This paper investigates whether in frictional granular packings, like in Hamiltonian amorphous elastic solids, the stress autocorrelation matrix presents long range anisotropic contributions just as elastic Green's functions. We find that in a standard model of frictional granular packing this is not the case. We prove quite generally that mechanical balance and material isotropy constrain the stress auto-correlation matrix to be fully determined by two spatially isotropic functions: the pressure and torque auto-correlations. The pressure and torque fluctuations being respectively normal and hyperuniform force the stress autocorrelation to decay as the elastic Green's function. Since we find the torque fluctuations to be hyper-uniform, the culprit is the pressure whose fluctuations decay slower than normally as a function of the system's size. Investigating the reason for these abnormal pressure fluctuations we discover that anomalous correlations build up already during the compression of the dilute system before jamming. Once jammed these correlations remain frozen. Whether this is true for frictional matter in general or is it the consequence of the model properties is a question that must await experimental scrutiny and possible alternative models.
Frictional constitutive law for very slow vertical withdrawing of a thin rod from a granular bed is experimentally studied. Using a very precise creep meter, geometry-dependent granular frictional constitutive law is particularly examined. In some previous works, a dimensionless number $I=\dotγD_g/\sqrt{p/ρ_g}$ has been used to characterize granular frictional constitutive laws, where $\dotγ$, $D_g$, $p$, and $ρ_g$ are the shear strain rate, grain diameter, confining pressure, and bulk density of granular bed, respectively. It has been considered that granular frictional constitutive law expre…
We extend a recent theory for the rheology of frictionless granular materials [K. Suzuki and H. Hayakawa, Phys. Rev. Lett. 2015, 115, 098001] to the case of frictional disks in two dimensions. Employing a frictional contact model for molecular dynamics simulations, we derive difference equations of the shear stress, the granular temperature, and the spin temperature from the generalized Green-Kubo formula, where all the terms are given by microscopic expressions. The numerical solutions of the difference equations not only describe the flow curve, but also reproduce the hysteresis of shear str…
When compressed frictional granular media are decompressed, generically a fragile configuration is created at low pressures. Typically this is accompanied by a giant frictional slippage as the fragile state collapses. We show that this instability is understood in terms of a scaling theory with theoretically computable amplitudes and exponents. The amplitude diverges in the thermodynamic limit hinting to the possibility of huge frictional slip events in decompressed granular media. The physics of this slippage is discussed in terms of the probability distribution functions of the tangential an…
We report a joint experimental and theoretical investigation of cyclic training of amorphous frictional granular assemblies, with special attention to memory formation and retention. Measures of dissipation and compactification are introduced, culminating with a proposed scaling law for the reducing dissipation and increasing memory. This scaling law is expected to be universal, insensitive to the details of the elastic and frictional interactions between the granules.
We perform numerical simulations of a two-dimensional frictional granular system under oscillatory shear confined by constant pressure. We found that the system undergoes dilatancy as the strain increases. We confirmed that compaction also takes place at an intermediate strain amplitude for a small mutual friction coefficient between particles. We also found that compaction depends on the confinement pressure while dilatancy little depends on the pressure.
Herein, we numerically study the rheology of a two-dimensional frictional granular system confined by constant pressure under oscillatory shear. Several scaling laws for the storage and loss moduli against the scaled strain amplitude have been found. The scaling laws in plastic regime for large strain amplitude can be understood by the angular distributions of the contact force. The scaling exponents are estimated by considering the physical mechanism.
