The yielding transition in amorphous solids under oscillatory shear deformation

Two-dimensional squishy glass: yielding under oscillatory shear

The yielding response to an imposed oscillatory shear is investigated for a model two-dimensional dense glass composed of bidisperse, deformable polymer rings, with the ring stiffness being the control parameter. In the quiescent glassy state, the more flexible rings exhibit a broader spectrum of shape fluctuations, which becomes increasingly constrained with increasing ring stiffness. Under shear, the highly packed rings yield, i.e. the thermal assembly loses rigidity, with the threshold yield strain increasing significantly with decreasing ring stiffness. Further, the rings display significant deviations in their shape compared to their unsheared counterparts. This study provides insights into the interplay between shape changes and translational rearrangements under shear, thus contributing to the understanding of yielding transition in densely packed, deformable polymer systems.

Protocol dependence for avalanches under constant stress in elastoplastic models

Close to the yielding transition, amorphous solids exhibit a jerky dynamics characterized by plastic avalanches. The statistics of these avalanches have been measured experimentally and numerically using a variety of different triggering protocols, assuming that all of them were equivalent for this purpose. In particular, two main classes of protocols have been studied, deformation under controlled strain or under controlled stress. In this work, we investigate different protocols to generate plasticity avalanches and conduct two-dimensional simulations of an elastoplastic model to examine the protocol dependence of avalanche statistics in yield-stress fluids. We demonstrate that when stress is controlled, the value and even the existence of the exponent governing the probability distribution function of avalanche sizes strongly depend on the protocol chosen to initiate avalanches. This confirms in finite dimension a scenario presented in a previous mean-field analysis. We identify a consistent stress-controlled protocol whose associated avalanches differ from the quasi-static ones in their fractal dimension and dynamical exponent. Remarkably, this protocol also seems to satisfy the scaling relations among exponents previously proposed. Our results underscore the necessity for a cautious interpretation of avalanche universality within elastoplastic models, and more generally within systems where several control parameters exist.

Avalanches in Cu-Zr-Al metallic glasses

Metallic glasses have mechanical properties, which exhibit avalanches in the disguise of stress drops. We study these phenomena in a classical metallic glass system Cu-Zr-Al by athermal quasistatic shear and varying the element concentrations and for pure Cu-Zr 50/50 case the cooling rate. The resulting mechanical properties are close to the behavior found experimentally. At small strains, the pristine systems are akin to other glassy systems with a so-called gap distribution with a small positive exponent. Critical avalanching behavior is found only approaching the yield point. The post-yield stress drops are universal, and the gap distribution becomes flat.

Vibrational lifetimes and viscoelastic properties of ultrastable glasses

Amorphous solids are viscoelastic. They dissipate energy when deformed at finite rate and finite temperature. We here use analytic theory and molecular simulations to demonstrate that linear viscoelastic dissipation can be directly related to the static and dynamic properties of the fundamental vibrational excitations of an amorphous system. We study ultrastable glasses that do not age, i.e., that remain in stable minima of the potential energy surface at finite temperature. Our simulations show four types of vibrational modes, which differ in spatial localization, similarity to plane waves and vibrational lifetimes. At frequencies below the Boson peak, the viscoelastic response can be split into contributions from plane-wave and quasilocalized modes. We derive a parameter-free expression for the viscoelastic storage and loss moduli for both of these modes. Our results show that the dynamics of microscopic dissipation, in particular the lifetimes of the modes, determine the viscoelastic response only at high frequency. Quasilocalized modes dominate the linear viscoelastic response at intermediate frequencies below the Boson peak.

Unified Understanding of Nonlinear Rheology near the Jamming Transition Point

When slowly sheared, jammed packings respond elastically before yielding. This linear elastic regime becomes progressively narrower as the jamming transition point is approached, and rich nonlinear rheologies such as shear softening and hardening or melting emerge. However, the physical mechanism of these nonlinear rheologies remains elusive. To clarify this, we numerically study jammed packings of athermal frictionless soft particles under quasistatic shear γ. We find the universal scaling behavior for the ratio of the shear stress σ and the pressure P, independent of the preparation protocol of the initial configurations. In particular, we reveal shear softening σ/P∼γ^{1/2} over an unprecedentedly wide range of strain up to the yielding point, which a simple scaling argument can rationalize.

