8 pages Revtex 4-1, 6 figures. An expanded version of the previous one, with substantial modifications in the Introduction and also some modifications in section 4. One figure modified and two new figures added. Changes made in response to criticism of colleagues and anonymous referees
We propose here that certain observational features of granular matter in the infrared limit, exhibiting the phenomenon of {\it jamming}, arise from an underlying effective general relativistic description. The proposal stems from the assumption (which we justify on physical grounds) that grains in granular matter move freely in an {\it effective} curved Riemannian space. The termination of their trajectories at the onset of jamming is obtained from the focussing of a converging congruence of geodesics in such a space, as a solution of the Raychaudhuri equation for such congruences. This may happen irrespective of whether or not the curvature is sourced by external stresses (via an effective Einstein equation), although the properties of the resultant jammed state solution do differ in the two cases. A definite prediction of this geometrical approach is the negative role played by those trajectories which twist about each other, in reaching the jammed state. The local symmetries of granular interaction, translational and rotational invariance (corresponding to `force balance' and `torque balance' in standard force-based approaches to jamming) are inherent in the effective general relativity framework. A recently-proposed effective elasticity model of the jammed state, based on a tensorial variant of standard electrostatics (Vector Charge Theory), is seen to be entirely subsumed within the linearized version of the effective general relativistic description.
Granular solid hydrodynamics, constructed to describe quasi-elastic and plastic motion of granular solid, is shown also capable of accounting for the rheology of granular dense flow. This makes it a unified, though still qualitative, hydrodynamic description, enabling one to tackle fluidization and jamming, the hysteretic transition between elasto-plastic motion and uniform dense flow.
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…
For the purpose of applying laws or principles originated from thermal systems to granular athermal systems, we may need to properly define the critical temperature concept in granular powders. The conventional environmental temperature in thermal systems is too weak to drive movements of particles in granular powders and cannot function as a thermal energy indicator. For maintaining the same functionality as in thermal systems, the temperature in granular powders is defined analogously and uniformly in this article. The newly defined granular temperature is utilized to describe and explain on…
We have performed a novel experiment on granular packs composed of automatically swelling particles. By analyzing the Voronoi structure of packs going through the jamming transition, we show that the local configuration of a jamming pack is strikingly similar to that of a glass-forming liquid, both in terms of their universal area distribution and the process of defect annealing. Furthermore, we demonstrate that an unambiguous structural signature of the jamming transition can be obtained from the pair correlation functions of a pack. Our study provides insights into the structural properties …
This paper describes methods to measure flow rate and jamming onset of granules discharged through a flat-bottom cylindrical hopper with a circular orifice. The intrinsic jamming onset for ideal particles (spherical, monodisperse, smooth) is experimentally measured by two independent methods, with good agreement. For non-ideal particles, the normalized jamming onset increases with elongated granule shape, broadened size distribution and increased friction as measured by the drained angle of repose. An empirical model of the jamming onset is introduced to quantify these effects over the range o…
Rheological properties of dense flows of hard particles are singular as one approaches the jamming threshold where flow ceases, both for granular flows dominated by inertia, and for over-damped suspensions. Concomitantly, the lengthscale characterizing velocity correlations appears to diverge at jamming. Here we review a theoretical framework that gives a scaling description of stationary flows of frictionless particles. Our analysis applies both to suspensions and inertial flows of hard particles. We report numerical results in support of the theory, and show the phase diagram that results wh…
We explore the initial moments of impact between two dense granular clusters in a two-dimensional geometry. The particles are composed of solid CO$_{2}$ and are levitated on a hot surface. Upon collision, the propagation of a dynamic "jamming front" produces a distinct regime for energy dissipation in a granular gas in which the translational kinetic energy decreases by over 90%. Experiments and associated simulations show that the initial loss of kinetic energy obeys a power law in time, $ΔE=-Kt^{3/2}$, a form that can be predicted from kinetic arguments.