We report a joint experimental and theoretical investigation of the probability distribution functions (pdf's) of the normal and tangential (frictional) forces in amorphous frictional media. We consider both the joint pdf of normal and tangential forces together, and the marginal pdf's of normal forces separately and tangential forces separately. A maximum entropy formalism is utilized for all these cases after identifying the appropriate constraints. Excellent agreements with both experimental and simulational data are reported. The proposed joint pdf (which appears new to the literature) pre…
In this study, we numerically investigated the mechanical responses and trajectories of frictional granular particles under oscillatory shear in the reversible phase where particle trajectories form closed loops below the yielding point. When the friction coefficient is small, the storage modulus exhibits softening, and the loss modulus remains finite in the quasi-static limit. As the friction coefficient increases, the softening and residual loss modulus are suppressed. The storage and loss moduli satisfy scaling laws if they are plotted as functions of the areas of the loop trajectories divi…
The shear modulus of jammed frictional granular materials with the harmonic repulsive interaction under an oscillatory shear is numerically investigated. It is confirmed that the storage modulus, the real part of the shear modulus, for frictional grains with sufficiently small strain amplitude $γ_0$ discontinuously emerges at the jamming transition point. The storage modulus for small $γ_0$ differs from that of frictionless grains even in the zero friction limit, while they are almost identical with each other for sufficiently large $γ_0$, where the transition becomes continuous. The stress-st…
The transition between shear-flowing and shear-arrested states of frictional granular matter is studied using constant-stress discrete element simulations. By subjecting a dilute system of frictional grains to a constant external shear stress and pressure, friction-dependent critical shear stress and density are clearly identified with both exhibiting a crossover between low and high friction. The critical shear stress bifurcates two nonequilibrium steady states: (i) steady state shear flow characterized by a constant deformation rate, and (ii) shear arrest characterized by temporally decaying…
We show how rigidity emerges in experiments of sheared frictional granular materials by using generalizations of two methods for identifying rigid structures. Both approaches, the force-based dynamical matrix and the topology-based rigidity percolation, agree with each other and identify similar rigid structures. As the system becomes jammed, at a contact number of $z=2.4\pm 0.1$, a rigid backbone interspersed with floppy, particle-filled holes of a broad range of sizes emerges, creating a sponge-like morphology. We also find that the pressure within rigid structures always exceeds the pressur…
We investigate the mechanical properties of inclined frictional granular layers prepared with different protocols by means of DEM numerical simulations. We perform an orthotropic elastic analysis of the stress response to a localized overload at the layer surface for several substrate tilt angles. The distance to the unjamming transition is controlled by the tilt angle $α$ with respect to the critical angle $α_c$. We find that the shear modulus of the system decreases with $α$, but tends to a finite value as $α\to α_c$. We also study the behaviour of various microscopic quantities with $α$, an…
Dense granular systems subjected to an imposed shear stress undergo stick-slip dynamics with systematic patterns of dilation-compaction. During each stick phase, as the frictional strength builds up, the granular system dilates to accommodate shear strain, developing stronger force networks. During each slip event, when the stored energy is released, particles experience large rearrangements and the granular network can significantly change. Here, we use numerical simulations of 3D, sheared frictional packings to show that the mean betweenness centrality -- a property of network of interpartic…
The failure of 2D numerical cohesive granular steps collapsing under gravity are simulated for a large range of cohesion. Focussing on the cumulative displacement of the grains, and defining a displacement threshold, we establish a sensible criterion for capturing the failure characteristics. We are able to locate the failure in time and to identify the different stages of the destabilisation. We find that the onset of the failure is delayed by increasing cohesion, but its duration becomes shorter. Defining a narrow displacement interval, a well-defined shear band revealing the failure comes o…
Stress transmission inside three dimensional granular packings is investigated using computer simulations. Localized force perturbation techniques are implemented for frictionless and frictional shallow, ordered, granular arrays confined by solid boundaries for a range of system sizes. Stress response profiles for frictional packings agree well with the predictions for the semi-infinite half plane of classical isotropic elasticity theory down to boxes of linear dimensions of approximately forty particle diameters and over several orders of magnitude in the applied force. The response profiles …
Simulations are used to study the steady shear rheology of dense suspensions of frictional particles exhibiting discontinuous shear thickening and shear jamming, in which finite-range cohesive interactions result in a yield stress. We develop a constitutive model that combines yielding behavior and shear thinning at low stress with the frictional shear thickening at high stresses, in good agreement with the simulation results. This work shows that there is a distinct difference between solids below the yield stress and in the shear-jammed state, as the two occur at widely separated stress leve…
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…
Simulation results are presented on the collapse of granular columns composed of rod-like particles. Columns can be stable and free-standing if either the friction coefficient is large enough, or the rods long enough. Destabilizing gravitational forces are counteracted by increased frictional forces between the rods. Different to columns made of spherical particles this is possible, because rod contacts can slide along the rod axes to generate the necessary "frictional cohesion".
