Self-organized criticality in a sheared granular stick-slip system

Stochastic methods for slip prediction in a sheared granular system

We consider a sheared granular system experiencing intermittent dynamics of stick-slip type via discrete element simulations. The considered setup consists of a two-dimensional system of soft frictional particles sandwiched between solid walls, one of which is exposed to a shearing force. The slip events are detected using stochastic state space models applied to various measures describing the system. The amplitudes of the events spread over more than four decades and present two distinctive peaks, one for the microslips and the other for the slips. We show that the measures describing the forces between the particles provide earlier detection of an upcoming slip event than the measures based solely on the wall movement. By comparing the detection times obtained from the considered measures, we observe that a typical slip event starts with a local change in the force network. However, some local changes do not spread globally over the force network. For the changes that become global, we find that their size strongly influences the further behavior of the system. If the size of a global change is large enough, then it triggers a slip event; if it is not, then a much weaker microslip follows. Quantification of the changes in the force network is made possible by formulating clear and precise measures describing their static and dynamic properties.

Mechanical excitation and marginal triggering during avalanches in sheared amorphous solids

We study plastic strain during individual avalanches in overdamped particle-scale molecular dynamics (MD) and mesoscale elastoplastic models (EPM) for amorphous solids sheared in the athermal quasistatic limit. We show that the spatial correlations in plastic activity exhibit a short length scale that grows as t^{3/4} in MD and ballistically in EPM, which is generated by mechanical excitation of nearby sites not necessarily close to their stability thresholds, and a longer lengthscale that grows diffusively for both models and is associated with remote marginally stable sites. These similarities in spatial correlations explain why simple EPMs accurately capture the size distribution of avalanches observed in MD, though the temporal profiles and dynamical critical exponents are quite different.

Adhesion as a trigger of droplet polarization in flowing emulsions

Tissues are subjected to large external forces and undergo global deformations during morphogenesis. We use synthetic analogues of tissues to study the impact of cell-cell adhesion on the response of cohesive cellular assemblies under such stresses. In particular, we use biomimetic emulsions in which the droplets are functionalized in order to exhibit specific droplet-droplet adhesion. We flow these emulsions in microfluidic constrictions and study their response to this forced deformation via confocal microscopy. We find that the distributions of avalanche sizes are conserved between repulsive and adhesive droplets. However, adhesion locally impairs the rupture of droplet-droplet contacts, which in turn pulls on the rearranging droplets. As a result, adhesive droplets are a lot more deformed along the axis of elongation in the constriction. This finding could shed light on the origin of polarization processes during morphogenesis.

On the Mechanism of Laboratory Earthquake Nucleation Highlighted by Acoustic Emission

Dynamics of granular media is the key to understanding behavior of many natural systems. In this work we concentrate on studying regularities of deformation of a gouge-filled fault. Confined granular layer – model fault – subjected to an external stress may display sudden slip owing to rearrangement of the granular layer. In nature fast slip along a fault results in an earthquake. To understand fault behavior better, we have conducted a comprehensive analysis of acoustic emission (AE) data that accompany stick-slip in granular media. Here we reveal and trace the emergence of two populations of AE. The first one is characterized by a waveform with a harsh onset, while the second one exhibits a gradual amplitude rise and a tremor-like waveform. During a regular stick-slip the statistical properties of the first population remains intact. The second one is very sensitive to alterations of stress conditions, and its scaling parameters correlate with the change of mechanical characteristics of the fault. Probably, AE populations were identified corresponding to two gouge-filled fault subsystems – a load-bearing granular network and an ensemble of relatively unloaded grains in the granular layer. The detected regularities point to a compound self-organization processes in fault zones and suggest that the final stage of earthquake preparation can be revealed in analyzing the scaling characteristics of seismic-acoustic data.

Structural relaxation affecting shear-transformation avalanches in metallic glasses

Avalanche behaviors, characterized by power-law statistics and structural relaxation that induces shear localization in amorphous plasticity, play an essential role in deciding the mechanical properties of amorphous metallic solids (i.e., metallic glasses). However, their interdependence is still not fully understood. To investigate the influence of structural relaxation on elementary avalanche behavior, we perform molecular-dynamics simulations for the shear deformation test of metallic glasses using two typical metallic-glass models comprising a less-relaxed (as-quenched) glass and a well-relaxed (well-aged) glass exhibiting a relatively homogeneous deformation and a shear-band-like heterogeneous deformation, respectively. The data on elementary avalanches obtained from both glass models follow the same power-law statistics with different maximum event sizes, and the well-relaxed glass shows shear localization. Evaluating the spatial correlation functions of the nonaffine squared displacements of atoms during each elementary avalanche event, we observe that the shapes of the elementary avalanche regions in the well-relaxed glasses tend to be anisotropic, whereas those in the less-relaxed glasses are relatively isotropic. Furthermore, we demonstrate that a temporal clustering in the direction of the avalanche propagation emerges, and a considerable correlation between the anisotropy and avalanche size exists in the well-relaxed glass model.

