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

Ductile and brittle yielding of athermal amorphous solids: A mean-field paradigm beyond the random-field Ising model

Amorphous solids can yield in either a ductile or brittle manner under strain: plastic deformation can set in gradually, or abruptly through a macroscopic stress drop. Developing a unified theory describing both ductile and brittle yielding constitutes a fundamental challenge of nonequilibrium statistical physics. Recently, it has been proposed that, in the absence of thermal effects, the nature of the yielding transition is controlled by physics akin to that of the quasistatically driven random field Ising model (RFIM), which has served as the paradigm for understanding the effect of quenched disorder in slowly driven systems with short-ranged interactions. However, this theoretical picture neglects both the dynamics of, and the elasticity-induced long-ranged interactions between, the mesoscopic material constituents. Here, we address these two aspects and provide a unified theory building on the Hébraud-Lequeux elastoplastic description. The first aspect is crucial to understanding the competition between the imposed deformation rate and the finite timescale of plastic rearrangements: We provide a dynamical description of the macroscopic stress drop, as well as predictions for the shifting of the brittle yield strain and the scaling of the peak susceptibility with inverse shear rate. The second is essential to capture properly the behavior in the limit of quasistatic driving, where avalanches of plasticity diverge with system size at any value of the strain. We fully characterise the avalanche behavior, which is radically different to that of the RFIM. In the quasistatic, infinite-size limit, we find that both models have mean-field Landau exponents, obscuring the effect of the interactions. We show, however, that the latter profoundly affect the behavior of finite systems approaching the spinodal-like brittle yield point, where we recover qualitatively the finite-size trends found in particle simulations. The interactions also modify the nature of the random critical point separating ductile and brittle yielding, where we predict critical behavior on top of the marginality present at any value of the strain. We finally discuss how all our predictions can be directly tested against particle simulations and eventually experiments, and make first steps in this direction.

Fabric-based jamming phase diagram for frictional granular materials

A jamming phase diagram maps the phase states of granular materials to their intensive properties such as shear stress and density (or packing fraction). We investigate how different phases in a jamming phase diagram of granular materials are related to their fabric structure via three-dimensional discrete element method simulations. Constant-volume quasi-static simple shear tests ensuring uniform shear strain field are conducted on bi-disperse spherical frictional particles. Specimens with different initial solid fractions are sheared until reaching steady state at a large shear strain (200%). The jamming threshold in terms of stress, non-rattler fraction, and coordination numbers (Z's) of different contact networks is discussed. The evolution of fabric anisotropy (F) of each contact network during shearing is also examined. By plotting the fabric data in the F-Z space, a unique critical fabric surface (CFS) becomes apparent across all specimens, irrespective of their initial phase states. Through the correlation of this CFS with fabric signals corresponding to jamming transitions, we introduce a novel jamming phase diagram in the fabric F-Z space, offering a convenient approach to distinguish the various phases of granular materials solely through the direct observation of geometrical arrangements of particles. This jamming phase diagram underscores the importance of the microstructure underlying the conventional jamming phenomenon and introduces a novel standpoint for interpreting the phase transitions of granular materials that have been exposed to processes such as compaction, shearing, and other complex loading histories.

High speed impact on granular media: breakdown of conventional inertial drag models

In this study, we extensively explore the impact process on granular media, particularly focusing on situations where the ratio of impact speed to acoustic speed is on the order of 0.01-1. This range significantly exceeds that considered in existing literature (0.0001-0.001). Our investigation involves a comprehensive comparison between our simulation data, obtained under high-speed conditions, and the established macroscopic drag models. In the high-speed regime, conventional drag force models prove inadequate, and the drag force cannot be separated into a depth-dependent static pressure and a depth-independent inertial drag, as suggested in previous literature. A detailed examination of the impact process in the high-speed limit is also presented, involving the spatio-temporal evolution of the force chain network, displacement field, and velocity field at the particle length scale. Unlike prior works demonstrating the exponential decay of pulses, we provide direct evidence of acoustic pulses propagating over long distances, reflecting from boundaries, and interfering with the original pulses. These acoustic pulses, in turn, induce large scale reorganization of the force chain network, and the granular medium continuously traverses different jammed states to support the impact load. Reorientation of the force chains leads to plastic dissipation and the eventual dissipation of the impact energy. Furthermore, we study the scaling of the early stage peak forces with the impact velocity and find that spatial dimensionality strongly influences the scaling.

Stability of a tilted granular monolayer: How many spheres can we pick before the collapse?

The triggering of avalanches is investigated using discrete element simulations for a process of random extraction of spheres. A monolayer, formed by identical spheres in a hexagonal configuration, is placed on a tilted plane surrounded by a small fence that sustains the spheres, mimicking the disposal of fruits in the market. Then, a random continuous extraction process of spheres is imposed until the collapse. For this simple numerical experiment, a phase diagram was obtained to visualize the occurrence of avalanches triggered by vacancies as a function of the tilting angle, system size, and friction coefficient. More importantly, a subzone was found where we can predict the critical number of extractions until the avalanche takes place. The prediction is made from an evolution model of the average coordination number based on statistical considerations. The theoretical prediction also gives a constant critical void fraction of spheres, which implies the system collapses at a critical packing fraction.