A two-dimensional dense fluid of frictional grains is shown to exhibit time-chaotic, spatially heterogeneous flow in a range of stress values, $σ$, chosen in the unstable region of s-shaped flow curves. Stress controlled simulations reveal a phase diagram with reentrant stationary flow for small and large stress $σ$. In between no steady flow state can be reached, instead the system either jams or displays time dependent heterogeneous strain rates $\dotγ({\bf r},t)$. The results of simulations are in agreement with the stability analysis of a simple hydrodynamic model, coupling stress and micr…
We study the rheological behavior of concentrated granular suspensions of simple spherical particles. Under controlled stress, the system exhibits an S-shaped flow curve (stress vs. shear rate) with a negative slope in between the low-viscosity Newtonian regime and the shear thickened regime. Under controlled shear rate, a discontinuous transition between the two states is observed. Stress visualization experiments with a novel fluorescent probe suggest that friction is at the origin of shear thickening. Stress visualization shows that the stress in the system remains homogeneous (no shear ban…
Frictional granular matter is shown to be fundamentally different in its plastic responses to external strains from generic glasses and amorphous solids without friction. While regular glasses exhibit plastic instabilities due to a vanishing of a real eigenvalue of the Hessian matrix, frictional granular materials can exhibit a previously unnoticed additional mechanism for instabilities, i.e. the appearance of a pair of complex eigenvalues leading to oscillatory exponential growth of perturbations which are tamed by dynamical nonlinearities. This fundamental difference appears crucial for the …
In this paper, we report on new experimental results on the effects of in-plane surface stretching on the friction of Poly(DiMethylSiloxane) (PDMS) rubber with smooth rigid probes. Friction-induced displacement fields are measured at the surface of the PDMS substrate under steady-state sliding. Then, the corresponding contact pressure and frictional stress distributions are determined from an inversion procedure. Using this approach, we show that the local frictional stress $τ$ is proportional to the local stretch ratio $λ$ at the rubber surface. Additional data using a triangular flat punch i…
We report results of 3D Discrete Element Method (DEM) simulations aiming at investigating the role of the boundary vibration in inducing frictional weakening in sheared granular layers. We study the role of different vibration amplitudes applied at various shear stress levels, for a granular layer in the stick-slip regime and in the steady-sliding regime. Results are reported in terms of friction drops and kinetic energy release associated with frictional weakening events. We find that larger vibration amplitude induces larger frictional weakening events. The results show evidence of a thresho…
The hyperstatic nature of granular packings of perfectly rigid disks is analyzed algebraically and through numerical simulation. The elementary loops of grains emerge as a fundamental element in addressing hyperstaticity. Loops consisting of an odd number of grains behave differently than those with an even number. For odd loops, the latent stresses are exterior and are characterized by the sum of frictional forces around each loop. For even loops, the latent stresses are interior and are characterized by the alternating sum of frictional forces around each loop. The statistics of these two ty…
We investigate the evolution of multi-scale mechanical properties towards the macroscopic mechanical instability in frictional granular media under multiaxial compressive loading. Spatial correlations of shear stress redistribution following nucleating contact sliding events and shear strain localization are investigated. We report growing correlation lengths associated to both shear stress and shear strain fields that diverge simultaneously as approaching the transition to a dense flow regime. This shows that the transition from quasi static to dense flow regime can be interpreted as a critic…
The granular jamming transition is experimentally investigated in a two-dimensional system of frictional, bi-dispersed disks subject to quasi-static, uniaxial compression at zero granular temperature. Currently accepted results show the jamming transition occurs at a critical packing fraction $ϕ_c$. In contrast, we observe the first compression cycle exhibits {\it fragility} - metastable configuration with simultaneous jammed and un-jammed clusters - over a small interval in packing fraction ($ϕ_1 < ϕ< ϕ_2$). The fragile state separates the two conditions that define $ϕ_c$ with an exponential …
Discrete particle simulations are used to study the shear rheology of dense, stabilized, frictional particulate suspensions in a viscous liquid, toward development of a constitutive model for steady shear flows at arbitrary stress. These suspensions undergo increasingly strong continuous shear thickening (CST) as solid volume fraction $ϕ$ increases above a critical volume fraction, and discontinuous shear thickening (DST) is observed for a range of $ϕ$. When studied at controlled stress, the DST behavior is associated with non-monotonic flow curves of the steady-state stress as a function of s…
