Disordered solids respond to quasistatic shear with intermittent avalanches of plastic activity, an example of the crackling noise observed in many nonequilibrium critical systems. The temporal power spectrum of activity within disordered solids consists of three distinct domains: a novel power-law rise with frequency at low frequencies indicating anticorrelation, white-noise at intermediate frequencies, and a power-law decay at high frequencies. As the strain rate increases, the white-noise regime shrinks and ultimately disappears as the finite strain rate restricts the maximum size of an avalanche. A new strain-rate- and system-size-dependent scaling theory is derived for power spectra in both the quasistatic and finite-strain-rate regimes. This theory is validated using data from overdamped two- and three-dimensional molecular dynamics simulations. We identify important exponents in the yielding transition including the dynamic exponent $z$ which relates the size of an avalanche to its duration, the fractal dimension of avalanches, and the exponent characterizing the divergence in correlations with strain rate. Results are related to temporal correlations within a single avalanche and between multiple avalanches.
We investigate avalanches associated with plastic rearrangements and the nature of structural change in the prototypical strong glass, silica, computationally. Although qualitative aspects of yielding in silica are similar to other glasses, we find that the statistics of avalanches exhibits non-trivial behaviour. Investigating the statistics of avalanches and clusters in detail, we propose and verify a new relation between exponents characterizing the size distribution of avalanches and clusters. Across the yielding transition, anomalous structural change and densification, associated with a s…
We study plastic strain during individual avalanches in overdamped particle-scale molecular dynamics (MD) and meso-scale elasto-plastic models (EPM) for amorphous solids sheared in the athermal quasi-static limit. We show that the spatial correlations in plastic activity exhibit a short lengthscale that grows as $t^{3/4}$ in MD and ballistically in EPM, and 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 similari…
We present the experimental and numerical studies of a 2D sheared amorphous material constituted of bidisperse photo-elastic 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 cut-offs vary with inter-particle 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 ava…
Under applied shear strain, granular and amorphous materials deform via particle rearrangements, which can be small and localized or organized into system-spanning avalanches. While the statistical properties of avalanches under quasi-static shear are well-studied, the dynamics during avalanches is not. In numerical simulations of sheared soft spheres, we find that avalanches can be decomposed into bursts of localized deformations, which we identify using an extension of persistent homology methods. We also study the linear response of unstable systems during an avalanche, demonstrating that e…
Using numerical simulations, we perform an extensive finite-size analysis of the transverse diffusion coefficient in a sheared 2D amorphous solid, over a broad range of strain rates, at temperatures up to the supercooled liquid regime. We thus obtain direct qualitative evidence for the persistence of correlations between elementary plastic events up to the vicinity of the glass transition temperature $T_g$. A quantitative analysis of the data, combined with a previous study of the $T$- and $\dotγ$-dependence of the macroscopic stress \cite{ChattorajCaroliLemaitre2010}, leads us to conclude tha…
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 mean-field theory predicts a universal value of this exponent, $τ_{\rm MF}=1.5$, numerical simulations have reported different values 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 were reported under differen…
We study the statistical properties of the yielding transition in model amorphous solids in the limit of slow, athermal deformation. Plastic flow occurs via alternating phases of elastic loading punctuated by rapid dissipative events in the form of collective avalanches. We investigate their characterization through energy vs. stress drops and at multiple stages of deformation, thus revealing a change of spatial extent of the avalanches and degree of stress correlations as deformation progresses. We show that the statistics of stress and energy drops only become comparable for large events in …
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 $β$ …
Molecular dynamics simulations with varying damping are used to examine the effects of inertia and spatial dimension on sheared disordered solids in the athermal, quasistatic limit. In all cases the distribution of avalanche sizes follows a power law over at least three orders of magnitude in dissipated energy or stress drop. Scaling exponents are determined using finite-size scaling for systems with thousands to millions of particles. Three distinct universality classes are identified corresponding to overdamped and underdamped limits, as well as a crossover damping that separates the two reg…
We investigate a rheological property of a dense granular material under shear. By a numerical experiment of the system with constant volume, we find a critical volume fraction at which the shear stress and the pressure behave as power-law functions of the shear strain rate. We also present a simple scaling argument that determines the power-law exponents. Using these results, we interpret a power-law behavior observed in the system under constant pressure.