Interplay between an Absorbing Phase Transition and Synchronization in a Driven Granular System

Absorbing phase transitions (APTs) are widespread in nonequilibrium systems, spanning condensed matter, epidemics, earthquakes, ecology, and chemical reactions. APTs feature an absorbing state in which the system becomes entrapped, along with a transition, either continuous or discontinuous, to an active state. Understanding which physical mechanisms determine the order of these transitions represents a challenging open problem in nonequilibrium statistical mechanics. Here, by numerical simulations and mean-field analysis, we show that a quasi-2D vibrofluidized granular system exhibits a novel form of APT. The absorbing phase is observed in the horizontal dynamics below a critical packing fraction, and can be continuous or discontinuous based on the emergent degree of synchronization in the vertical motion. Our results provide a direct representation of a feasible experimental scenario, showcasing a surprising interplay between dynamic phase transition and synchronization.

From creep to flow: Granular materials under cyclic shear

When unperturbed, granular materials form stable structures that resemble the ones of other amorphous solids like metallic or colloidal glasses. Whether or not granular materials under shear have an elastic response is not known, and also the influence of particle surface roughness on the yielding transition has so far remained elusive. Here we use X-ray tomography to determine the three-dimensional microscopic dynamics of two granular systems that have different roughness and that are driven by cyclic shear. Both systems, and for all shear amplitudes Γ considered, show a cross-over from creep to diffusive dynamics, indicating that rough granular materials have no elastic response and always yield, in stark contrast to simple glasses. For the system with small roughness, we observe a clear dynamic change at Γ ≈ 0.1, accompanied by a pronounced slowing down and dynamical heterogeneity. For the large roughness system, the dynamics evolves instead continuously as a function of Γ. We rationalize this roughness dependence using the potential energy landscape of the systems: The roughness induces to this landscape a micro-corrugation with a new length scale, whose ratio over the particle size is the relevant parameter. Our results reveal the unexpected richness in relaxation mechanisms for real granular materials.

Loss of memory of an elastic line on its way to limit cycles

Oscillatory-driven amorphous materials forget their initial configuration and converge to limit cycles. Here we investigate this memory loss under a nonquasistatic drive in a minimal model system, with quenched disorder and memory encoded in a spatial pattern, where oscillating protocols are formally replaced by a positive-velocity drive. We consider an elastic line driven athermally in a quenched disorder with biperiodic boundary conditions and tunable system size, thus controlling the area swept by the line per cycle as would the oscillation amplitude. The convergence to disorder-dependent limit cycle is strongly coupled to the nature of its velocity dynamics depending on system size. Based on the corresponding phase diagram, we propose a generic scenario for memory formation in disordered systems under finite driving rate.

Reversible-to-irreversible transition of colloidal polycrystals under cyclic athermal quasistatic deformation

Cyclic loading on granular packings and amorphous media exhibits a transition from reversible elastic behavior to irreversible plasticity. The present study compares the irreversibility transition and microscopic details of colloidal polycrystals under oscillatory tensile-compressive and shear strain. Under both modes, the systems exhibit a reversible to irreversible transition. However, the strain amplitude at which the transition is observed is larger in the shear strain than in the tensile-compressive mode. The threshold strain amplitude is confirmed by analyzing the dynamical properties, such as mobility and atomic strain (von Mises shear strain and the volumetric strain). The structural changes are quantified using a hexatic order parameter. Under both modes of deformation, dislocations and grain boundaries in polycrystals disappear, and monocrystals are formed. We also recognize the dislocation motion through grains. The key difference is that strain accumulates diagonally in oscillatory tensile-compressive deformation, whereas in shear deformation, strain accumulation is along the x or y axis.

Analysis of the heat transfer fluctuations in the Rayleigh-Bénard convection of concentrated emulsions with finite-size droplets

Employing numerical simulations, we provide an accurate insight into the heat transfer mechanism in the Rayleigh-Bénard convection of concentrated emulsions with finite-size droplets. We focus on the unsteady dynamics characterizing the thermal convection of these complex fluids close to the transition from conductive to convective states, where the heat transfer phenomenon, expressed in terms of the Nusselt number Nu, is characterized by pronounced fluctuations triggered by collective droplet motion [F. Pelusi et al., Soft Matter, 2021, 17(13), 3709-3721]. By systematically increasing the droplet concentration, we show how these fluctuations emerge along with the segregation of "extreme events" in the boundary layers, causing intermittent bursts in the heat flux fluctuations. Furthermore, we quantify the extension S and the duration of the coherent droplet motion accompanying these extreme events via a suitable statistical analysis involving the droplet displacements. We show how the increase in droplet concentration results in a power-law behaviour of the probability distribution function of S and and how this outcome is robust at changing the analysis protocol. Our work offers a comprehensive picture, linking macroscopic heat transfer fluctuations with the statistics of droplets at the mesoscale.

