Granular packings display the remarkable phenomenon of dilatancy [1], wherein their volume increases upon shear deformation. Conventional wisdom and previous results suggest that dilatancy, as also the related phenomenon of shear-induced jamming, requires frictional interactions [2, 3]. Here, we investigate the occurrence of dilatancy and shear jamming in frictionless packings. We show that the existence of isotropic jamming densities ϕj above the minimal density, the J-point density ϕJ [4, 5], leads both to the emergence of shear-induced jamming and dilatancy. Packings at ϕJ form a significant threshold state into which systems evolve in the limit of vanishing pressure under constant pressure shear, irrespective of the initial jamming density ϕj. While packings for different ϕj display equivalent scaling properties under compression [6], they exhibit striking differences in rheological behaviour under shear. The yield stress under constant volume shear increases discontinuously with density when ϕj > ϕJ, contrary to the continuous behavior in generic packings that jam at ϕJ [4, 7].
We investigate experimentally the mechanical response of a monolayer of bi-disperse frictional grains to an inhomogeneous shear perturbation 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 0.001 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 dilat…
The dilatancy angle describes the propensity of a granular medium to dilate under an applied shear. Using a simple spin model (the ``tetris'' model) which accounts for geometrical ``frustration'' effects, we study such a dilatancy angle as a function of density. An exact mapping can be drawn with a directed percolation process which proves that there exists a critical density $ρ_c$ above which the system expands and below which it contracts under shear. When applied to packings constructed by a random deposition under gravity, the dilatancy angle is shown to be strongly anisotropic, and it con…
We examine the jamming transition in a two-dimensional granular polymer system using compressional simulations. The jamming density ϕ_c decreases with increasing length of the granular chain due to the formation of loop structures, in excellent agreement with recent experiments. The jamming density can be further reduced in mixtures of granular chains and granular rings, also as observed in experiment. We show that the nature of the jamming in granular polymer systems has pronounced differences from the jamming behavior observed for polydisperse two-dimensional disk systems at Point J. This re…
We investigate the rheology of sheared granular materials near the jamming transition point. We numerically determine the values of the critical fraction and the exponents for the jamming transition using a finite size scaling and the nonlinear minimization method known as the Levenberg-Marquardt algorithm. The exponents are close to our previous theoretical prediction, but there is a small discrepancy, if the critical point is independently determined.
Critical behaviors of sheared dense and frictionless granular materials in the vicinity of the jamming transition are numerically investigated. From the extensive molecular dynamics simulation, we verify the validity of the scaling theory near the jamming transition proposed by Otsuki and Hayakawa (Prog. Theor. Phys., 121, 647 (2009)). We also clarify the critical behaviors of the shear viscosity and the pair correlation function based on both a phenomenology and the simulation.
The critical rheology of sheared frictional granular materials near jamming transition is numer- ically investigated. It is confirmed that there exist a true critical density which characterizes the onset of the yield stress, and two fictitious critical densities which characterize the scaling laws of rheological properties. We find the existence of a hysteresis loop between two of the critical densities for each friction coefficient. It is noteworthy that the critical scaling law for frictionless jamming transition seems to be still valid even for frictional jamming despite using fictitious c…
We introduce a stochastic microscopic model to investigate the jamming and reorganization of grains induced by an object moving through a granular medium. The model reproduces the experimentally observed periodic sawtooth fluctuations in the jamming force and predicts the period and the power spectrum in terms of the controllable physical parameters. It also predicts that the avalanche sizes, defined as the number of displaced grains during a single advance of the object, follow a power-law, $P(s)\sim s^{-τ}$, where the exponent is independent of the physical parameters.