Evolution of force networks during stick-slip motion of an intruder in a granular material: Topological measures extracted from experimental data

In quasi-two-dimensional experiments with photoelastic particles confined to an annular region, an intruder constrained to move in a circular path halfway between the annular walls experiences stick-slip dynamics. We discuss the response of the granular medium to the driven intruder, focusing on the evolution of the force network during sticking periods. Because the available experimental data do not include precise information about individual contact forces, we use an approach developed in our previous work [Basak et al., J. Eng. Mech. 147, 04021100 (2021)0733-939910.1061/(ASCE)EM.1943-7889.0002003] based on networks constructed from measurements of the integrated strain magnitude on each particle. These networks are analyzed using topological measures based on persistence diagrams, revealing that force networks evolve smoothly but in a nontrivial manner throughout each sticking period, even though the intruder and granular particles are stationary. Characteristic features of persistence diagrams show identifiable slip precursors. In particular, the number of generators describing the structure and complexity of force networks increases consistently before slips. Key features of the dynamics are similar for granular materials composed of disks or pentagons, but some details are consistently different. In particular, we find significantly larger fluctuations of the measures computed based on persistence diagrams and, therefore, of the underlying networks, for systems of pentagonal particles.

Compacting an assembly of soft balls far beyond the jammed state: Insights from three-dimensional imaging

Very soft grain assemblies have unique shape-changing capabilities that allow them to be compressed far beyond the rigid jammed state by filling void spaces more effectively. However, accurately following the formation of these systems by monitoring the creation of new contacts, monitoring the changes in grain shape, and measuring grain-scale stresses is challenging. We developed an experimental method that overcomes these challenges and connects their microscale behavior to their macroscopic response. By tracking the local strain energy during compression, we reveal a transition from granular-like to continuous-like material. Mean contact geometry is shown to vary linearly with the packing fraction, which is supported by a mean field approximation. We also validate a theoretical framework which describes the compaction from a local view. Our experimental framework provides insights into the granular micromechanisms and opens perspectives for rheological analysis of highly deformable grain assemblies in various fields ranging from biology to engineering.

Universal behavior in fragmenting brittle, isotropic solids across material properties

A bonded particle model is used to explore how variations in the material properties of brittle, isotropic solids affect critical behavior in fragmentation. To control material properties, a model is proposed which includes breakable two- and three-body particle interactions to calibrate elastic moduli and mode I and mode II fracture toughnesses. In the quasistatic limit, fragmentation leads to a power-law distribution of grain sizes which is truncated at a maximum grain mass that grows as a nontrivial power of system size. In the high-rate limit, truncation occurs at a mass that decreases as a power of increasing rate. A scaling description is used to characterize this behavior by collapsing the mean-square grain mass across rates and system sizes. Consistent scaling persists across all material properties studied, although there are differences in the evolution of grain size distributions with strain as the initial number of grains at fracture and their subsequent rate of production depend on Poisson's ratio. This evolving granular structure is found to induce a unique rheology where the ratio of the shear stress to pressure, an internal friction coefficient, decays approximately as the logarithm of increasing strain rate. The stress ratio also decreases at all rates with increasing strain as fragmentation progresses and depends on elastic properties of the solid.

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.

Cross over to collective rearrangements near the dry-wet transition in two-dimensional foams

Liquid foams respond plastically to external perturbations over some critical magnitude. This rearrangement process is directly related to the mechanical properties of the foams, playing a significant role in determining foam lifetime, deformability, elasticity, and fluidity. In this paper, we experimentally investigate the rearrangement dynamics of foams near a dry-wet transition. When a foam transforms from a dry state to a wet state, it is found that considering collective events, separated T1 events propagate in dry foams, while T1 events occur simultaneously in wet foams. This cross over to collective rearrangements is closely related to the change in local bubble arrangements and mobility. Furthermore, it is also found that a probability of collective rearrangement events occurring follows a Poisson distribution, suggesting that there is little correlation between discrete collective rearrangement events. These results constitute progress in understanding the dynamical properties of soft jammed systems, relevant for biological and material sciences as well as food science.