Bond Orientation-Determined Enthalpic Stress in Polymer Glasses upon Deformation

The mechanical properties of polymer glass are determined by both intermolecular local packing structures and aligned intrachain configurations. These configurations involve multiple space scales, and the underlying mechanism is not well understood yet. By applying mechanical stimulation to cold-drawn polymer glasses, the present simulation work shows a one-to-one correspondence between arising retractive stress and the segment orientation parameter on the length scale of the intrachain connecting bond. Such retractive stress is a newly produced enthalpic stress when segment orientation on the length scale of bonds and particle mobility coexist. This reveals a potential mechanism of how the intrachain orientation on the length scale of bonds influences the mechanical behaviors of polymer glasses.

Investigation of the yielding transition in concentrated colloidal systems via rheo-XPCS

We probe the microstructural yielding dynamics of a concentrated colloidal system by performing creep/recovery tests with simultaneous collection of coherent scattering data via X-ray Photon Correlation Spectroscopy (XPCS). This combination of rheology and scattering allows for time-resolved observations of the microstructural dynamics as yielding occurs, which can be linked back to the applied rheological deformation to form structure-property relations. Under sufficiently small applied creep stresses, examination of the correlation in the flow direction reveals that the scattering response recorrelates with its predeformed state, indicating nearly complete microstructural recovery, and the dynamics of the system under these conditions slows considerably. Conversely, larger creep stresses increase the speed of the dynamics under both applied creep and recovery. The data show a strong connection between the microstructural dynamics and the acquisition of unrecoverable strain. By comparing this relationship to that predicted from homogeneous, affine shearing, we find that the yielding transition in concentrated colloidal systems is highly heterogeneous on the microstructural level.

Theory of rigidity and numerical analysis of density of states of two-dimensional amorphous solids with dispersed frictional grains in the linear response regime

Using the Jacobian matrix, we obtain a theoretical expression of rigidity and the density of states of two-dimensional amorphous solids consisting of frictional grains in the linear response to an infinitesimal strain, in which we ignore the dynamical friction caused by the slip processes of contact points. The theoretical rigidity agrees with that obtained by molecular dynamics simulations. We confirm that the rigidity is smoothly connected to the value in the frictionless limit. We find that there are two modes in the density of states for sufficiently small k_{T}/k_{N}, which is the ratio of the tangential to normal stiffness. Rotational modes exist at low frequencies or small eigenvalues, whereas translational modes exist at high frequencies or large eigenvalues. The location of the rotational band shifts to the high-frequency region with an increase in k_{T}/k_{N} and becomes indistinguishable from the translational band for large k_{T}/k_{N}.

An exact expression of three-body system for the complex shear modulus of frictional granular materials

We propose a simple model comprising three particles to study the nonlinear mechanical response of jammed frictional granular materials under oscillatory shear. Owing to the introduction of the simple model, we obtain an exact analytical expression of the complex shear modulus for a system including many monodispersed disks, which satisfies a scaling law in the vicinity of the jamming point. These expressions perfectly reproduce the shear modulus of the many-body system with low strain amplitudes and friction coefficients. Even for disordered many-body systems, the model reproduces the results by introducing a single fitting parameter.

Eigenvalue analysis of stress-strain curve of two-dimensional amorphous solids of dispersed frictional grains with finite shear strain

The stress-strain curve of two-dimensional frictional dispersed grains interacting with a harmonic potential without considering the dynamical slip under a finite strain is determined by using eigenvalue analysis of the Hessian matrix. After the configuration of grains is obtained, the stress-strain curve based on the eigenvalue analysis is in almost perfect agreement with that obtained by the simulation, even if there are plastic deformations caused by stress avalanches. Unlike the naive expectation, the eigenvalues in our model do not indicate any precursors to the stress-drop events.

Coupled Dynamical Phase Transitions in Driven Disk Packings

Under the influence of oscillatory shear, a monolayer of frictional granular disks exhibits two dynamical phase transitions: a transition from an initially disordered state to an ordered crystalline state and a dynamic active-absorbing phase transition. Although there is no reason a priori for these to be at the same critical point, they are. The transitions may also be characterized by the disk trajectories, which are nontrivial loops breaking time-reversal invariance.