We study the rheology of cornstarch suspensions, a dense system of non-Brownian particles that exhibits shear thickening, i.e. a viscosity that increases with increasing shear rate. Using MRI velocimetry we show that the suspension has a yield stress. From classical rheology it follows that as a function of the applied stress the suspension is first solid (yield stress), then liquid and then solid again when it shear thickens. The onset shear rate for thickening is found to depend on the measurement geometry: the smaller the gap of the shear cell, the lower the shear rate at which thickening o…
We investigate the jamming transition in packings of emulsions and granular materials via molecular dynamics simulations. The emulsion model is composed of frictionless droplets interacting via nonlinear normal forces obtained using experimental data acquired by confocal microscopy of compressed emulsions systems. Granular materials are modeled by Hertz-Mindlin deformable spherical grains with Coulomb friction. In both cases, we find power-law scaling for the vanishing of pressure and excess number of contacts as the system approaches the jamming transition from high volume fractions. We find …
We study the origin of the scaling behavior in frictionless granular media above the jamming transition by analyzing their linear response. The response to local forcing is non-self-averaging and fluctuates over a length scale that diverges at the jamming transition. The response to global forcing becomes increasingly non-affine near the jamming transition. This is due to the proximity of floppy modes, the influence of which we characterize by the local linear response. We show that the local response also governs the anomalous scaling of elastic constants and contact number.
We study the rheological properties of a granular suspension subject to constant shear stress by constant volume molecular dynamics simulations. We derive the system `flow diagram' in the volume fraction/stress plane $(ϕ,F)$: at low $ϕ$ the flow is disordered, with the viscosity obeying a Bagnold-like scaling only at small $F$ and diverging as the jamming point is approached; if the shear stress is strong enough, at higher $ϕ$ an ordered flow regime is found, the order/disorder transition being marked by a sharp drop of the viscosity. A broad jamming region is also observed where, in analogy w…
The dynamics of the jamming transition in a three-dimensional granular system under vertical vibration is studied using diffusing-wave spectroscopy. When the maximum acceleration of the external vibration is large, the granular system behaves like a fluid, with the dynamic correlation function G(t) relaxing rapidly. As the acceleration of vibration approaches the gravitational acceleration g, the relaxation of G(t) slows down dramatically, and eventually stops. Thus the system undergoes a phase transition and behaves like a solid. Near the transition point, we find that the structural relaxati…
We present experiments on several distinct effective temperatures in a granular system at a sequence of increasing packing densities and at a sequence of decreasing driving rates. This includes single-grain measurements based on the mechanical energies of both the grains and an embedded oscillator, as well as a collective measurement based on the Einstein relation between diffusivity and mobility, which all probe different time scales. Remarkably, all effective temperatures agree. Furthermore, mobility data along the two trajectories collapse when plotted vs effective temperature and exhibit a…
We provide a comprehensive picture of the jamming phase diagram by connecting the athermal, granular ensemble of jammed states and the equilibrium fluid through the inherent structure paradigm for a system hard discs confined to a narrow channel. The J-line is shown to be divided into packings that are thermodynamically accessible from the equilibrium fluid and inaccessible packings. The J-point is found to occur at the transition between these two sets of packings and is located at the maximum the inherent structure distribution. A general thermodynamic argument suggests that the density of t…
Quasi-2D bidisperse amorphous systems of steel beads are fluidized by a uniform upflow of air, so that the beads roll on a horizontal plane. The short-time ballistic motion of the beads is stochastic, with non-Gaussian speed distributions and with different average kinetic energies for the two species. The approach to jamming is studied as a function of increasing bead area fraction and also as a function of decreasing air speed. The structure of the system is measured in terms of both the Voronoi tessellation and the pair distribution function. The dynamics of the system is measured in terms …
Studying the jamming transition of granular and colloidal systems, has lead to a proliferation of theoretical and numerical results formulated in the language of the eigenspectrum of the dynamical matrix for these disordered system. Only recently however, these modes have been accessed experimentally in colloidal and granular media, computing the eigenmodes of the covariance matrix of the particle positions. At the same time new conceptual and methodological questions have appeared, regarding the interpretation of these results. In the present paper, we first give an overview of the theoretica…
