Shear stress fluctuations in the granular liquid and solid phases

Breakdown of Scaling and Friction Weakening in Intermittent Granular Flow

Many materials are produced, processed and stored as grains, while granularity of matter can be crucial in triggering potentially catastrophic geological events like landslides, avalanches and earthquakes. The response of grain assemblies to shear stress is therefore of utmost relevance to both human and natural environment. At low shear rate a granular system flows intermittently by distinct avalanches. In such state the avalanche velocity in time is expected to follow a symmetrical and universal average behavior, whose dependence on the slip size reduces to a scale factor. Analyzing data from long lasting experiments, we observe a breakdown of this scaling: While in short slips velocity shows indeed a self-similar and symmetric profile, it does not in long slips. The investigation of frictional response in these different regimes evidences that this breakdown can be traced back to the onset of a friction weakening, which is of dynamical origin and can amplify instabilities exactly in this critical state, the most frequent state for natural hazards.

Flow-Arrest Transitions in Frictional Granular Matter

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 creep to a statically stable state. The onset of arrest below critical shear stress occurs at a time t_{c} that exhibits a heavy-tailed distribution, whose mean and variance diverge as a power law at the critical shear stress with a friction-dependent exponent that also exhibits a crossover between low and high friction. These observations indicate that granular arrest near critical shear stress is highly unpredictable and is strongly influenced by interparticle friction.

Force fluctuations on a wall in interaction with a granular lid-driven cavity flow

The force fluctuations experienced by a boundary wall subjected to a lid-driven cavity flow are investigated by means of numerical simulations based on the discrete-element method. The time-averaged dynamics inside the cavity volume and the resulting steady force on the wall are governed by the boundary macroscopic inertial number, the latter being derived from the shearing velocity and the confinement pressure imposed at the top. The force fluctuations are quantified through measuring both the autocorrelation of force time series and the distributions of grain-wall forces, at distinct spatial scales from particle scale to wall scale. A key result is that the grain-wall force distributions are entirely driven by the boundary macroscopic inertial number, whatever the spatial scale considered. In particular, when the wall scale is considered, the distributions are found to evolve from nearly exponential to nearly Gaussian distributions by decreasing the macroscopic inertial number. The transition from quasistatic to dense inertial flow is well identified through remarkable changes in the shapes of the distributions of grain-wall forces, accompanied by a loss of system memory in terms of the mesoscale force transmitted toward the wall.

Increasing 'ease of sliding' also increases friction: when is a lubricant effective?

We investigate experimentally the effective Coulomb friction exerted by a granular medium on a shearing plate, varying the medium depth. The plate is driven by a spring connected to a motor turning at a constant speed and, depending on the system configuration, performs continuous sliding or stick and slip in different proportions. We introduce an order parameter which discriminates between the different regimes expressing the fraction of time spent in slipping. At low driving speed, starting from zero layers of interstitial granular material, the average friction coefficient decreases when a few layers are added, while the order parameter stays close to zero. By further increasing the granular depth, the friction undergoes a sudden increase but the order parameter does not change notably. At an intermediate driving speed, however, both the friction and the order parameter undergo a sudden increase, which for the order parameter amounts to several orders of magnitude, indicating that the plate is more braked but nevertheless keeps sliding more easily. For medium-high driving speeds, full sliding is obtained for only one layer of interstitial matter, where friction has a minimum, and is maintained for all increasing depths while friction increases. These observations show that the ease of slipping is not determined by friction alone, rather by the highly complex interplay between driving velocity, friction, and the depth of the medium.

Fast Physically Accurate Rendering of Multimodal Signatures of Distributed Fracture in Heterogeneous Materials

This paper proposes a fast, physically accurate method for synthesizing multimodal, acoustic and haptic, signatures of distributed fracture in quasi-brittle heterogeneous materials, such as wood, granular media, or other fiber composites. Fracture processes in these materials are challenging to simulate with existing methods, due to the prevalence of large numbers of disordered, quasi-random spatial degrees of freedom, representing the complex physical state of a sample over the geometric volume of interest. Here, I develop an algorithm for simulating such processes, building on a class of statistical lattice models of fracture that have been widely investigated in the physics literature. This algorithm is enabled through a recently published mathematical construction based on the inverse transform method of random number sampling. It yields a purely time domain stochastic jump process representing stress fluctuations in the medium. The latter can be readily extended by a mean field approximation that captures the averaged constitutive (stress-strain) behavior of the material. Numerical simulations and interactive examples demonstrate the ability of these algorithms to generate physically plausible acoustic and haptic signatures of fracture in complex, natural materials interactively at audio sampling rates.

High-velocity drag friction in granular media near the jamming point

Drag friction that acts on a disk in a two-dimensional granular medium is studied at high packing fractions. We concentrate on a high-velocity region, in which the dynamic component of the force, obtained as an average of a strongly fluctuating force, clearly scales with velocity squared. We find that the total force composed of dynamic and static components, as well as its fluctuation, diverges with practically the same exponent as the packing fraction approaches the jamming point. To explain the critical behavior, we propose a simple theory equipped with a diverging length scale, which agrees well with the data and elucidates physical pictures for the divergence.

Influence of vibration amplitude on dynamic triggering of slip in sheared granular layers

We perform a systematic statistical investigation of the effect of harmonic boundary vibrations on a sheared granular layer undergoing repetitive, fully dynamic stick-slip motion. The investigation is performed using two-dimensional discrete element method simulations. The main objective consists of improving the understanding of dynamic triggering of slip events in the granular layer. Here we focus on how the vibration amplitude affects the statistical properties of the triggered slip events. The results provide insight into the granular physical controls of dynamic triggering of failure in sheared granular layers.