We study the internal dynamical processes taking place in a granular packing below yield stress. At all packing fractions and down to vanishingly low applied shear, a logarithmic creep is evidenced. The experiments are analyzed under the scope of a visco-elastic model introducing an internal "fluidity" variable. For all experiments, the creep dynamics can be rescaled onto a unique curve which displays jamming at the random-close-packing limit. At each packing fraction, a stress value is evidenced, corresponding to the onset of internal granular reorganisation leading to a slowing down the cree…
Diverging correlation lengths on either side of the jamming transition are used to formulate a rheological model of granular shear flow, based on the propagation of stress through force chain networks. The model predicts three distinct flow regimes, characterized by the shear rate dependence of the stress tensor, that have been observed in both simulations and experiments. The boundaries separating the flow regimes are quantitatively determined and testable. In the limit of jammed granular solids, the model predicts the observed anomalous scaling of the shear modulus and a new relation for the…
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.
This paper is aimed at pursuing a recent discussion about the comparison between Self-Organised Criticality, the jamming process and the percolation theory in the problem of a silo discharge [I. Zuriguel, A. Garcimartin, D. Maza, L.A.Pugnaloni, J.M.Pastor, "Jamming during the discharge of granular matter from a silo", Phys.Rev.E 71, 051303 (2005)]. Statistics of blocking a silo is investigated from different models: percolation, self organised criticality..
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.
Data61, CSIRO（澳大利亚联邦科学与工业研究组织数据61中心）；University of Queensland（昆士兰大学）
Granular jamming is a popular soft robotics technology that has seen recent widespread applications including industrial gripping, surgical robotics and haptics. However, to date the field has not fully exploited the fundamental science of the jamming phase transition, which has been rigorously studied in the field of statistical and condensed matter physics. This work introduces vibration as a means to improve the properties of granular jamming grippers through vibratory fluidisation and the exploitation of resonant modes within the granular material. We show that vibration in soft jamming gr…
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…
Rheological properties of a dense granular material consisting of frictionless spheres are investigated. It is found that the shear stress, the pressure, and the kinetic temperature obey critical scaling near the jamming transition point, which is considered as a critical point. These scaling laws have some peculiar properties in view of conventional critical phenomena because the exponents depend on the interparticle force models so that they are not universal. It is also found that these scaling laws imply the relation between the exponents that describe the growing correlation length.
Supercooled liquids and dense colloids exhibit anomalous behaviour known as "spatially heterogeneous dynamics" (SHD), which becomes increasingly pronounced with approach to the glass transition. Recently, SHD has been observed in confined granular packings under slow shear near the onset of jamming, bolstering speculation that the two transitions are related. Here, we report measurements of SHD in a system of air-driven granular beads, as a function of both density and effective temperature. On approach to jamming, the dynamics become progressively slower and more spatially heterogeneous. The …
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 establish that the rheological curve of dry granular media is non-monotonic, both in the presence and absence of external mechanical agitations. In the presence of weak vibrations, the non-monotonic flow curves govern a hysteretic transition between slow but steady and fast, inertial flows. In the absence of vibrations, the non-monotonic flow curve governs the yielding behavior of granular media. Finally, we show that non-monotonic flow curves can be seen in at least two different flow geometries and for several granular materials.
Granular jamming has been identified as a fundamental mechanism for the operation of robotic grippers. In this work, we show, that soft particles like expanded polystyrene beads lead to significantly larger gripping forces in comparison to rigid particles. In contradiction to naive expectation, the combination of jamming and elasticity gives rise to very different properties of the jammed phase, compared to hard-particle systems. This may be of interest also beyond the application in robotic grippers.