PhotoElasticFinger: Robot Tactile Fingertip Based on Photoelastic Effect

The sense of touch is fundamental for a one-to-one mapping between the environment and a robot that physically interacts with the environment. Herein, we describe a tactile fingertip design that can robustly detect interaction forces given data collected from a camera. This design is based on the photoelastic effect observed in silicone matter. Under the force applied to the silicone rubber, owing to the stress-induced birefringence, the light propagating within the silicone rubber is subjected to the angular phase shift, where the latter is proportional to the increase in the image brightness in the camera frames. We present the calibration and test results of the photoelastic sensor design on a bench using a robot arm and with a certified industrial force torque sensor. We also discuss the applications of this sensor design and its potential relationship with human mechano-transduction receptors. We achieved a force sensing range of up to 8 N with a force resolution of around 0.5 N. The photoelastic tactile fingertip is suitable for robot grasping and might lead to further progress in robust tactile sensing.

Critical Scaling of Solid Fragmentation at Quasistatic and Finite Strain Rates

Using two-dimensional simulations of sheared, brittle solids, we characterize the resulting fragmentation and explore its underlying critical nature. Under quasistatic loading, a power-law distribution of fragment masses emerges after fracture which grows with increasing strain. With increasing strain rate, the maximum size of a grain decreases and a shallower distribution is produced. We propose a scaling theory for distributions based on a fractal scaling of the largest mass with system size in the quasistatic limit or with a correlation length that diverges as a power of rate in the finite-rate limit. Critical exponents are measured using finite-size scaling techniques.

Experimental validation of a micromechanically based compaction law for mixtures of soft and hard grains

In this Letter, we report on an experimental study which analyzes the compressive behavior of two-dimensional bidisperse granular assemblies made of soft (hyperelastic) and hard grains in varying proportions (κ is the portion of soft grains). By means of a recently developed uniaxial compression setup [Vu and Barés, Phys. Rev. E 100, 042907 (2019)]2470-004510.1103/PhysRevE.100.042907 and using an advanced digital image correlation method, we follow, beyond the jamming point, the evolution of the main mechanical observables, from the global scale down to the strain field inside each deformable grain. First, we validate experimentally and extend to the uniaxial case a recently proposed micromechanical compaction model linking the evolution of the applied pressure P to the packing fraction ϕ [Cantor et al., Phys. Rev. Lett. 124, 208003 (2020)]0031-900710.1103/PhysRevLett.124.208003. Second, we reveal two different linear regimes depending on whether the system is above or below a crossover strain unraveling a transition from a discrete to a continuous-like system. Third, the evolution of these linear laws is found to vary linearly with κ. These results provide a comprehensive experimental and theoretical framework that can now be extended to a more general class of polydisperse soft granular systems.

Relaxation and Aging of Nanosphere Assemblies at a Water-Oil Interface

The relaxation and aging of an assembly of spherical nanoparticles (NPs) at a water-oil interface are characterized in situ by grazing incidence X-ray photon correlation spectroscopy. The dynamics of the interfacial assembly is measured while the interface saturates with NPs. Weak attractions between NPs lead to gel-like structures in the assembly, where the in-plane ordering is inhibited by the broad size distribution of the NPs. Structural rearrangements on the length scale of the NP-NP center-to-center distances proceed by intermittent fluctuations instead of continuous cooperative motions. The coexistence of rapid and slow NP populations is confirmed, as commonly observed in soft glass-forming materials. Dynamics are increasingly slowed as the NPs initially segregate to the locally clustered interface. The structural relaxation of the NPs in these localized clusters is 5 orders of magnitude slower than that of free particles in the bulk. When the interface is nearly saturated, the time for relaxation increases suddenly due to the onset of local jamming, and the dynamics slow exponentially afterward until the system reaches collective jamming by cooperative rearrangements. This investigation provides insights into structural relaxations near the glass transition and the evolution of the structure and dynamics of the assemblies as they transition from an isotropic liquid to a dense disordered film.

Softer than soft: Diving into squishy granular matter

Softer than soft, squishy granular matter is composed of grains capable of significantly changing their shape (typically a deformation larger than 10%) without tearing or breaking. Because of the difficulty to test these materials experimentally and numerically, such a family of discrete systems remains largely ignored in the granular matter physics field despite being commonly found in nature and industry. Either from a numerical, experimental, or analytical point of view, the study of highly deformable granular matter involves several challenges covering, for instance: (i) the need to include a large diversity of grain rheology, (ii) the need to consider large material deformations, and (iii) analysis of the effects of large body distortion on the global scale. In this article, we propose a thorough definition of these squishy granular systems and we summarize the upcoming challenges in their study.

Dynamic Reconfiguration of Compressed 2D Nanoparticle Monolayers

A Gibbs monolayer of jammed, or nearly jammed, spherical nanoparticles was imaged at a liquid surface in real time by in-situ scanning electron microscopy performed at the single-particle level. At nanoparticle areal fractions above that for the onset of two-dimensional crystallization, structural reorganizations of the mobile polymer-coated particles were visualized after a stepwise areal compression. When the compression was small, slow shearing near dislocations and reconfigured nanoparticle bonding were observed at crystal grain boundaries. At larger scales, domains grew as they rotated into registry by correlated but highly intermittent motions. Simultaneously, the areal density in the middle of the monolayer increased. When the compression was large, the jammed monolayers exhibited out-of-plane deformations such as wrinkles and bumps. Due to their large interfacial binding energy, few (if any) of the two-dimensionally mobile nanoparticles returned to the liquid subphase. Compressed long enough (several hours or more), monolayers transformed into solid nanoparticle films, as evidenced by their cracking and localized rupturing upon subsequent areal expansion. These observations provide mechanistic insights into the dynamics of a simple model system that undergoes jamming/unjamming in response to mechanical stress.