Annealing glasses by cyclic shear deformation

A major challenge in simulating glassy systems is the ability to generate configurations that may be found in equilibrium at sufficiently low temperatures, in order to probe static and dynamic behavior close to the glass transition. A variety of approaches have recently explored ways of surmounting this obstacle. Here, we explore the possibility of employing mechanical agitation, in the form of cyclic shear deformation, to generate low energy configurations in a model glass former. We perform shear deformation simulations over a range of temperatures, shear rates, and strain amplitudes. We find that shear deformation induces faster relaxation toward low energy configurations, or overaging, in simulations at sufficiently low temperatures, consistently with previous results for athermal shear. However, for temperatures at which simulations can be run until a steady state is reached with or without shear deformation, we find that the inclusion of shear deformation does not result in any speed up of the relaxation toward low energy configurations. Although we find the configurations from shear simulations to have properties indistinguishable from an equilibrium ensemble, the cyclic shear procedure does not guarantee that we generate an equilibrium ensemble at a desired temperature. In order to ensure equilibrium sampling, we develop a hybrid Monte Carlo algorithm that employs cyclic shear as a trial generation step and has acceptance probabilities that depend not only on the change in internal energy but also on the heat dissipated (equivalently, work done). We show that such an algorithm, indeed, generates an equilibrium ensemble.

Anisotropic correlations of plasticity on the yielding of metallic glasses

We report computer simulations on the shear deformation of CuZr metallic glasses at zero and room temperatures. Shear bands emerge in athermal alloys at strain γ_{c}, with a finite-size effect found. The correlation of nonaffine displacement exhibits an exponential decay even after yielding in thermal alloys, but transits to a power law at γ>γ_{c} in athermal ones. The algebraic exponent is around -1 for the decay inside shear bands, consistent with the theoretical prediction in random elastic media. We quantify the anisotropic correlation with harmonic projection, finding the spectrum is weak in the exponential-decay regime, while it displays a strong polar and quadrupolar symmetry in the power-law regime. The nonvanishing quadrupolar symmetry at long distance signifies the nonlocality of plastic correlation in the athermal alloys. In contrast, the plastic correlation was found to be isotropic and localized at the yielding in the thermal alloys without shear bands.

Rheological response of a glass-forming liquid having large bidispersity

Using extensive numerical simulations, we investigate the flow behaviour of a model glass-forming binary mixture whose constituent particles have a large size ratio. The rheological response to applied shear is studied in the regime where the larger species are spatially predominant. We demonstrate that the macroscopic rigidity that emerges with increasing density occurs in the regime where the larger species undergo a glass transition while the smaller species continue to be highly diffusive. We analyse the interplay between the timescale imposed by the shear and the quiescent relaxation dynamics of the two species to provide a microscopic insight into the observed rheological response. Finally, by tuning the composition of the mixture, we illustrate that the systematic insertion of the smaller particles affects the rheology by lowering of viscosity of the system.

Softening and Residual Loss Modulus of Jammed Grains under Oscillatory Shear in an Absorbing State

From a theoretical study of the mechanical response of jammed materials comprising frictionless and overdamped particles under oscillatory shear, we find that the material becomes soft, and the loss modulus remains nonzero even in an absorbing state where any irreversible plastic deformation does not exist. The trajectories of the particles in this region exhibit hysteresis loops. We succeed in clarifying the origin of the softening of the material and the residual loss modulus with the aid of Fourier analysis. We also clarify the roles of the yielding point in the softening to distinguish the plastic deformation from reversible deformation in the absorbing state.

Mean-Field Theory of Yielding under Oscillatory Shear

We study a mean field elastoplastic model, embedded within a disordered landscape of local yield barriers, to shed light on the behavior of athermal amorphous solids subject to oscillatory shear. We show that the model presents a genuine dynamical transition between an elastic and a yielded state, and qualitatively reproduces the dependence on the initial degree of annealing found in particle simulations. For initial conditions prepared below the analytically derived threshold energy, we observe a nontrivial, nonmonotonic approach to the yielded state. The timescale diverges as one approaches the yielding point from above, which we identify with the fatigue limit. We finally discuss the connections to brittle yielding under uniform shear.

Cooperative effects driving the multi-periodic dynamics of cyclically sheared amorphous solids

When subject to cyclic forcing, amorphous solids can reach periodic, repetitive states, where the system behaves plastically, but the particles return to their initial positions after one or more forcing cycles, where the latter response is called multi-periodic. It is known that plasticity in amorphous materials is mediated by local rearrangements called ``soft spots' or ``shear transformation zones'.Experiments and simulations indicate that soft spots can be modeled as hysteretic two-state entities interacting via quadrupolar displacement fields generated when they switch states and that these interactions can give rise to multi-periodic behavior. However, how interactions facilitate multi-periodicity is unknown. Here we show, using a model of random interacting two-state systems and molecular dynamics simulations, that multi-periodicity arises from oscillations in the magnitudes of the switching field of soft spots which cause soft spots to be active during some forcing cycles and idle during others. We demonstrate that these oscillations result from cooperative effects facilitated by the frustrated interactions between the soft spots. The presence of such mechanisms has implications for manipulating memory in frustrated hysteretic systems.