We investigate the rigidity transition associated with shear jamming in frictionless, as well as frictional, disk packings in the quasi-static regime and at low shear rates. For frictionless disks, the transition is under quasistatic shear is discontinuous, with an instantaneous emergence of a system spanning rigid cluster at the jamming transition. For frictional systems, the transition appears continuous for finite shear rates, but becomes sharper for lower shear rates. In the quasi-static limit, it is discontinuous as in the frictionless case. Thus, our results show that the rigidity transi…
We present extensive computational results for the effective temperature, defined by the fluctuation-dissipation relation between the mean square displacement and the average displacement of grains, under the action of a weak, external perturbation, of a sheared, bi-disperse granular packing of compressible spheres. We study the dependence of this parameter on the shear rate and volume fractions, the type of particle and the observable in the fluctuation-dissipation relation. We find the same temperature for different tracer particles in the system. The temperature becomes independent on the s…
The Jamming of soft spheres at zero temperature, the J-point, has been extensively studied both numerically and theoretically and can now be considered as a safe location in the space of models, where a street lamp has been lit up. However, a recent work by Ikeda et al, 2013 reveals that, in the Temperature/Packing fraction parameter space, experiments on colloids are actually rather far away from the scaling regime illuminated by this lamp. Is it that the J-point has little to say about real system? What about granular media? Such a-thermal, frictional, systems are a-priori even further away …
We demonstrate that a highly frustrated anisotropic Josephson junction array(JJA) on a square lattice exhibits a zero-temperature jamming transition, which shares much in common with those in granular systems. Anisotropy of the Josephson couplings along the horizontal and vertical directions plays roles similar to normal load or density in granular systems. We studied numerically static and dynamic response of the system against shear, i. e. injection of external electric current at zero temperature. Current-voltage curves at various strength of the anisotropy exhibit universal scaling feature…
We present the experimental studies of highly strained soft bidisperse granular systems made of hyperelastic and plastic particles. We explore the behavior of granular matter deep in the jammed state from local field measurement from the grain scale to the global scale. By mean of digital image correlation and accurate image recording we measure for each compression step the evolution of the particle geometries and their right Cauchy-Green strain tensor fields. We analyze the evolution of the usual macroscopic observables (stress, packing fraction, coordination, fraction of non-rattlers, \text…
Granular media jam into a panoply of metastable states. The way in which these states are achieved depends on the nature of local and global constraints on grains; here we investigate this issue by means of a non-equilibrium stochastic model of a hindered granular column near its jamming limit. Grains feel the constraints of grains above and below them differently, depending on their position. A rich phase diagram with four dynamical phases (ballistic, activated, logarithmic and glassy) is revealed. The statistics of the jamming time and of the metastable states reached as attractors of the ze…
Granular materials jam when developing a network of contact forces able to resist the applied stresses. Through numerical simulations of the dynamics of the jamming process, we show that the jamming transition does not occur when the kinetic energy vanishes. Rather, as the system jams, the kinetic energy becomes dominated by rattlers particles, that scatter withing their cages. The relaxation of the kinetic energy in the jammed configuration exhibits a double power-law decay, which we interpret in terms of the interplay between backbone and rattlers particles.
The dynamics of a bi-dimensional dense granular packing under cyclic shear is experimentally investigated close to the jamming transition. Measurement of multi-point correlation functions are produced. The self-intermediate scattering function, displaying slower than exponential relaxation, suggests dynamic heterogeneity. Further analysis of four point correlation functions reveal that the grain relaxations are strongly correlated and spatially heterogeneous, especially at the time scale of the collective rearrangements. Finally, a dynamical correlation length is extracted from spatio-temporal…
The existence of universal scaling in the vicinity of the jamming transition of sheared granular materials is predicted by a phenomenology. The critical exponents are explicitly determined, which are independent of the spatial dimension. The validity of the theory is verified by the molecular dynamics simulation.