Energy exponents of avalanches and Hausdorff dimensions of collapse patterns

A simple numerical model to simulate athermal avalanches is presented. The model is inspired by the "porous collapse" process where the compression of porous materials generates collapse cascades, leading to power law distributed avalanches. The energy (E), amplitude (A_{max}), and size (S) exponents are derived by computer simulation in two approximations. Time-dependent "jerk" spectra are calculated in a single avalanche model where each avalanche is simulated separately from other avalanches. The average avalanche profile is parabolic, the scaling between energy and amplitude follows E∼A_{max}^{2}, and the energy exponent is ε = 1.33. Adding a general noise term in a continuous event model generates infinite avalanche sequences which allow the evaluation of waiting time distributions and pattern formation. We find the validity of the Omori law and the same exponents as in the single avalanche model. We then add spatial correlations by stipulating the ratio G/N between growth processes G (linked to a previous event location) and nucleation processes N (with new, randomly chosen nucleation sites). We found, in good approximation, a power law correlation between the energy exponent ε and the Hausdorff dimension H_{D} of the resulting collapse pattern H_{D}-1∼ɛ^{-3}. The evolving patterns depend strongly on G/N with the distribution of collapse sites equally power law distributed. Its exponent ɛ_{topo} would be linked to the dynamical exponent ε if each collapse carried an energy equivalent to the size of the collapse. A complex correlation between ɛ,ɛ_{topo}, and H_{D} emerges, depending strongly on the relative occupancy of the collapse sites in the simulation box.

Quasistatic kinetic avalanches and self-organized criticality in deviatorically loaded granular media

The behavior of granular media under quasistatic loading has recently been shown to attain a stable evolution state corresponding to a manifold in the space of micromechanical variables. This state is characterized by sudden transitions between metastable jammed states, involving the partial micromechanical rearrangement of the granular medium. Using numerical simulations of two-dimensional granular media under quasistatic biaxial compression, we show that the dynamics in the stable evolution state is characterized by scale-free avalanches well before the macromechanical stationary flow regime traditionally linked to a self-organized critical state. This, together with the nonuniqueness and the nonmonotony of macroscopic deformation curves, suggests that the statistical avalanche properties and the susceptibilities of the system cannot be reduced to a function of the macromechanical state. The associated scaling exponents are nonuniversal and depend on the interactions between particles. For stiffer particles (or samples at low confining pressure) we find distributions of avalanche properties compatible with the predictions of mean-field theory. The scaling exponents decrease below the mean-field values for softer interactions between particles. These lower exponents are consistent with observations for amorphous solids at their critical point. We specifically discuss the relationship between microscopic and macroscopic variables, including the relation between the external stress drop and the internal potential energy released during kinetic avalanches.

Unified view of avalanche criticality in sheared glasses

Plastic events in sheared glasses are considered an example of so-called avalanches, whose sizes obey a power-law probability distribution with the avalanche critical exponent τ. Although the so-called mean-field depinning (MFD) theory predicts a universal value of this exponent, τ_{MFD}=1.5, such a simplification is now known to connote qualitative disagreement with realistic systems. Numerically and experimentally, different values of τ have been reported depending on the literature. Moreover, in the elastic regime, it has been noted that the critical exponent can be different from that in the steady state, and even criticality itself is a matter of debate. Because these confusingly varying results have been reported under different setups, our knowledge of avalanche criticality in sheared glasses is greatly limited. To gain a unified understanding, in this work, we conduct a comprehensive numerical investigation of avalanches in Lennard-Jones glasses under athermal quasistatic shear. In particular, by excluding the ambiguity and arbitrariness that has crept into the conventional measurement schemes, we achieve high-precision measurement and demonstrate that the exponent τ in the steady state follows the prediction of MFD theory, τ_{MFD}=1.5. Our results also suggest that there are two qualitatively different avalanche events. This binariness leads to the nonuniversal behavior of the avalanche size distribution and is likely to be the cause of the varying values of τ reported thus far. To investigate the dependence of criticality and universality on applied shear, we further study the statistics of avalanches in the elastic regime and the ensemble of the first avalanche event in different samples, which provide information about the unperturbed system. We show that while the unperturbed system is indeed off-critical, criticality gradually develops as shear is applied. The degree of criticality is encoded in the fractal dimension of the avalanches, which starts from zero in the off-critical unperturbed state and saturates in the steady state. Moreover, the critical exponent τ is consistent with the prediction of the MFD τ_{MFD} universally, regardless of the amount of applied shear, once the system becomes critical.

