits a discontinuity at c followed by a power-law increase for > c [2 -5]. The pressure is also predicted to increase as a power law above c .A number of recent theoretical studies address jamming, and we note work that may be relevant to granular systems. Silbert, O'Hern et al. have shown in computer simulations of frictionless particles [2 -4] that (a) for increasing , Z increases discontinuously at the transition point from zero to a finite number, Z c , corresponding to the isostatic value (needed for mechanical stability), (b) for both two-and three-dimensional systems, Z is expected to continue increasing as ÿ c above c , where 0:5, (c) the pressure P is expected to grow above c as ÿ c , where f ÿ 1 in the simulations, and f is the exponent for the interparticle potential. More recent simulations by Donev et al. for hard spheres in three dimensions found a slightly higher value for , 0:6, in maximally random jammed packings [5]. It is interesting to note that a model for foam exhibits quite similar behavior for Z [6]. Henkes and Chakraborty [7] constructed a mean-field theory of the jamming transition in 2D based on entropy arguments. These authors predict power-law scaling for P and Z in terms of a variable , which is the pressure derivative of the entropy. By eliminating , one obtains an algebraic relation between P and Z ÿ Z c from these predictions, which we present below in the context of our data.While the simulations agree among themselves at least qualitatively, so far, these novel features have not been identified in experiments. Hen...

The contacts between cohesive, frictional particles with sizes in the range 0.1-10 µm are the subject of this study. Discrete element model (DEM) simulations rely on realistic contact force models-however, too much details make both implementation and interpretation prohibitively difficult. A rather simple, objective contact model is presented, involving the physical properties of elastic-plastic repulsion, dissipation, adhesion, friction as well as rollingand torsion-resistance. This contact model allows to model bulk properties like friction, cohesion and yield-surfaces. Very loose packings and even fractal agglomerates have been reported in earlier work. The same model also allows for pressure-sintering and tensile strength tests as presented in this study.

In the Brazil nut problem (BNP), hard spheres with larger diameters rise to the top. There are various explanations (percolation, reorganization, convection), but a broad understanding or control of this effect is by no means achieved. A theory is presented for the crossover from BNP to the reverse Brazil nut problem (RBNP) based on a competition between the percolation effect and the condensation of hard spheres. The crossover condition is determined, and theoretical predictions are compared to Molecular Dynamics simulations in two and three dimensions. Rosato et al.[1] demonstrated via Molecular Dynamics (MD) simulations that hard spheres with large diameters segregate to the top when subjected to vibrations or shaking. In the literature, this phenomenon is called the Brazil nut problem (BNP) [2]. Besides a broad experience in the applied and engineering sciences [2,3], there exist more recent approaches to understanding this effect through model experiments [4][5][6][7]. The BNP has been attributed to the following phenomena: the percolation effect, where the smaller ones pass through the holes created by the larger ones [2], geometrical reorganization, through which small particles readily fill small openings below the large particles [3,5] and global convection which brings the large particles up but does not allow for re-entry in the downstream [4]. Since most experiments were carried out with a single large grain in a sea of smaller ones [4][5][6], it is not quite clear which of these observed mechanisms apply for the segregation of binary mixtures. For example, while the convection is responsible for the rise of the single large grain, MD simulations [8] and hydrodynamic models [9] clearly indicate that convection cells are absent in the bulk, but confined near the wall when the width of the container is much larger than 1

We experimentally determine ensemble-averaged responses of granular packings to point forces, and we compare these results to recent models for force propagation in a granular material. We used 2D granular arrays consisting of photoelastic particles: either disks or pentagons, thus spanning the range from ordered to disordered packings. A key finding is that spatial ordering of the particles is a key factor in the force response. Ordered packings have a propagative component that does not occur in disordered packings.PACS numbers: 46.10.+z, 47.20.-k Granular systems have captured much recent interest due to their rich phenomenology, and important applications [1]. Even in the absence of strong spatial disorder of the grains, static arrays show inhomogeneous spatial stress profiles called stress (or force) chains [2]. Forces are carried primarily by a tenuous network that is a fraction of the total number of grains.A fundamental unresolved issue concerns how granular materials respond to applied forces, and there are several substantially different models. A broad group of conventional continuum models (e.g. elasto-plastic, . . .) posit an elastic response for material up to the point of plastic deformation [3]. The stresses in portions of such a system below plastic yield have an elastic response and satisfy an elliptic partial differential equation (PDE); those parts that are plastically deforming satisfy a hyperbolic PDE. Several fundamentally different models have recently been proposed. The q-model of Coppersmith et al.[4] assumes a regular lattice of grains, and randomness is introduced at the contacts. This model successfully predicts the distribution of forces in the large force limit, as verified by several static and quasistatic experiments and models [4][5][6]. In the continuum limit, this model reduces to the diffusion equation, since the forces effectively propagate by a random walk. Another model (the Oriented Stress Linearity-OSL-model) of Bouchaud et al. [7], has a constitutive law, justified through a microscopic model, of the form σ zz = µσ xz + ησ xx (in 2D) in order to close the stress balance conditions ∂σ ij /∂x j = ρg i . This leads to wave-like hyperbolic PDEs describing the spatial variation of stresses. In later work, these authors considered weak randomness in the lattice The range of predictions among the models is perhaps best appreciated by noting that the different pictures predict qualitatively different PDEs for the variation of stresses within a sample: e.g. for elasto-plastic models an elliptic or hyperbolic PDE; for the q-model, a parabolic PDE; and for the OSL model without randomness, a hyperbolic PDE. The impact of equation type extends to the boundary conditions needed to determine a solution: e.g. hyperbolic equations require less boundary information than an elliptic equation.Here, we explore these issues through experiments on a 2D granular system consisting of photoelastic (i.e birefringent under strain) polymer particles [6] that are either disks or pentagons. By vi...

Dry, frictional, steady-state granular flows down an inclined, rough surface are studied with discrete particle simulations. From this exemplary flow situation, macroscopic fields, consistent with the conservation laws of continuum theory, are obtained from microscopic data by time-averaging and spatial smoothing (coarse-graining). Two distinct coarse-graining length scale ranges are identified, where the fields are almost independent of the smoothing length w. The smaller, sub-particle length scale, w d, resolves layers in the flow near the base boundary that cause oscillations in the macroscopic fields. The larger, particle length scale, w ≈ d, leads to smooth stress and density fields, but the kinetic stress becomes scale-dependent; however, this scale-dependence can be quantified and removed. The macroscopic fields involve density, velocity, granular temperature, as well as strain-rate, stress, and fabric (structure) tensors. Due to the plane strain flow, each tensor can be expressed in an inherently anisotropic form with only four objective, coordinate frame invariant variables. For example, the stress is decomposed as: (i) the isotropic pressure, (ii) the "anisotropy" of the deviatoric stress, i.e., the ratio of deviatoric stress (norm) and pressure, (iii) the anisotropic stress distribution between the principal directions, and (iv) the orientation of its eigensystem. The strain rate tensor sets the reference system, and each objective stress (and fabric) variable can then be related, via discrete particle simulations, to the inertial number, I. This represents the plane strain special case of a general, local, and objective constitutive model. The resulting model is compared to existing theories and clearly displays small, but significant deviations from more simplified theories in all variables -on both the different length scales. C 2013 AIP Publishing LLC. [http://dx