We investigate the full phase diagram of a column of grains near jamming, as a function of varying levels of frustration. Frustration is modelled by the effect of two opposing fields on a grain, due respectively to grains above and below it. The resulting four dynamical regimes (ballistic, logarithmic, activated and glassy) are characterised by means of the jamming time of zero-temperature dynamics, and of the statistics of attractors reached by the latter. Shape effects are most pronounced in the cases of strong and weak frustration, and essentially disappear around a mean-field point.
Shear modulus of frictionless granular materials near the jamming transition under oscillatory shear is numerically investigated. It is found that the shear modulus $G$ satisfies a scaling law to interpolate between $G \sim (ϕ- ϕ_J)^{1/2}$ and $G \sim γ_0^{-1/2}(ϕ-ϕ_J)$ for a linear spring model of the elastic interaction between contacting grains, where $ϕ$, $ϕ_J$, and $γ_0$ are, respectively, the volume fraction of grains, the fraction at the jamming point, and the amplitude of the oscillatory shear. The linear relation between the shear modulus and $ϕ- ϕ_J$ can be understood by slip avalanc…
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, phi_c. Above phi_c, Z and the pressure, P are predicted to increase as power laws in phi-phi_c. In experiments using photoelastic disks we corroborate a rapid increase in Z at phi_c and power-law behavior above phi_c for Z and P. Specifically we find power-law increase as a function of phi-phi_c for Z-Z_c with an exponent beta around 0.5, and for P with an exponent psi around 1.1. These exponents are in …
In order to study analytically the nature of the jamming transition in granular material, we have considered a cavity method mean field theory, in the framework of a statistical mechanics approach, based on Edwards' original idea. For simplicity we have applied the theory to a lattice model and a transition with exactly the same nature of the glass transition in mean field models for usual glass formers is found. The model is also simulated in three dimensions under tap dynamics and a jamming transition with glassy features is observed. In particular two step decays appear in the relaxation fu…
When a sandpile relaxes under vibration, it is known that its measured angle of repose is bistable in a range of values bounded by a material-dependent maximal angle of stability; thus, at the same angle of repose, a sandpile can be stationary or avalanching, depending on its history. In the nearly jammed slow dynamical regime, sandpile collapse to a zero angle of repose can also occur, as a rare event. We claim here that fluctuations of {\it dilatancy} (or local density) are the key ingredient that can explain such varied phenomena. In this work, we model the dynamics of the angle of repose a…
We investigate universal features of the jamming transition in granular materials, colloids and glasses. We show that the jamming transition in these systems has common features: slowing of response to external perturbation, and the onset of structural heterogeneities.
In this work we present an experimental study of the jamming that stops the free flow of grains from a silo discharging by gravity. When the outlet size is not much bigger than the beads, granular material jams the outlet of the container due to the formation of an arch. Statistical data from the number of grains fallen between consecutive jams are presented. The information that they provide can help to understand the jamming phenomenon. As the ratio between the size of the orifice and the size of the beads is increased, the probability that an arch blocks the outlet decreases. We show here t…
Non-linear sound is an extreme phenomenon typically observed in solids after violent explosions. But granular media are different. Right when they jam, these fragile and disordered solids exhibit a vanishing rigidity and sound speed, so that even tiny mechanical perturbations form supersonic shocks. Here, we perform simulations in which two-dimensional jammed granular packings are dynamically compressed, and demonstrate that the elementary excitations are strongly non-linear shocks, rather than ordinary phonons. We capture the full dependence of the shock speed on pressure and impact intensity…
We carry out numerical simulations to study transport behavior about the jamming transition of a model granular material in two dimensions at zero temperature. Shear viscosity ηis computed as a function of particle volume density ρand applied shear stress σ, for diffusively moving particles with a soft core interaction. We find an excellent scaling collapse of our data as a function of the scaling variable σ/|ρ_c-ρ|^Δ, where ρ_c is the critical density at σ=0 ("point J"), and Δis the crossover scaling critical exponent. Our results show that jamming is a true critical phenomenon, extending to …