The role of friction in statistics and scaling laws of avalanches

We investigate statistics and scaling laws of avalanches in two-dimensional frictional particles by numerical simulations. We find that the critical exponent for avalanche size distributions is governed by microscopic friction between the particles in contact, where the exponent is larger and closer to mean-field predictions if the friction coefficient is finite. We reveal that microscopic "slips" between frictional particles induce numerous small avalanches which increase the slope, as well as the power-law exponent, of avalanche size distributions. We also analyze statistics and scaling laws of the avalanche duration and maximum stress drop rates, and examine power spectra of stress drop rates. Our numerical results suggest that the microscopic friction is a key ingredient of mean-field descriptions and plays a crucial role in avalanches observed in real materials.

Controlling crackling dynamics by triggering low-intensity avalanches

We examine the effect of small, spatially localized excitations applied periodically in different manners, on the crackling dynamics of a brittle crack driven slowly in a heterogeneous solid. When properly adjusted, these excitations are observed to radically modify avalanche statistics and considerably limit the magnitude of the largest events. Surprisingly, this does not require information on the front loading state at the time of excitation; applying it either at a random location or at the most loaded point gives the same results. Subsequently, we unravel how the excitation amplitude, spatial extent, and frequency govern the effect. We find that the excitation efficiency is ruled by a single reduced parameter, namely the injected power per unit front length; the suppression of extreme avalanches is maximum at a well-defined optimal value of this control parameter. analysis opens another way to control the largest events in crackling dynamics. Beyond fracture problems, it may be relevant for crackling systems described by models of the same universality class, such as the wetting of heterogeneous substrates or magnetic walls in amorphous magnets.

Criticality in sheared, disordered solids. I. Rate effects in stress and diffusion

Rate effects in sheared disordered solids are studied using molecular dynamics simulations of binary Lennard-Jones glasses in two and three dimensions. In the quasistatic (QS) regime, systems exhibit critical behavior: the magnitudes of avalanches are power-law distributed with a maximum cutoff that diverges with increasing system size L. With increasing rate, systems move away from the critical yielding point and the average flow stress rises as a power of the strain rate with exponent 1/β, the Herschel-Bulkley exponent. Finite-size scaling collapses of the stress are used to measure β as well as the exponent ν which characterizes the divergence of the correlation length. The stress and kinetic energy per particle experience fluctuations with strain that scale as L^{-d/2}. As the largest avalanche in a system scales as L^{α}, this implies α<d/2. The diffusion rate of particles diverges as a power of decreasing rate before saturating in the QS regime. A scaling theory for the diffusion is derived using the QS avalanche rate distribution and generalized to the finite strain rate regime. This theory is used to collapse curves for different system sizes and confirm β/ν.

Sound damping in soft particle packings: the interplay between configurational disorder and inelasticity

We numerically investigate sound damping in disordered two-dimensional soft particle packings. We simulate evolution of standing waves of particle displacements and analyze time correlation functions of particle velocities and power spectra. We control the strength of inelastic interactions between the particles in contact to show how the inelasticity affects anomalous sound characteristics of disordered systems: Increasing the strength of inelastic interactions, we find that (i) sound softening vanishes and (ii) attenuation coefficients exhibit a transition from the Rayleigh law to quadratic growth. We also report (iii) how the Ioffe-Regel limit frequencies depend on the strength of inelasticity as useful information for experiments and applications of the sound in disordered media. Our findings suggest that sound damping in soft particle packings is determined by the interplay between elastic heterogeneities and inelasticity.

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.

Contact network changes in ordered and disordered disk packings

We investigate the mechanical response of packings of purely repulsive, frictionless disks to quasistatic deformations. The deformations include simple shear strain at constant packing fraction and at constant pressure, "polydispersity" strain (in which we change the particle size distribution) at constant packing fraction and at constant pressure, and isotropic compression. For each deformation, we show that there are two classes of changes in the interparticle contact networks: jump changes and point changes. Jump changes occur when a contact network becomes mechanically unstable, particles "rearrange", and the potential energy (when the strain is applied at constant packing fraction) or enthalpy (when the strain is applied at constant pressure) and all derivatives are discontinuous. During point changes, a single contact is either added to or removed from the contact network. For repulsive linear spring interactions, second- and higher-order derivatives of the potential energy/enthalpy are discontinuous at a point change, while for Hertzian interactions, third- and higher-order derivatives of the potential energy/enthalpy are discontinuous. We illustrate the importance of point changes by studying the transition from a hexagonal crystal to a disordered crystal induced by applying polydispersity strain. During this transition, the system only undergoes point changes, with no jump changes. We emphasize that one must understand point changes, as well as jump changes, to predict the mechanical properties of jammed packings.