We investigate experimentally the dynamics of an intruder dragged by a constant force in an assembly of horizontally vibrated grains close to jamming. At moderate packing fractions, the intruder moves rapidly as soon as the force is applied. Above some threshold value of the packing fraction which increases with the applied force, the intruder exhibits an intermittent creep motion with strong fluctuations reminiscent of a crackling noise signal. These fluctuations behave in a critical manner at the jamming transition unveilled in a previous study. The transition separates a regime where the in…
Jammed states of frictional granular systems can be induced by shear strain at densities below the isostatic jamming density ($ϕ_c$). It remains unclear, however, how much friction affects this so-called shear-jamming. Friction appears in two ways in this type of experiment: friction between particles, and friction between particles and the base on which they rest. Here, we study how particle-bottom friction, or basal friction, affects shear jamming in quasi-two dimensional experiments. In order to study this issue experimentally, we apply simple shear to a disordered packing of photoelastic d…
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 …
CSIRO（联邦科学与工业研究组织）；University of Queensland（昆士兰大学）；Queensland University of Technology（昆士兰科技大学）；University of Melbourne（墨尔本大学）
We test grip strength and shock absorption properties of various granular material in granular jamming robotic components. The granular material comprises a range of natural, manufactured, and 3D printed material encompassing a wide range of shapes, sizes, and Shore hardness. Two main experiments are considered, both representing compelling use cases for granular jamming in soft robotics. The first experiment measures grip strength (retention force measured in Newtons) when we fill a latex balloon with the chosen grain type and use it as a granular jamming gripper to pick up a range of test ob…
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.
CSIRO（联邦科学与工业研究组织）；Queensland University of Technology（昆士兰科技大学）；University of Queensland（昆士兰大学）
Granular jamming has recently become popular in soft robotics with widespread applications including industrial gripping, surgical robotics and haptics. Previous work has investigated the use of various techniques that exploit the nature of granular physics to improve jamming performance, however this is generally underrepresented in the literature compared to its potential impact. We present the first research that exploits vibration-based fluidisation actively (e.g., during a grip) to elicit bespoke performance from granular jamming grippers. We augment a conventional universal gripper with …
Classical soil mechanics results are used to propose the equation of the jamming transition surface in the (stress, specific volume) space. Taking axis-ymmetric conditions, labelling q the deviatoric stress and p' the mean pressure applied on the granular skeleton, and considering normal range of pressure (10 kPa-10MPa) the equation of the surface of jamming transition is v = vo-m ln(p'/p'o)+ md ln(1+q q/(M' M' p' p')); M' is related to the friction angle, m and md are two constants which depend on soil characteristics; p'o is a "unit" pressure.
CSIRO（联邦科学与工业研究组织）；Queensland University of Technology（昆士兰科技大学）；Griffith University（格里菲斯大学）
Fruit harvesting has recently experienced a shift towards soft grippers that possess compliance, adaptability, and delicacy. In this context, pneumatic grippers are popular, due to provision of high deformability and compliance, however they typically possess limited grip strength. Jamming possesses strong grip capability, however has limited deformability and often requires the object to be pushed onto a surface to attain a grip. This paper describes a hybrid gripper combining pneumatics (for deformation) and jamming (for grip strength). Our gripper utilises a torus (donut) structure with two…
We investigate the mixing characteristics of dry granular material while draining down a silo with multiple exit orifices. The mixing in the silo, which otherwise consists of noninteracting stagnant and flow regions, is observed to improve significantly when the flow through specific orifices is stopped intermittently. This momentary stoppage of flow through the orifice is either controlled manually or is chosen by the system itself when the orifice width is small enough to cause spontaneous jamming and unjamming. We observe that the overall mixing behavior shows a systematic dependence on the…
The jamming transition is accompanied by a rich phenomenology, such as hysteresis or non-local effects, which is still not well understood. Here we experimentally investigate a model frictionless granular layer flowing down an inclined plane, as a way to disentangle generic collective effects from those arising from frictional interactions. We find that thin frictionless granular layers are devoid of hysteresis, yet the layer stability is increased as it gets thinner. Rheological laws obtained for different layer thicknesses can be collapsed into a unique master curve, supporting that non-loca…