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.

Dynamics of a grain-scale intruder in a two-dimensional granular medium with and without basal friction

We report on a series of experiments in which a grain-sized intruder is pushed by a spring through a two-dimensional granular material composed of photoelastic disks in a Couette geometry. We study the intruder dynamics as a function of packing fraction for two types of supporting substrates: A frictional glass plate and a layer of water for which basal friction forces are negligible. We observe two dynamical regimes: Intermittent flow, in which the intruder moves freely most of the time but occasionally gets stuck, and stick-slip dynamics, in which the intruder advances via a sequence of distinct, rapid events. When basal friction is present, we observe a smooth crossover between the two regimes as a function of packing fraction, and we find that reducing the interparticle friction coefficient causes the stick-slip regime to shift to higher packing fractions. When basal friction is eliminated, we observe intermittent flow at all accessible packing fractions. For all cases, we present results for the statistics of stick events, the intruder velocity, and the force exerted on the intruder by the grains. Our results indicate the qualitative importance of basal friction at high packing fractions and suggest a possible connection between intruder dynamics in a static material and clogging dynamics in granular flows.

Seismicity in sheared granular matter

We report on experiments investigating the dynamics of a slider that is pulled by a spring across a granular medium consisting of a vertical layer of photoelastic disks. The motion proceeds through a sequence of discrete events, analogous to seismic shocks, in which elastic energy stored in the spring is rapidly released. We measure the statistics of several properties of the individual events: the energy loss in the spring, the duration of the movement, and the temporal profile of the slider motion. We also study certain conditional probabilities and the statistics of mainshock-aftershock sequences. At low driving rates, we observe crackling with Omori-Utsu, Båth, and waiting time laws similar to those observed in seismic dynamics. At higher driving rates, where the sequence of events shows strong periodicity, we observe scaling laws and asymmetrical event shapes that are clearly distinguishable from those in the crackling regime.

Local and global avalanches in a two-dimensional sheared granular medium

We present the experimental and numerical studies of a two-dimensional sheared amorphous material composed of bidisperse photoelastic disks. We analyze the statistics of avalanches during shear including the local and global fluctuations in energy and changes in particle positions and orientations. We find scale-free distributions for these global and local avalanches denoted by power laws whose cutoffs vary with interparticle friction and packing fraction. Different exponents are found for these power laws depending on the quantity from which variations are extracted. An asymmetry in time of the avalanche shapes is evidenced along with the fact that avalanches are mainly triggered by the shear bands. A simple relation independent of the intensity is found between the number of local avalanches and the global avalanches they form. We also compare these experimental and numerical results for both local and global fluctuations to predictions from mean-field and depinning theories.

Universal slip dynamics in metallic glasses and granular matter - linking frictional weakening with inertial effects

Slowly strained solids deform via intermittent slips that exhibit a material-independent critical size distribution. Here, by comparing two disparate systems - granular materials and bulk metallic glasses - we show evidence that not only the statistics of slips but also their dynamics are remarkably similar, i.e. independent of the microscopic details of the material. By resolving and comparing the full time evolution of avalanches in bulk metallic glasses and granular materials, we uncover a regime of universal deformation dynamics. We experimentally verify the predicted universal scaling functions for the dynamics of individual avalanches in both systems, and show that both the slip statistics and dynamics are independent of the scale and details of the material structure and interactions, thus settling a long-standing debate as to whether or not the claim of universality includes only the slip statistics or also the slip dynamics. The results imply that the frictional weakening in granular materials and the interplay of damping, weakening and inertial effects in bulk metallic glasses have strikingly similar effects on the slip dynamics. These results are important for transferring experimental results across scales and material structures in a single theory of deformation dynamics.

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.