We have recently developed some simple continuum models of static granular media which display "fragile" behaviour: they predict that the medium is unable to support certain types of infinitesimal load (which we call "incompatible" loads) without plastic rearrangement. We argue that a fragile description may be appropriate when the mechanical integrity of the medium arises adaptively, in response to a load, through an internal jamming process. We hypothesize that a network of force chains (or "granular skeleton") evolves until it can just support the applied load, at which point it comes to re…
In the framework of schematic hard spheres lattice models we discuss Edwards' Statistical Mechanics approach to granular media. As this approach appears to hold here to a very good approximation, by analytical calculations of Edwards' partition function at a mean field level we derive the system phase diagram and show that ``jamming'' corresponds to a phase transition from a ``fluid'' to a ``glassy'' phase, observed when crystallization is avoided. The nature of such a ``glassy'' phase turns out to be the same found in mean field models for glass formers. In the same context, we also briefly d…
In the framework of schematic hard spheres lattice models for granular media we investigate the phenomenon of the ``jamming transition''. In particular, using Edwards' approach, by analytical calculations at a mean field level, we derive the system phase diagram and show that ``jamming'' corresponds to a phase transition from a ``fluid'' to a ``glassy'' phase, observed when crystallization is avoided. Interestingly, the nature of such a ``glassy'' phase turns out to be the same found in mean field models for glass formers.
Dry granular materials such as sand, gravel, pills, or agricultural grains, can become rigid when compressed or sheared. At low density, one can distort the shape of a container of granular material without encountering any resistance. Under isotropic compression, the material will reach a certain {\it jamming} density and then resist further compression. {\em Shear jamming} occurs when resistance to shear emerges in a system at a density lower than the jamming density, and the elastic properties of such states have important implications for industrial and geophysical processes. We report on …
We present here the preliminary results obtained for two experiments on randomly agitated granular assemblies using a novel way of shaking. First we discuss the transport properties of a 2D model system undergoing classical shaking that show the importance of large scale dynamics for this type of agitation and offer a local view of the microscopic motions of a grain. We then develop a new way of vibrating the system allowing for random accelerations smaller than gravity. Using this method we study the evolution of the free surface as well as results from a light scattering method for a 3D mode…
The physical properties of granular materials have been extensively studied in recent years. So far, however, there exists no theoretical framework which can explain the observations in a unified manner beyond the phenomenological jamming diagram [1]. This work focuses on the case of static granular matter, where we have constructed a statistical ensemble [2] which mirrors equilibrium statistical mechanics. This ensemble, which is based on the conservation properties of the stress tensor, is distinct from the original Edwards ensemble and applies to packings of deformable grains. We combine it…
We present simple models of particulate materials whose mechanical integrity arises from a jamming process. We argue that such media are generically "fragile", that is, they are unable to support certain types of incremental loading without plastic rearrangement. In such models, fragility is naturally linked to the marginal stability of force chain networks (granular skeletons) within the material. Fragile matter exhibits novel mechanical responses that may be relevant to both jammed colloids and cohesionless assemblies of poured, rigid grains.
In the late 1980s, Sam Edwards proposed a possible statistical-mechanical framework to describe the properties of disordered granular materials. A key assumption underlying the theory was that all jammed packings are equally likely. In the intervening years it has never been possible to test this bold hypothesis directly. Here we present simulations that provide direct evidence that at the unjamming point, all packings of soft repulsive particles are equally likely, even though generically, jammed packings are not. Typically, jammed granular systems are observed precisely at the unjamming poin…
We report the simultaneous softening and compaction of a confined dense granular pack in acoustic resonance experiments. Elastic softening is manifested by a reduction of the shear-wave speed, as the wave amplitude increases beyond some threshold. No macroscopic rearrangement of grains or dilatancy is observed; instead, elastic softening is accompanied by a tiny amount of compaction on the scale of grain asperities. We explain these apparent contradictory observations using a theoretical model, based on shear transformation zones (STZs), of soft spots and slipping contacts. It predicts a linea…