Avalanches, Clusters, and Structural Change in Cyclically Sheared Silica Glass

We investigate avalanches and clusters associated with plastic rearrangements and the nature of structural change in the prototypical strong glass, silica, computationally. We perform a detailed analysis of avalanches, and of spatially disconnected clusters that constitute them, for a wide range of system sizes. Although qualitative aspects of yielding in silica are similar to other glasses, the statistics of clusters exhibits significant differences, which we associate with differences in local structure. Across the yielding transition, anomalous structural change and densification, associated with a suppression of tetrahedral order, is observed to accompany strain localization.

Reversible to Irreversible Transitions for Cyclically Driven Particles on Periodic Obstacle Arrays

We examine the collective dynamics of disks moving through a square array of obstacles under cyclic square wave driving. Below a critical density we find that system organizes into a reversible state in which the disks return to the same positions at the end of every drive cycle. Above this density, the dynamics are irreversible and the disks do not return to the same positions after each cycle. The critical density depends strongly on the angle θ between the driving direction and a symmetry axis of the obstacle array, with the highest critical densities appearing at commensurate angles such as θ=0{degree sign} and θ=45{degree sign} and the lowest critical densities falling at θ=arctan(0.618), the inverse of the golden ratio, where the flow is the most frustrated. As the density increases, the number of cycles required to reach a reversible state grows as a power law with an exponent near ν=1.36, similar to what is found in periodically driven colloidal and superconducting vortex systems.

Turbulent-like velocity fluctuations in two-dimensional granular materials subject to cyclic shear

We perform a systematic experimental study to investigate the velocity fluctuations in the two-dimensional granular matter of low and high friction coefficients subjected to cyclic shear of a range of shear amplitudes, whose velocity fields are strikingly turbulent-like with vortices of different scales. The scaling behaviors of both the transverse velocity power spectra E_T(k) ∝ k^-α_T and, more severely, the longitudinal velocity power spectra E_L(k) ∝ k^-α_L are affected by the prominent peak centered around k ≈ 2π of the inter-particle distance due to the static structure factor of the hard-particle nature in contrast to the real turbulence. To reduce the strong peak effect to the actual values of α_ν (the subscript 'ν' refers to either T or L), we subsequently analyze the second-order velocity structure functions of S(2)ν(r) in real space, which show the power-law scalings of S(2)ν(r) ∝ r^β_ν for both modes. From the values of β_ν, we deduce the corresponding α_ν from the scaling relations of α_ν = β_ν + 2. The deduced values of α_ν increase continuously with the shear amplitude γ_m, showing no signature of yielding transition, and are slightly larger than α_ν = 2.0 at the limit of γ_m → 0, which corresponds to the elastic limit of the system, for all γ_m. The inter-particle friction coefficients show no significant effect on the turbulent-like velocity fluctuations. Our findings suggest that the turbulent-like collective particle motions are governed by both the elasticity and plasticity in cyclically sheared granular materials.

Metastability as a Mechanism for Yielding in Amorphous Solids under Cyclic Shear

We consider the yielding behavior of amorphous solids under cyclic shear deformation and show that it can be mapped into a random walk in a confining potential with an absorbing boundary. The resulting dynamics is governed by the first passage time into the absorbing state and suffices to capture the essential qualitative features recently observed in atomistic simulations of amorphous solids. Our results provide insight into the mechanism underlying yielding and its robustness. When the possibility of activated escape from absorbing states is added, it leads to a unique determination of a threshold energy and yield strain, suggesting thereby an appealing approach to understanding fatigue failure.

Emergent Fractal Energy Landscape as the Origin of Stress-Accelerated Dynamics in Amorphous Solids

The ageing dynamics in a multiplicity of metastable glasses are investigated at various thermomechanical conditions. By using data analytics to deconvolute the integral effects of environmental factors (e.g., energy level, temperature, stress), and by directly scrutinizing the minimum energy pathways for local excitations, we demonstrate external shear would make the system's energy landscape surprisingly fractal and create an emergent low-barrier mode with highly tortuous pathways, leading to an accelerated relaxation. This finding marks a departure from the classic picture of shear-induced simple bias of energy landscape. The insights and implications of this study are also discussed.