Acoustic resonance in periodically sheared glass: damping due to plastic events

Using molecular dynamics simulation, we study acoustic resonance in a low-temperature model glass by applying a small periodic shear at a boundary wall. Shear wave resonance occurs as the frequency ω approaches ωl = πc⊥l/L (l = 1, 2…). Here, c⊥ is the transverse sound speed and L is the cell width. At resonance, large-amplitude sound waves appear after many cycles even if the applied strain γ0 is very small. They then induce plastic events, which are heterogeneous on the mesoscopic scale and intermittent on timescales longer than the oscillation period tp = 2π/ω. We visualize them together with the extended elastic strains around them. These plastic events serve to damp sounds. We obtain the nonlinear damping Q-1 = tan δ due to the plastic events near the first resonance at ω ≅ ω1, which is linear in γ0 and independent of ω. After many resonant cycles, we observe an increase in the shear modulus (measured after switching-off the oscillation). We also observe catastrophic plastic events after a very long time (∼103tp), which induce system-size elastic strains and cause a transition from resonant to off-resonant states. At resonance, stroboscopic diffusion becomes detectable.

Sheared Amorphous Packings Display Two Separate Particle Transport Mechanisms

Shearing granular materials induces nonaffine displacements. Such nonaffine displacements have been studied extensively, and are known to correlate with plasticity and other mechanical features of amorphous packings. A well known example is shear transformation zones as captured by the local deviation from affine deformation, D_{min}^{2}, and their relevance to failure and stress fluctuations. We analyze sheared frictional athermal disc packings and show that there exists at least one additional mesoscopic transport mechanism that superimposes itself on top of local diffusive motion. We evidence this second transport mechanism in a homogeneous system via a diffusion tensor analysis and show that the trace of the diffusion tensor equals the classic D_{min}^{2} when this second mesoscopic transport is corrected for. The new transport mechanism is consistently observed over a wide range of volume fractions and even for particles with different friction coefficients and is consistently observed also upon shear reversal, hinting at its relevance for memory effects.

Asymmetric Damage Avalanche Shape in Quasibrittle Materials and Subavalanche (Aftershock) Clusters

Crackling dynamics is characterized by a release of incoming energy through intermittent avalanches. The shape, i.e., the internal temporal structure of these avalanches, gives insightful information about the physical processes involved. It was experimentally shown recently that progressive damage toward compressive failure of quasibrittle materials can be mapped onto the universality class of interface depinning when considering scaling relationships between the global characteristics of the microcracking avalanches. Here we show, for three concrete materials and from a detailed analysis of the acoustic emission waveforms generated by microcracking events, that the shape of these damage avalanches is strongly asymmetric, characterized by a very slow decay. This remarkable asymmetry, at odds with mean-field depinning predictions, could be explained, in these quasibrittle materials, by retardation effects induced by enhanced viscoelastic processes within a fracture process zone generated by the damage avalanche as it progresses. It is associated with clusters of subavalanches, or aftershocks, within the main avalanche.

Depletion attraction impairs the plasticity of emulsions flowing in a constriction

We study the elasto-plastic behavior of dense attractive emulsions under a mechanical perturbation. The attraction is introduced through non-specific depletion interactions between the droplets and is controlled by changing the concentration of surfactant micelles in the continuous phase. We find that such attractive forces are not sufficient to induce any measurable modification on the scalings between the local packing fraction and the deformation of the droplets. However, when the emulsions are flowed through 2D microfluidic constrictions, we uncover a measurable effect of attraction on their elasto-plastic response. Indeed, we measure higher levels of deformation inside the constriction for attractive droplets. In addition, we show that these measurements correlate with droplet rearrangements that are spatially delayed in the constriction for higher attraction forces.

Intruder in a two-dimensional granular system: Effects of dynamic and static basal friction on stick-slip and clogging dynamics

We present simulation results for an intruder pulled through a two-dimensional granular system by a spring using a model designed to mimic the experiments described by Kozlowski et al. [Phys. Rev. E 100, 032905 (2019)2470-004510.1103/PhysRevE.100.032905]. In that previous study the presence of basal friction between the grains and the base was observed to change the intruder dynamics from clogging to stick-slip. Here we first show that our simulation results are in excellent agreement with the experimental data for a variety of experimentally accessible friction coefficients governing interactions of particles with each other and with boundaries. We then use simulations to explore a broader range of parameter space, focusing on the friction between the particles and the base. We consider both static and dynamic basal friction coefficients, which are difficult to vary smoothly in experiments. The simulations show that dynamic friction strongly affects the stick-slip behavior when the coefficient is decreased below 0.1, while static friction plays only a marginal role.

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.