A method of modifying the roughness of soda-lime glass spheres is presented, with the purpose of tuning inter-particle friction. The effect of chemical etching on the surface topography and the bulk frictional properties of grains is systematically investigated. The surface roughness of the grains is measured using white light interferometry and characterised by the lateral and vertical roughness length scales. The underwater angle of repose is measured to characterise the bulk frictional behaviour. We observe that the co-efficient of friction depends on the vertical roughness length scale. We…
Torque Hyperuniformity in Frictional Granular Matter - Theory and Experiments
Hangzhou International Innovation Institute, Beihang University（北京航空航天大学杭州创新研究院）；School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院）；Institute of Natural Sciences, Shanghai Jiao Tong University（上海交通大学自然科学研究院）；Sino-Europe Complex Science Center, School of Mathematics, North University of China（中意复杂科学中心，中北大学数学系）；Department of Chemical Physics, the Weizmann Institute of Science（魏茨曼科学研究所化学物理系）
The mechanical response of static, unconfined, overcompressed face centred cubic, granular arrays is studied using large-scale, discrete element method simulations. Specifically, the stress response due to the application of a localised force perturbation - the Green function technique - is obtained in granular packings generated over several orders of magnitude in both the particle friction coefficient and the applied forcing. We observe crossover behaviour in the mechanical state of the system characterised by the changing nature of the resulting stress response. The transition between aniso…
We computationally study the frictional properties of sheared granular media subjected to harmonic vibration applied at the boundary. Such vibrations are thought to play an important role in weakening flows, yet the independent effects of amplitude, frequency, and pressure on the process have remained unclear. Based on a dimensional analysis and DEM simulations, we show that, in addition to a previously proposed criterion for peak acceleration that leads to breaking of contacts, weakening requires the absolute amplitude squared of the displacement is sufficiently large relative to the confinin…
Impact dynamics is measured for spherical and cylindrical projectiles of many different densities dropped onto a variety non-cohesive granular media. The results are analyzed in terms of the material-dependent scaling of the inertial and frictional drag contributions to the total stopping force. The inertial drag force scales similar to that in fluids, except that it depends on the internal friction coefficient. The frictional drag force scales as the square-root of the density of granular medium and projectile, and hence cannot be explained by the combination of granular hydrostatic pressure …
We study agitated frictional disks in two dimensions with the aim of developing a scaling theory for their diffusion over time. As a function of the area fraction $ϕ$ and mean-square velocity fluctuations $\langle v^2\rangle$ the mean-square displacement of the disks $\langle d^2\rangle$ spans 4-5 orders of magnitude. The motion evolves from a subdiffusive form to a complex diffusive behabvior at long times. The statistics of $\langle d^n\rangle$ at all times are multiscaling, since the probability distribution function (pdf) of displacements has very broad wings. Even where a diffusion consta…
In stark contrast to the jamming of frictionless hard-sphere (hard-disk if in two dimensions) packings, the critical jamming of frictional packings is much more elusive and still under intense debate. Here we show that frictional hard-disk packings self-organize near a critical jamming state when subjected to quasi-static steady-state cyclic shear, displaying scale-free fluctuations in particle velocity fields as characterized by the power spectra $E(k)\propto k^{-α}$ for both longitudinal and transverse modes in wavevector space, with $α\approx2.0\pm0.15$, and the nearly flat spectra $E(ω)\pr…
Theoretical treatments of frictional granular matter often assume that it is legitimate to invoke classical elastic theory to describe its coarse-grained mechanical properties. Here we show, based on experiments and numerical simulations, that this is generically not the case since stress auto-correlation functions decay more slowly than the elastic Green's function. It was shown theoretically that standard elastic decay demands pressure and torque density fluctuations to be normal, with possibly one of them being hyperuniform. Generic compressed frictional assemblies exhibit however abnormal …