Critical yielding rheology: from externally deformed glasses to active systems

We use extensive computer simulations to study the yielding transition under two different loading schemes: standard simple shear dynamics and self-propelled dense active systems. In the active systems, a yielding transition toward an out-of-equilibrium flowing state known as the liquid phase is observed when self-propulsion is increased. The range of self-propulsions in which this pure liquid regime exists appears to vanish upon approaching the so-called 'jamming point' at which the solidity of soft-sphere packings is lost. Such an 'active yielding' transition shares similarities with the generic yielding transition for shear flows. A Herschel-Bulkley law is observed along the liquid regime in both loading scenarios, with a clear difference in the critical scaling exponents between the two, suggesting the existence of different universality classes for the yielding transition under different driving conditions. In addition, we present the direct measurements of growing length and time scales for both driving scenarios. A comparison with theoretical predictions from the recent literature reveals poor agreement with our numerical results.

Critical behavior of density-driven and shear-driven reversible-irreversible transitions in cyclically sheared vortices

Random assemblies of particles subjected to cyclic shear undergo a reversible–irreversible transition (RIT) with increasing a shear amplitude d or particle density n, while the latter type of RIT has not been verified experimentally. Here, we measure the time-dependent velocity of cyclically sheared vortices and observe the critical behavior of RIT driven by vortex density B as well as d. At the critical point of each RIT, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$B_{\mathrm {c}}$$\end{document}Bc and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_{\mathrm {c}}$$\end{document}dc, the relaxation time \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau $$\end{document}τ to reach the steady state shows a power-law divergence. The critical exponent for B-driven RIT is in agreement with that for d-driven RIT and both types of RIT fall into the same universality class as the absorbing transition in the two-dimensional directed-percolation universality class. As d is decreased to the average intervortex spacing in the reversible regime, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau (d)$$\end{document}τ(d) shows a significant drop, indicating a transition or crossover from a loop-reversible state with vortex-vortex collisions to a collisionless point-reversible state. In either regime, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau (d)$$\end{document}τ(d) exhibits a power-law divergence at the same \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_{\mathrm {c}}$$\end{document}dc with nearly the same exponent.

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.

An Insight into Amorphous Shear Band in Magnetorheological Solid by Atomic Force Microscope

Micro mechanism consideration is critical for gaining a thorough understanding of amorphous shear band behavior in magnetorheological (MR) solids, particularly those with viscoelastic matrices. Heretofore, the characteristics of shear bands in terms of formation, physical evolution, and response to stress distribution at the localized region have gone largely unnoticed and unexplored. Notwithstanding these limitations, atomic force microscopy (AFM) has been used to explore the nature of shear band deformation in MR materials during stress relaxation. Stress relaxation at a constant low strain of 0.01% and an oscillatory shear of defined test duration played a major role in the creation of the shear band. In this analysis, the localized area of the study defined shear bands as varying in size and dominantly deformed in the matrix with no evidence of inhibition by embedded carbonyl iron particles (CIPs). The association between the shear band and the adjacent zone was further studied using in-phase imaging of AFM tapping mode and demonstrated the presence of localized affected zone around the shear band. Taken together, the results provide important insights into the proposed shear band deformation zone (SBDZ). This study sheds a contemporary light on the contentious issue of amorphous shear band deformation behavior and makes several contributions to the current literature.

Models for the Yielding Behavior of Amorphous Solids

Investigations of plastic deformation and yielding of amorphous solids reveal a strong dependence of their yielding behavior on the degree of annealing. Above a threshold degree of annealing, the nature of yielding changes qualitatively, becoming progressively more discontinuous. Theoretical investigations of yielding in amorphous solids have almost exclusively focused on uniform deformation, but cyclic deformation reveals intriguing features that remain uninvestigated. Focusing on athermal cyclic deformation, I investigate a family of models, which reproduce key features observed in simulations, and provide an interpretation for the intriguing presence of a threshold energy.

Barrier-controlled nonequilibrium criticality in reactive particle systems

Nonequilibrium critical phenomena generally exist in many dynamic systems, like chemical reactions and some driven-dissipative reactive particle systems. Here, by using computer simulation and theoretical analysis, we demonstrate the crucial role of the activation barrier on the criticality of dynamic phase transitions in a minimal reactive hard-sphere model. We find that at zero thermal noise, with increasing the activation barrier, the type of transition changes from a continuous conserved directed percolation into a discontinuous dynamic transition by crossing a tricritical point. A mean-field theory combined with field simulation is proposed to explain this phenomenon. The possibility of Ising-type criticality in the nonequilibrium system at finite thermal noise is also discussed.