Fiber bundle models for stress release and energy bursts during granular shearing

Fiber bundle models (FBMs) offer a versatile framework for representing transitions from progressive to abrupt failure in disordered material. We report a FBM-based description of mechanical interactions and associated energy bursts during shear deformation of granular materials. For strain-controlled shearing, where elements fail in a sequential order, we present analytical expressions for strain energy release and failure statistics. Results suggest that frequency-magnitude characteristics of fiber failure vary considerably throughout progressive shearing. Predicted failure distributions were in good agreement with experimentally observed shear stress fluctuations and associated bursts of acoustic emissions. Experiments also confirm a delayed release of acoustic emission energy relative to shear stress buildup, as anticipated by the model. Combined with data-rich acoustic emission measurements, the modified FBM offers highly resolved contact-scale insights into granular media dynamics of shearing processes.

Journey of an intruder through the fluidization and jamming transitions of a dense granular media

We study experimentally the motion of an intruder dragged into an amorphous monolayer of horizontally vibrated grains at high packing fractions. This motion exhibits two transitions. The first transition separates a continuous motion regime at comparatively low packing fractions and large dragging force from an intermittent motion one at high packing fraction and low dragging force. Associated to these different motions, we observe a transition from a linear rheology to a stiffer response. We thereby call "fluidization" this first transition. A second transition is observed within the intermittent regime when the intruder's motion is made of intermittent bursts separated by long waiting times. We observe a peak in the relative fluctuations of the intruder's displacements and a critical scaling of the burst amplitudes' distributions. This transition occurs at the jamming point phi(J) defined as the point where the static pressure (i.e., the pressure measured in the absence of vibration) vanishes. Investigating the motion of the surrounding grains, we show that below the fluidization transition, there is a permanent wake of free volume behind the intruder. This transition is marked by the evolution of the reorganization patterns around the intruder, which evolve from compact aggregates in the flowing regime to long-range branched shapes in the intermittent regime, suggesting an increasing role of the stress fluctuations. Remarkably, the distributions of the kinetic energy of these reorganization patterns also exhibit a critical scaling at the jamming transition.

Creep motion of an intruder within a granular glass close to jamming

We experimentally study the dynamics of an intruder dragged at a constant force in a horizontally vibrated monolayer of grains. At moderate packing fractions, the intruder moves rapidly as soon as the force is applied. Above some threshold value it has an intermittent creep motion with strong fluctuations reminiscent of "crackling noise". These fluctuations are critical at the jamming transition varphi_{J} unveiled in a previous study. The transition separates a regime with local free volume rearrangements from a regime where the displacement field is strongly heterogeneous and resembles force chain patterns.

Modeling the rheology of suspensions with high-viscosity solvents: a predictive multiscale approach

In this paper, a multiscale approach spanning atomistic and mesoscopic regimes to model the rheology of suspensions that have strongly interacting particles in highly viscous solvents is presented. The model suspensions studied here have 65% sucrose solution-a Newtonian fluid with a viscosity of 170 cP at room temperature-as the solvent phase with ceramic particles of sizes on the order of a few microms as the dispersed (solute) phase. A multiscale approach is proposed to quantitatively account for the effect of the properties of constituent materials on the bulk rheology of the suspension apart from the effect of hydrodynamic factors. A dissipative particle dynamics-type particle-based approach is adopted to which material-specific, mesoscopic force fields developed using molecular dynamics are fed. Issues pertaining to the handling of the vast spectrum of time and length scales present and an appropriate Gallilean-invariant thermostat for solvent dynamics are addressed and resolved. Numerical calculations compare reasonably well to experimentally measured viscosities up to reasonably high Peclet numbers (approximately 10(4)).

Transition from rolling to jamming in thin granular layers

We study the granular jamming transition for sheared layers of spherical beads ranging in thickness from 1 to 3 times the grain diameter d. As the layer thickness increases slightly above d, the measured friction jumps discontinuously from 0.02 to >0.1, marking the transition from rolling to jamming. Above a critical layer thickness for jamming, the effective granular pressure displays a power law increase with thickness. For thin layers, friction and P increases as the packing fraction decreases near the jamming transition, in contrast to expectations for bulk granular matter.

Spreading of a granular droplet

The influence of controlled vibrations on the granular rheology is investigated in a specifically designed experiment in which a granular film spreads under the action of horizontal vibrations. A nonlinear diffusion equation is derived theoretically that describes the evolution of the deposit shape. A self-similar parabolic shape (the "granular droplet") and a spreading dynamics are predicted that both agree quantitatively with the experimental results. The theoretical analysis is used to extract effective friction coefficients between the base and the granular layer under sustained and controlled vibrations. A shear thickening regime characteristic of dense granular flows is evidenced at low vibration energy, both for glass beads and natural sand. Conversely, shear thinning is observed at high agitation.

Brownian forces in sheared granular matter

We present results from a series of experiments on a granular medium sheared in a Couette geometry and show that their statistical properties can be computed in a quantitative way from the assumption that the resultant from the set of forces acting in the system performs a Brownian motion. The same assumption has been utilized, with success, to describe other phenomena, such as the Barkhausen effect in ferromagnets, and so the scheme suggests itself as a more general description of a wider class of driven instabilities.