We introduce a Magnetic Resonance Imaging technique to study the geometry of shear zones of soft, low-frictional and hard, frictional granular materials and their mixtures. Hydrogel spheres serve as the soft, low-frictional material component, while mustard seeds represent rigid, frictional grains. Some of the hydrogel spheres are doped with CuSO4 salt to serve as tracers. A split-bottom shear cell is sheared stepwise and the shear profiles are determined from the differences of tomograms after successive shear steps, using Particle Imaging Velocimetry.We find that the shear zone geometry diff…
This paper addresses the issue of the determination of the frictional stress distribution from the inversion of the measured surface displacement field for sliding interfaces between a glass lens and a rubber (poly(dimethylsiloxane)) substrate. Experimental results show that high lateral strains are achieved at the periphery of the sliding contacts. As a consequence, an accurate inversion of the displacement field requires that finite strains and non linear response of the rubber substrate are taken into account. For that purpose, a Finite Element (FE) inversion procedure is implemented where …
We present an orthotropic elastic analysis of frictional granular layers under gravity by studying their stress response to a localized overload at the layer surface for several substrate tilt angles. The distance to the unjamming transition is controlled by the tilt angle α with respect to the critical angle α_c. We find that the shear modulus of the system decreases with α, but reaches a finite value as αtends to α_c. We also analyze the vibration modes of the system and show that the soft modes play an increasing, though not crucial, role approaching the transition.
The dynamics of amorphous granular matter with frictional interactions cannot be derived in general from a Hamiltonian and therefore displays oscillatory instabilities stemming from the onset of complex eigenvalues in the stability matrix. These instabilities were discovered in the context of one and two dimensional systems, while the three dimensional case was never studied in detail. Here we fill this gap by deriving and demonstrating the presence of oscillatory instabilities in a three dimensional granular packing. We study binary assemblies of spheres of two sizes interacting via classical…
A granular system composed of frictional glass beads is simulated using the Discrete Element Method. The inter-grain forces are based on the Hertz contact law in the normal direction with frictional tangential force. The damping due to collision is also accounted for. Systems are loaded at various stresses and their quasi-static elastic moduli are characterized. Each system is subjected to an extensive dynamic testing protocol by measuring the resonant response to a broad range of AC drive amplitudes and frequencies via a set of diagnostic strains. The system, linear at small AC drive amplitud…
Multi-phase flows encountered in nature or in industry, exhibit non trivial rheological properties, that can be understood better thanks to model materials and appropriate rheometers. Here, we use model unsaturated granular materials: assemblies of frictional spherical particles bonded by a small quantity of a wetting liquid, over a rough inclined plane. Our results show steady uniform flows for a wide range of parameters (the inclination angle and the mass flow-rate). A theoretical model, based on the Mohr-Coulomb yield criterion extended to inertial flows: $τ$ = $τ$c + $μ$(I)P, in which $τ$c…
The linear-frictional contact model is the most commonly used contact mechanism for discrete element (DEM) simulations of granular materials. Linear springs with a frictional slider are used for modeling interactions in directions normal and tangential to the contact surface. Although the model is simple in two dimensions, its implementation in 3D faces certain subtle challenges, and the particle interactions that occur within a single time-step require careful modeling with a robust algorithm. The paper details a 3D algorithm that accounts for the changing direction of the tangential force wi…
The physical mechanisms that bring about the propulsion of a rotating helix in a granular medium are considered. A propulsive motion along the axis of the rotating helix is induced by both symmetry breaking due to the helical shape, and the anisotropic frictional forces undergone by all segments of the helix in the medium. Helix dynamics is studied as a function of helix rotation speed and its geometrical parameters. The effect of the granular pressure and the applied external load were also investigated. A theoretical model is developed based on the anisotropic frictional force experienced by…
Granular flows down inclined channels with smooth boundaries are common in nature and in the industry. Nevertheless, the common setup of flat boundaries has comparatively been much less investigated than the bumpy boundaries one, which is used by most experimental and numerical studies to avoid sliding effects. Using DEM numerical simulations with side walls we recover quantitatively experimental results. At larger angles we predict a rich behavior, including granular convection and inverted density profiles suggesting a Rayleigh-Bénard type of instability. In many aspects flows on a flat base…