Common dependence on stress for the statistics of granular avalanches and earthquakes

Both earthquake size-distributions and aftershock decay rates obey power laws. Recent studies have demonstrated the sensibility of their parameters to faulting properties such as focal mechanism, rupture speed or fault complexity. The faulting style dependence may be related to the magnitude of the differential stress, but no model so far has been able to reproduce this behaviour. Here we investigate the statistical properties of avalanches in a dissipative, bimodal particulate system under slow shear. We find that the event size-distribution obeys a power law only in the proximity of a critical volume fraction, whereas power-law aftershock decay rates are observed at all volume fractions accessible in the model. Then, we show that both the exponent of the event size-distribution and the time delay before the onset of the power-law aftershock decay rate are decreasing functions of the shear stress. These results are consistent with recent seismological observations of earthquake size-distribution and aftershock statistics.

Avalanche contribution to shear modulus of granular materials

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∼(ϕ-ϕJ)(1/2) and G∼γ0(-1/2)(ϕ-ϕJ) for a linear spring model of the elastic interaction between contacting grains, where ϕ, ϕJ, and γ0 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-ϕJ can be understood by slip avalanches.

Size and density avalanche scaling near jamming

The current microscopic picture of plasticity in amorphous materials assumes local failure events to produce displacement fields complying with linear elasticity. Indeed, the flow properties of nonaffine systems, such as foams, emulsions and granular materials close to jamming, that produce a fluctuating displacement field when failing, are still controversial. Here we show, via a thorough numerical investigation of jammed materials, that nonaffinity induces a critical scaling of the flow properties dictated by the distance to the jamming point. We rationalize this critical behavior by introducing a new universal jamming exponent and hyperscaling relationships, and we use these results to describe the volume fraction dependence of the friction coefficient.

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.

Solid-on-solid single-block dynamics under mechanical vibration

The suppression of friction between sliding objects, modulated or enhanced by mechanical vibrations, is well established. However, the precise conditions of occurrence of these phenomena are not well understood. Here we address these questions focusing on a simple spring-block model, which is relevant to investigate friction both at the atomistic as well as the macroscopic scale. This allows us to investigate the influence on friction of the properties of the external drive, of the geometry of the surfaces over which the block moves, and of the confining force. Via numerical simulations and a theoretical study of the equations of motion, we identify the conditions under which friction is suppressed and/or recovered, and we evidence the critical role played by surface modulations and by the properties of the confining force.

Observation of spatio-temporal structure in stick-slip motion of an adhesive gel sheet

We studied the sliding friction between an adhesive gel sheet and a glass substrate. In this system, the probability distribution of the force drop obeys a power law similar to that found in earthquakes and granular systems. We observed the motion of the slip regions at the frictional interfaces and obtained the spatial distributions of shear strain by image analysis. The frictional force evaluated by the image analysis is in good agreement with the actual force measured by a load cell. This indicates that the present method provides a powerful tool to study the spatio-temporal structure in the heterogeneous stick-slip motions in sliding friction.

Unjamming dynamics: the micromechanics of a seismic fault model

The unjamming transition of granular systems is investigated in a seismic fault model via three dimensional molecular dynamics simulations. A two-time force-force correlation function, and a susceptibility related to the system response to pressure changes, allow us to characterize the stick-slip dynamics, consisting in large slips and microslips leading to creep motion. The correlation function unveils the micromechanical changes occurring both during microslips and slips. The susceptibility encodes the magnitude of the incoming microslip.

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.

Regular to chaotic transition of stick-slip motion in sliding friction of an adhesive gel-sheet

Spatio-temporal pattern of the stick-slip motion of a gel-sheet pulled on a glass substrate is observed. The sliding takes place via the propagation of the wave of detachment (Schallamach wave). At large pull velocity, the detached region is a stripe which moves regularly with constant speed and the frictional force shows a periodic time dependence. As the pull velocity is decreased, the detached region is separated into bubbles which move around irregularly. In the irregular state, the frictional force shows chaotic time dependence and the statistics of the event of the force drop obeys a power law similar to the Gutenberg-Richter law known in earthquakes. In the regular region, the detachment wave is analyzed theoretically and the velocity and lengths are obtained as a function of the pull velocity. The transition from the regular to chaotic behavior is shown to be related to the spontaneous wetting of the gel.