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 significan…
Confinement of a slender body into a granular array induces stress localization in the geometrically nonlinear structure, and jamming, reordering, and vertical dislocation of the surrounding granular medium. By varying the initial packing density of grains and the length of a confined elastica, we identify the critical length necessary to induce jamming, and demonstrate an intricate coupling between folds that localize along grain boundaries. Above the jamming threshold, the characteristic length of elastica deformation is shown to scale with the length over which force field fluctuations prop…
The drainage of particulate foams is studied under conditions where the particles are not trapped individually by constrictions of the interstitial pore space. The drainage velocity decreases continuously as the particle volume fraction $ϕ_{p}$ increases. The suspensions jam - and therefore drainage stops - for values $ϕ_{p}^{*}$ which reveal a strong effect of the particle size. In accounting for the particular geometry of the foam, we show that $ϕ_{p}^{*}$ accounts for unusual confinement effects when the particles pack into the foam network. We model quantitatively the overall behavior of t…
We have explored isotropically jammed states of semi-2D granular materials through cyclic compression. In each compression cycle, systems of either identical ellipses or bi-disperse 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, ϕm, above which P persists over many cycles; below ϕm, 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…
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…
Unlike dry granular materials, a dense granular suspension like cornstarch in water can strongly resist extensional flows. At low extension rates, such a suspension behaves like a viscous liquid, but rapid extension results in a response where stresses far exceed the predictions of lubrication hydrodynamics and capillarity. To understand this remarkable mechanical response, we experimentally measure the normal force imparted by a large bulk of the suspension on a plate moving vertically upward at a controlled velocity. We observe that above a velocity threshold, the peak force increases by ord…
We have investigated the spatiotemporal chaotic dynamics of unjamming and jamming of particles in a toy-model system -- a rotating drum partially filled with bidisperse disks to create avalanches. The magnitudes of the first Lyapunov vector $δu(t)$ and velocity $v(t)$ of particles are directly measured for the first time to yield insights into their spatial correlation $C_{δu,v}$, which is stronger near the unjamming but is weaker near the jamming transition, consistent with the recent work of Banigan et al., Nature Phys. $\bf{9}$, 288, (2013). $v(t)$ shows rich dynamics: it grows exponentiall…
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…
Experiments with acoustic waves guided along the mechanically free surface of an unconsolidated granular packed structure provide information on the elasticity of granular media at very low pressures that are naturally controlled by the gravitational acceleration and the depth beneath the surface. Comparison of the determined dispersion relations for guided surface acoustic modes with a theoretical model reveals the dependencies of the elastic moduli of the granular medium on pressure. The experiments confirm recent theoretical predictions that relaxation of the disordered granular packing thr…
This paper establishes a link between the non-local behaviour of granular materials and the presence of transient clusters of jammed particles within the flow. These clusters are first evidenced in simulated dense granular flows subjected to plane shear, and are found to originate from a mechanism of multiple orthogonal shear banding. A continuum non-local model, similar in form to the non-local Cooperative model, is then derived by considering the spatial redistribution of vorticity induced by these clusters. The non-locality length scale is thus expressed in terms of the cluster size. The pu…
We investigate experimentally the mechanical response to shear of a 2D packing of grains across the jamming transition. First, we develop a dedicated experimental setup, together with tracking and photoelastic techniques in order to prepare the packing in a controlled fashion and to quantify the stress and strain tensors at the grain scale. Second, we install a inflating probe (a 2D "balloon"), which shears the packing with a cylindrical symmetry. We probe experimentally stresses and strains for strain amplitudes as low as $10^{-3}$ and for a range of packing fractions within $2\%$ variation a…
We present a series of measurements examining the penetration force required to push a flat plate vertically through a dense granular medium, focusing in particular on the effects of the bottom boundary of the vessel containing the medium. Our data demonstrate that the penetration force near the bottom is strongly affected by the surface properties of the bottom boundary, even many grain diameters above the bottom. Furthermore, the data indicate an intrinsic length scale for the interaction of the penetrating plate with the vessel bottom via the medium. This length scale, which corresponds to …