Yielding in an amorphous solid subject to constant stress at finite temperatures

Understanding the nature of the yield transition is a long-standing problem in the physics of amorphous solids. Here we use molecular dynamics simulations to study the response of amorphous solids to constant stresses at finite temperatures. We compare amorphous solids that are prepared using fast and slow quenches and show that for thermal systems, the steady-state velocity exhibits a continuous transition from very slow creep to a finite strain rate as a function of the stress. This behavior is observed for both well-annealed and poorly annealed systems. However, the transient dynamics is different in the latter and involves overcoming an energy barrier. Due to the different simulation protocol, the strain rate as a function of stress and temperature follows a scaling relation that is different from the ones that are shown for systems where the strain is controlled. Collapsing the data using this scaling relation allows us to calculate critical exponents for the dynamics close to yield, including an exponent for thermal rounding. We also demonstrate that strain slips due to avalanche events above yield follow standard scaling relations and we extract critical exponents that are comparable to the ones obtained in previous studies that performed simulations of both molecular dynamics and elastoplastic models using strain-rate control.

Topology of the energy landscape of sheared amorphous solids and the irreversibility transition

Recent experiments and simulations of amorphous solids plastically deformed by an oscillatory drive have found a surprising behavior-for small strain amplitudes the dynamics can be reversible, which is contrary to the usual notion of plasticity as an irreversible form of deformation. This reversibility allows the system to reach limit cycles in which plastic events repeat indefinitely under the oscillatory drive. It was also found that reaching reversible limit cycles can take a large number of driving cycles and it was surmised that the plastic events encountered during the transient period are not encountered again and are thus irreversible. Using a graph representation of the stable configurations of the system and the plastic events connecting them, we show that the notion of reversibility in these systems is more subtle. We find that reversible plastic events are abundant and that a large portion of the plastic events encountered during the transient period are actually reversible in the sense that they can be part of a reversible deformation path. More specifically, we observe that the transition graph can be decomposed into clusters of configurations that are connected by reversible transitions. These clusters are the strongly connected components of the transition graph and their sizes turn out to be power-law distributed. The largest of these are grouped in regions of reversibility, which in turn are confined by regions of irreversibility whose number proliferates at larger strains. Our results provide an explanation for the irreversibility transition-the divergence of the transient period at a critical forcing amplitude. The long transients result from transition between clusters of reversibility in a search for a cluster large enough to contain a limit cycle of a specific amplitude. For large enough amplitudes, the search time becomes very large, since the sizes of the limit cycles become incompatible with the sizes of the regions of reversibility.

Shear modulus and reversible particle trajectories of frictional granular materials under oscillatory shear

In this study, we numerically investigated the mechanical responses and trajectories of frictional granular particles under oscillatory shear in the reversible phase where particle trajectories form closed loops below the yielding point. When the friction coefficient is small, the storage modulus exhibits softening, and the loss modulus remains finite in the quasi-static limit. As the friction coefficient increases, the softening and residual loss modulus are suppressed. The storage and loss moduli satisfy scaling laws if they are plotted as functions of the areas of the loop trajectories divided by the strain amplitude and diameter of grains, at least for small values of the areas.

How to study a persistent active glassy system

We explore glassy dynamics of dense assemblies of soft particles that are self-propelled by active forces. These forces have a fixed amplitude and a propulsion direction that varies on a timescaleτ_p, the persistence timescale. Numerical simulations of such active glasses are computationally challenging when the dynamics is governed by large persistence times. We describe in detail a recently proposed scheme that allows one to study directly the dynamics in the large persistence time limit, on timescales around and well above the persistence time. We discuss the idea behind the proposed scheme, which we call 'activity-driven dynamics', as well as its numerical implementation. We establish that our prescription faithfully reproduces all dynamical quantities in the appropriate limitτ_p→ ∞. We deploy the approach to explore in detail the statistics of Eshelby-like plastic events in the steady state dynamics of a dense and intermittent active glass.

The role of annealing in determining the yielding behavior of glasses under cyclic shear deformation

Yielding behavior in amorphous solids has been investigated in computer simulations using uniform and cyclic shear deformation. Recent results characterize yielding as a discontinuous transition, with the degree of annealing of glasses being a significant parameter. Under uniform shear, discontinuous changes in stresses at yielding occur in the high annealing regime, separated from the poor annealing regime in which yielding is gradual. In cyclic shear simulations, relatively poorly annealed glasses become progressively better annealed as the yielding point is approached, with a relatively modest but clear discontinuous change at yielding. To understand better the role of annealing on yielding characteristics, we perform athermal quasistatic cyclic shear simulations of glasses prepared with a wide range of annealing in two qualitatively different systems-a model of silica (a network glass) and an atomic binary mixture glass. Two strikingly different regimes of behavior emerge. Energies of poorly annealed samples evolve toward a unique threshold energy as the strain amplitude increases, before yielding takes place. Well-annealed samples, in contrast, show no significant energy change with strain amplitude until they yield, accompanied by discontinuous energy changes that increase with the degree of annealing. Significantly, the threshold energy for both systems corresponds to dynamical cross-over temperatures associated with changes in the character of the energy landscape sampled by glass-forming liquids.