Ultra-low breakdown voltage and origin of 1/f(2) noise in metallic nanorod arrays

The application of a dc voltage to an array of copper nanorods causes field evaporation of atoms from the tips, resulting in their progressive sharpening and a further increase in the local field. The process is self-limited by the build-up of space charge on the nanorod tips. From an analysis of the conductance noise recorded across the nanorod array, we show that the conduction mechanism bears a strong analogy with the stick-slip problem in sliding friction. The in situ sharpening results in an unprecedented lowering of the breakdown voltage of air by over 90%, as compared to plane parallel electrodes.

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.

Assessment of long-range correlation in time series: how to avoid pitfalls

Due to the ubiquity of time series with long-range correlation in many areas of science and engineering, analysis and modeling of such data is an important problem. While the field seems to be mature, three major issues have not been satisfactorily resolved. (i) Many methods have been proposed to assess long-range correlation in time series. Under what circumstances do they yield consistent results? (ii) The mathematical theory of long-range correlation concerns the behavior of the correlation of the time series for very large times. A measured time series is finite, however. How can we relate the fractal scaling break at a specific time scale to important parameters of the data? (iii) An important technique in assessing long-range correlation in a time series is to construct a random walk process from the data, under the assumption that the data are like a stationary noise process. Due to the difficulty in determining whether a time series is stationary or not, however, one cannot be 100% sure whether the data should be treated as a noise or a random walk process. Is there any penalty if the data are interpreted as a noise process while in fact they are a random walk process, and vice versa? In this paper, we seek to gain important insights into these issues by examining three model systems, the autoregressive process of order 1, on-off intermittency, and Lévy motions, and considering an important engineering problem, target detection within sea-clutter radar returns. We also provide a few rules of thumb to safeguard against misinterpretations of long-range correlation in a time series, and discuss relevance of this study to pattern recognition.

Shear stress fluctuations in the granular liquid and solid phases

We report on experimentally observed shear stress fluctuations in both granular solid and fluid states, showing that they are non-Gaussian at low shear rates, reflecting the predominance of correlated structures (force chains) in the solidlike phase, which also exhibit finite rigidity to shear. Peaks in the rigidity and the stress distribution's skewness indicate that a change to the force-bearing mechanism occurs at the transition to fluid behavior, which, it is shown, can be predicted from the behavior of the stress at lower shear rates. In the fluid state stress is Gaussian distributed, suggesting that the central limit theorem holds. The fiber bundle model with random load sharing effectively reproduces the stress distribution at the yield point and also exhibits the exponential stress distribution anticipated from extant work on stress propagation in granular materials.

Slowly sheared dense granular flows: crystallization and nonunique final states

Simultaneous time-resolved measurements of internal structure, granular volume, and boundary shear force are reported for dense granular packing steadily sheared under a fixed normal load. We identify features of the crystallization transition for a deep shear flow, whose height-dependent local mean velocity spans more than five orders of magnitude. This structural change is accompanied by a significant decrease of granular volume and shear force, with a more rapid falloff of particle velocity with depth than occurs in the disordered state. Boundary conditions can have a profound influence on the crystallization of the entire packing. We find that continuously sheared flow can exhibit nonunique final states even under identical boundary conditions; a few cycles of oscillatory pretreatment can initiate states that evolve into either a crystallized or a disordered final state after long-term unidirectional shearing. On the other hand, the disordered state can be stabilized after being sufficiently compacted by unidirectional shear. These experiments raise interesting questions about how prior history is recorded in the internal structure of granular packings, affecting their instantaneous rheology and long-term evolution in response to shear.

Intermittency of energy in rapid granular shear flows

Hard-disk simulations are used for two-dimensional rapid granular shear flows of circular disks between two rotating cylinders. The intermittency effects associated with the rate of the energy dissipation of collisions are studied. The statistics of intermittent signals of energy dissipation reveals that a power law governs the dynamics of rapid shear granular flows. A dynamical system approach based on the Gledzer-Ohkitani-Yamada shell model of turbulence is employed to reproduce signals for energy dissipation that are statistically consistent with those from simulations. The results suggest that rapid granular flows can be analyzed by appropriate turbulent models.

Basin of attraction of a bounded self-organized critical state

The robustness of the self-organized critical (SOC) state observed in the motion of an annular plate rotating over a granular medium is studied in this paper. In particular, we investigate the effect of parameters to which the emergent SOC state may be sensitive, including the initialization scheme, driving velocity, and confining pressure. The results indicate that the critical state is not a universal attractor, but has a finite basin of attraction. Furthermore, this state is only one of the three observed, which compare well with subcritical, critical, and supercritical states. The results call into question the precise definition of the term "self-organized criticality," an issue we address.