The behavior of granular media under quasi-static 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 regim…
We present a two-dimensional system which exhibits features of self-organized criticality. The avalanches which occur on the surface of a pile of rice are found to exhibit finite size scaling in their probability distribution. The critical exponents are $τ$ = 1.21(2) for the avalanche size distribution and $D$ = 1.99(2) for the cut-off size. Furthermore the geometry of the avalanches is studied leading to a fractal dimension of the active sites of $d_B$ = 1.58(2). Using a set of scaling relations, we can calculate the roughness exponent $α= D - d_B$ = 0.41(3) and the dynamic exponent $z = D(2 …
Zero-temperature Avalanche Criticality Governing Dynamical Heterogeneity in Supercooled Liquids
Toyota Central R&D Labs., Inc.（丰田中央研究所）；D3 Center, The University of Osaka（大阪大学D3中心）；Department of Physics, The University of Osaka（大阪大学物理系）；Department of Physics, Nagoya University（名古屋大学物理系）；Division of Chemical Engineering, Graduate School of Engineering Science, The University of Osaka（大阪大学工学研究科化学工程专修）
The penetration of magnetic flux into a thin film of YBa$_2$Cu$_3$O$_{7-x}$ is studied when the external field is ramped slowly. In this case the flux penetrates in bursts or avalanches. The size of these avalanches is distributed according to a power law with an exponent of $τ$ = 1.29(2). The additional observation of finite-size scaling of the avalanche distributions, with an avalanche dimension D = 1.89(3), gives strong indications towards self-organized criticality in this system. Furthermore we determine exponents governing the roughening dynamics of the flux surface using some universal …
Potential energy landscape picture of zero-temperature avalanche criticality governing dynamics in supercooled liquids
Toyota Central R&D Labs., Inc.（丰田中央研究所）；D3 Center, The University of Osaka（大阪大学D3中心）；Department of Physics, The University of Osaka（大阪大学物理系）；Department of Physics, Nagoya University（名古屋大学物理系）；Division of Chemical Engineering, Graduate School of Engineering Science, The University of Osaka（大阪大学工学研究科化学工程专攻）
We study the nature of the frictional jamming transition within the framework of rigidity percolation theory. Slowly sheared frictional packings are decomposed into rigid clusters and floppy regions with a generalization of the pebble game including frictional contacts. We discover a second-order transition controlled by the emergence of a system-spanning rigid cluster accompanied by a critical cluster size distribution. Rigid clusters also correlate with common measures of rigidity. We contrast this result with frictionless jamming, where the rigid cluster size distribution is noncritical.
The local and global dynamics of a sheared granular medium are studied in a model experiment as a function of several macroscopic parameters. We observe that by changing the shear rate or the loading stiffness, the system crackles, with intermittent slip avalanches, or exhibits periodic motion. By analyzing the global force, induced while shearing, we capture the transition from the crackling to the periodic regime and associated scaling laws. We deduce a novel dynamic phase diagram as a function of the shear rate and the system's stiffness. Using photo-elasticimetry, we also capture the grain…
Simulations are used to determine the effect of inertia on athermal shear of a two-dimensional binary Lennard-Jones glass. In the quasistatic limit, shear occurs through a series of rapid avalanches. The distribution of avalanches is analyzed using finite-size scaling with thousands to millions of particles. Inertia takes the system to a new underdamped universality class rather than driving the system away from criticality. Scaling exponents are determined for the underdamped and overdamped limits and a critical damping that separates the two regimes. Systems are in the overdamped universalit…
It is a common belief that power-law distributed avalanches are inherently unpredictable. This idea affects phenomena as diverse as evolution, earthquakes, superconducting vortices, stock markets, etc; from atomic to social scales. It mainly comes from the concept of ``Self-organized criticality" (SOC), where criticality is interpreted in the way that at any moment, any small avalanche can eventually cascade into a large event. Nevertheless, this work demonstrates experimentally the possibility of avalanche prediction in the classical paradigm of SOC: a sandpile. By knowing the position of eve…
We study stress time series caused by plastic avalanches in athermally sheared disordered materials. Using particle-based simulations and a mesoscopic elasto-plastic model, we analyze size and shear-rate dependence of the stress-drop durations and size distributions together with their average temporal shape. We find critical exponents different from mean-field predictions, and a clear asymmetry for individual avalanches. We probe scaling relations for the rate dependency of the dynamics and we report a crossover towards mean-field results for strong driving.
Much recent effort has focused on glassy and jamming properties of spherical particles. Very little is known about such phenomena for non-spherical particles, and we take a first step by studying ellipses. We find important differences between the dynamical and structural properties of disks and two-dimensional ellipses subject to continuous Couette shear. In particular, ellipses show slow dynamical evolution, without a counterpart in disks, in the mean velocity, local density, orientational order, and local stress. starting from an unjammed state, ellipses can first jam under shear, and then …
In a model of self-organized criticality unstable sites discharge to just one of their neighbors. For constant discharge ratio $α$ and for a certain range of values of the input energy, avalanches are simple branchless Pólya random walks, and their scaling properties can be derived exactly. If $α$ fluctuates widely enough, avalanches become branched, due to multiple discharges, and behave like those of the stochastic sandpile. At the threshold for branched behaviour, peculiar scaling and anomalous diffusive transport are observed.
We study hidden scale invariance in the glassy phase of the Kob-Andersen binary Lennard-Jones system. After cooling below the glass transition, we generate a so-called isomorph from the fluctuations of potential energy and virial in the NVT ensemble -- a set of density, temperature pairs for which structure and dynamics are identical when expressed in appropriate reduced units. To access dynamical features we shear the system using the SLLOD algorithm coupled with Lees-Edwards boundary conditions, and study the statistics of stress fluctuations and the particle displacements transverse to the …
Thermal activation drives a finite-size crossover from scale-free to runaway avalanches in amorphous solids
Instituto de Física del Sur (IFISUR), Universidad Nacional del Sur (UNS), CONICET（南方物理研究所，南国立大学，阿根廷国家科学研究委员会）；Instituto de Nanociencia y Nanotecnología, CNEA–CONICET, Centro Atómico Bariloche（纳米科学与技术研究所，巴里洛切原子能委员会-阿根廷国家科学研究委员会，巴里洛切原子中心）
This paper presents experimental evidence and theoretical models supporting that dry friction stick-slip is described by self-organized criticality. We use the data, obtained with a pin-on-disc tribometer set to measure lateral force to examine the variation of the friction force as a function of time. We study nominally flat surfaces of aluminum and steel. The probability distribution of force jumps follows a power law with exponents $μ$ in the range 2.2 -- 5.4. The frequency power spectrum follows a $1/{f^α}$ pattern with $α$ in the range 1 -- 2.6. In addition, we present an explanation of t…