Force fluctuations at the transition from quasi-static to inertial granular flow

We analyse the rheology of gravity-driven, dry granular flows in experiments where individual forces within the flow bulk are measured. We release photoelastic discs at the top of an incline to create a quasi-static erodible bed over which flows a steady 2D avalanche. The flowing layers we produce are dense (φ ≈ 0.8), thin (h ≈ 10d), and in the slow to intermediate flow regime (I = 0.1 to 1). Using particle tracking and photoelastic force measurements we report coarse-grained profiles for packing fraction, velocity, shear rate, inertial number, and stress tensor components. In addition, we define a quantitative measure for the rate of generation of new force chain networks and we observe that fluctuations extend below the boundary between dense flow and quasi-static layers. Finally, we evaluate several existing definitions for granular fluidity, and make comparisons among them and the behaviour of our experimentally-measured stress tensor components. Our measurements of the non-dimensional stress ratio μ show that our experiments lie within the local rheological regime, yet we observe rearrangements of the force network extending into the quasi-static layer where shear rates vanish. This elucidates why non-local rheological models rely on the notion of stress diffusion, and we thus propose non-local effects may in fact be dependent on the local force network fluctuation rate.

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.

Shear-Jammed, Fragile, and Steady States in Homogeneously Strained Granular Materials

We study the jamming phase diagram of sheared granular material using a novel Couette shear setup with a multiring bottom. The setup uses small basal friction forces to apply a volume-conserving linear shear with no shear band to a granular system composed of frictional photoelastic discs. The setup can generate arbitrarily large shear strain due to its circular geometry, and the shear direction can be reversed, allowing us to measure a feature that distinguishes shear-jammed from fragile states. We report systematic measurements of the stress, strain, and contact network structure at phase boundaries that have been difficult to access by traditional experimental techniques, including the yield stress curve and the jamming curve close to ϕ_{SJ}≈0.75, the smallest packing fraction supporting a shear-jammed state. We observe fragile states created under large shear strain over a range of ϕ<ϕ_{SJ}. We also find a transition in the character of the quasistatic steady flow centered around ϕ_{SJ} on the yield curve as a function of packing fraction. Near ϕ_{SJ}, the average contact number, fabric anisotropy, and nonrattler fraction all show a change of slope. Above ϕ_{F}≈0.7 the steady flow shows measurable deviations from the basal linear shear profile, and above ϕ_{b}≈0.78 the flow is localized in a shear band.

Soft-grain compression: Beyond the jamming point

We present the experimental studies of highly strained soft bidisperse granular systems made of hyperelastic and plastic particles. We explore the behavior of granular matter deep in the jammed state from local field measurement from the grain scale to the global scale. By means of a dedicated digital image correlation code and an accurate image recording method, we measure for each compression step the evolution of the particle geometries and their right Cauchy-Green strain tensor fields. We analyze the evolution of the usual macroscopic observables (stress, packing fraction, coordination, fraction of nonrattlers, etc.) along the compression process through the jamming point and far beyond. Analyzing the evolution of the local strain statistics, we evidence a crossover in the material behavior deep in the jammed state for both sorts of particles. We show that this crossover is due to a competition between material compression, dilation, and shear, so its position depends on the particle material. We argue that the strain field is a reliable observable to describe the evolution of a granular system through the jamming transition and deep in the dense packing state whatever the material behavior.

Seismiclike organization of avalanches in a driven long-range elastic string as a paradigm of brittle cracks

Crack growth in heterogeneous materials sometimes exhibits crackling dynamics, made of successive impulselike events with specific scale-invariant time and size organization reminiscent of earthquakes. Here, we examine this dynamics in a model which identifies the crack front with a long-range elastic line driven in a random potential. We demonstrate that, under some circumstances, fracture grows intermittently, via scale-free impulse organized into aftershock sequences obeying the fundamental laws of statistical seismology. We examine the effects of the driving rate and system overall stiffness (unloading factor) onto the scaling exponents and cutoffs associated with the time and size organization. We unravel the specific conditions required to observe a seismiclike organization in the crack propagation problem. Beyond failure problems, implications of these results to other crackling systems are finally discussed.

Photoelastic study of dense granular free-surface flows

In this study, we perform experiments that reveal the distribution of dynamic forces in the bulk of granular free-surface flows. We release photoelastic disks from an incline to create steady two-dimensional avalanches. These gravity-driven dry granular flows are in the slow to intermediate regime (I≤1), dense (φ≈0.8), and thin (h≈10d). The transition between solidlike (quasisteady) and fluidlike (inertial) regimes is observable for certain experimental settings. We measure constant density and quasilinear velocity profiles through particle tracking at several points down the chute, for two different basal topographies. The photoelastic technique allows the visualization and quantification of instantaneous forces transmitted between particles during individual collisions. From the measured forces we obtain coarse-grained profiles of all stress tensor components at various positions along the chute. The discreteness of the system leads to highly fluctuating individual force chains which form preferentially in the directions of the bulk external forces: in this case, gravity and shear. The behavior of the coarse-grained stress tensor within a dynamic granular flow is analogous to that of a continuous fluid flow, in that we observe a hydrostatic increase of the mean pressure with depth. Furthermore, we identify a preferential direction for the principal stress orientation, which depends on the local magnitudes of the frictional and gravitational forces. These results allow us to draw an analogy between discrete and continuous flow models.