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 consider a model for driven particulate matter in which absorbing states can be reached both by particle isolation and by particle caging. The model predicts a non-equilibrium phase diagram in which analogues of hydrodynamic and elastic reversibility emerge at low and high volume fractions respectively, partially separated by a diffusive, non-absorbing region. We thus find a single phase boundary that spans the onset of chaos in sheared suspensions to the onset of yielding in jammed packings. This boundary has the properties of a non-equilibrium second order phase transition, leading us to …
We investigate the flow and jamming through small apertures of a column of granular disks via a pseudo-dynamic model. We focus on the effect that the preparation of the granular assembly has on the size of the avalanches obtained. Ensembles of packings with different mean packing fractions are created by tapping the system at different intensities. Surprisingly, packing fraction is not a good indicator of the ability of the deposit to jam a given orifice. Different mean avalanche sizes are obtained for deposits with the same mean packing fraction that were prepared with very different tap inte…
The dynamical properties of a dense horizontally vibrated bidisperse granular monolayer are experimentally investigated. The quench protocol produces states with a frozen structure of the assembly, but the remaining degrees of freedom associated with contact dynamics control the appearance of macroscopic rigidity. We provide decisive experimental evidence that this transition is a critical phenomenon, with increasingly collective and heterogeneous rearrangements occurring at length scales much smaller than the grains' diameter, presumably reflecting the contact force network fluctuations. Dyna…
When dense granular systems are exposed to external forcing, they evolve on the time scale that is typically related to the externally imposed one (shear or compression rate, for example). This evolution could be characterized by observing temporal evolution of contact networks. However, it is not immediately clear whether the force networks, defined on contact networks by considering force interactions between the particles, evolve on a similar time scale. To analyze the evolution of these networks, we carry out discrete element simulations of a system of soft frictional disks exposed to comp…
We numerically study the linear response of two-dimensional frictional granular materials under oscillatory shear. The storage modulus $G'$ and the loss modulus $G''$ in the zero strain rate limit depend on the initial strain amplitude of the oscillatory shear before measurement. The shear jammed state (satisfying $G'>0$) can be observed at an amplitude greater than a critical initial strain amplitude. The fragile state is defined by the emergence of liquid-like and solid-like states depending on the form of the initial shear. In this state, the observed $G'$ after the reduction of the strain …
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 experimental results on the shape of arches that block the outlet of a two dimensional silo. For a range of outlet sizes, we measure some properties of the arches such as the number of particles involved, the span, the aspect ratio, and the angles between mutually stabilizing particles. These measurements shed light on the role of frictional tangential forces in arching. In addition, we find that arches tend to adopt an aspect ratio (the quotient between height and half the span) close to one, suggesting an isotropic load. The comparison of the experimental results with data from nu…
We study experimentally the relaxation towards mechanical equilibrium of a granular pile which has just experienced an avalanche and discuss it in the more general context of the granular jamming transition. Two coexisting dynamics are observed in the surface layer: a short time exponential decay consisting in rapid and independent moves of grains and intermittent bursts consisting in spatially correlated moves lasting for longer time. The competition of both dynamics results in long-lived intermittent transients, the total duration of which can late more than a thousand of seconds. We measure…
Jamming is a common feature of out of equilibrium systems showing slow relaxation dynamics. Here we review our efforts in understanding jamming in granular materials using experiments and computer simulations. We first obtain an estimation of an effective temperature for a slowly sheared granular material very close to jamming. The measurement of the effective temperature is realized in the laboratory by slowly shearing a closely-packed ensemble of spherical beads confined by an external pressure in a Couette geometry. All the probe particles, independent of their characteristic features, equi…
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…