Ice: the paradigm of wild plasticity

Ice plasticity has been thoroughly studied, owing to its importance in glaciers and ice sheets dynamics. In particular, its anisotropy (easy basal slip) has been suspected for a long time, then fully characterized 40 years ago. More recently emerged the interest of ice as a model material to study some fundamental aspects of crystalline plasticity. An example is the nature of plastic fluctuations and collective dislocation dynamics. Twenty years ago, acoustic emission measurements performed during the deformation of ice single crystals revealed that plastic 'flow' proceeds through intermittent dislocation avalanches, power law distributed in size and energy. This means that most of ice plasticity takes place through few, very large avalanches, thus qualifying associated plastic fluctuations as 'wild'. This launched an intense research activity on plastic intermittency in the Material Science community. The interest of ice in this debate is reviewed, from a comparison with other crystalline materials. In this context, ice appears as an extreme case of plastic intermittency, characterized by scale-free fluctuations, complex space and time correlations as well as avalanche triggering. In other words, ice can be considered as the paradigm of wild plasticity. This article is part of the theme issue 'The physics and chemistry of ice: scaffolding across scales, from the viability of life to the formation of planets'.

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.

Transition rates for slip-avalanches in soft athermal disks under quasi-static simple shear deformations

We study slip-avalanches in two-dimensional soft athermal disks by quasi-static simulations of simple shear deformations. Sharp drops in shear stress, or slip-avalanches, are observed intermittently during steady state. Such stress drops are caused by restructuring of the contact networks, accompanied by drastic changes of the interaction forces, Δf. The changes of the forces happen heterogeneously in space, indicating that collective non-affine motions of the disks are most pronounced when slip-avalanches occur. We analyze and predict the statistics for the force changes, Δf, by transition rates of the contact forces and angles, where slip-avalanches are characterized by wide power-law tails. We find that the transition rates are described by a q-Gaussian distribution regardless of the area fraction of the disks. Because the transition rates quantify structural changes of the force-chains, our findings are an important step towards linking macroscopic observations to a microscopic theory of slip-avalanches in the experimentally accessible quasi-static regime.

Crackling to periodic dynamics in granular media

We study the local and global dynamics of sheared granular materials in a stick-slip experiment, using a slider and a spring. The system crackles, with intermittent slip avalanches, or exhibits irregular or periodic dynamics, depending on the shear rate and loading stiffness. The global force on the slider during shearing captures the transitions from the crackling to the periodic regime. We deduce a dynamic phase diagram as a function of the shear rate and the loading stiffness and associated scaling laws. Using photoelastic particles, we also capture the grain-scale stress evolution, and investigate the microscopic behavior in the different regimes.

Crackling Dynamics in the Mechanical Response of Knitted Fabrics

Crackling noise, which occurs in a wide range of situations, is characterized by discrete events of various sizes, often correlated in the form of avalanches. We report experimental evidence that the mechanical response of a knitted fabric displays such broadly distributed events both in the force signal and in the deformation field, with statistics analogous to that of earthquakes or soft amorphous materials. A knit consists of a regular network of frictional contacts, linked by the elasticity of the yarn. When deformed, the fabric displays spatially extended avalanchelike yielding events resulting from collective interyarn contact slips. We measure the size distribution of these avalanches, at the stitch level from the analysis of nonelastic displacement fields and externally from force fluctuations. The two measurements yield consistent power law distributions reminiscent of those found in other avalanching systems. Our study shows that a knitted fabric is not only a thread-based metamaterial with highly sought after mechanical properties, but also an original, model system, with topologically protected structural order, where an intermittent, scale-invariant response emerges from minimal ingredients, and thus a significant landmark in the study of out-of-equilibrium universality.

Anisotropic particles strengthen granular pillars under compression

We probe the effects of particle shape on the global and local behavior of a two-dimensional granular pillar, acting as a proxy for a disordered solid, under uniaxial compression. This geometry allows for direct measurement of global material response, as well as tracking of all individual particle trajectories. In general, drawing connections between local structure and local dynamics can be challenging in amorphous materials due to lower precision of atomic positions, so this study aims to elucidate such connections. We vary local interactions by using three different particle shapes: discrete circular grains (monomers), pairs of grains bonded together (dimers), and groups of three bonded in a triangle (trimers). We find that dimers substantially strengthen the pillar and the degree of this effect is determined by orientational order in the initial condition. In addition, while the three particle shapes form void regions at distinct rates, we find that anisotropies in the local amorphous structure remain robust through the definition of a metric that quantifies packing anisotropy. Finally, we highlight connections between local deformation rates and local structure.