Simple and Broadly Applicable Definition of Shear Transformation Zones

Plastic deformation in amorphous solids is known to be carried by stress-induced localized rearrangements of a few tens of particles, accompanied by the conversion of elastic energy to heat. Despite their central role in determining how glasses yield and break, the search for a simple and generally applicable definition of the precursors of those plastic rearrangements-the so-called shear transformation zones (STZs)-is still ongoing. Here we present a simple definition of STZs-based solely on the harmonic approximation of a glass's energy. We explain why and demonstrate directly that our proposed definition of plasticity carriers in amorphous solids is more broadly applicable compared to anharmonic definitions put forward previously. Finally, we offer an open-source library that analyzes low-lying STZs in computer glasses and in laboratory materials such as dense colloidal suspensions for which the harmonic approximation is accessible. Our results constitute a physically motivated methodological advancement towards characterizing mechanical disorder in glasses, and understanding how they yield.

An energy-landscape-based crossover temperature in glass-forming liquids

The systematic identification of temperature scales in supercooled liquids that are key to understanding those liquids' underlying glass properties, and their formation-history dependence, is a challenging task. Here, we study the statistics of particles' squared displacements δr² between equilibrium liquid configurations at temperature T and their underlying inherent states, using computer simulations of 11 different computer glass formers. We show that the relative fluctuations of δr² are nonmonotonic in T, exhibiting a maximum whose location defines the crossover temperature T_X. Therefore, T_X marks the point of maximal heterogeneity during the process of tumbling down the energy landscape, starting from an equilibrium liquid state at temperature T down to its underlying inherent state. We extract T_X for the 11 employed computer glasses, ranging from tetrahedral glasses to packs of soft elastic spheres, and demonstrate its usefulness in putting the elastic properties of different glasses on the same footing. Interestingly, we further show that T_X marks the crossover between two distinct regimes of the mean ⟨δr²⟩: a high temperature regime in which ⟨δr²⟩ scales approximately as T^0.5 and a deeply supercooled regime in which ⟨δr²⟩ scales approximately as T^1.3. Further research directions are discussed.

Period multiplication cascade at the order-by-disorder transition in uniaxial random field XY magnets

Uniaxial random field disorder induces a spontaneous transverse magnetization in the XY model. Adding a rotating driving field, we find a critical point attached to the number of driving cycles needed to complete a limit cycle, the first discovery of this phenomenon in a magnetic system. Near the critical drive, time crystal behavior emerges, in which the period of the limit cycles becomes an integer n > 1 multiple of the driving period. The period n can be engineered via specific disorder patterns. Because n generically increases with system size, the resulting period multiplication cascade is reminiscent of that occurring in amorphous solids subject to oscillatory shear near the onset of plastic deformation, and of the period bifurcation cascade near the onset of chaos in nonlinear systems, suggesting it is part of a larger class of phenomena in transitions of dynamical systems. Applications include magnets, electron nematics, and quantum gases.

Elucidating the G″ overshoot in soft materials with a yield transition via a time-resolved experimental strain decomposition

Materials that exhibit yielding behavior are used in many applications, from spreadable foods and cosmetics to direct write three-dimensional printing inks and filled rubbers. Their key design feature is the ability to transition behaviorally from solid to fluid under sufficient load or deformation. Despite its widespread applications, little is known about the dynamics of yielding in real processes, as the nonequilibrium nature of the transition impedes understanding. We demonstrate an iteratively punctuated rheological protocol that combines strain-controlled oscillatory shear with stress-controlled recovery tests. This technique provides an experimental decomposition of recoverable and unrecoverable strains, allowing for solid-like and fluid-like contributions to a yield stress material's behavior to be separated in a time-resolved manner. Using this protocol, we investigate the overshoot in loss modulus seen in materials that yield. We show that this phenomenon is caused by the transition from primarily solid-like, viscoelastic dissipation in the linear regime to primarily fluid-like, plastic flow at larger amplitudes. We compare and contrast this with a viscoelastic liquid with no yielding behavior, where the contribution to energy dissipation from viscous flow dominates over the entire range of amplitudes tested.

Thermodynamic equivalence of cyclic shear and deep cooling in glass formers

The extreme slowing down associated with glass formation in experiments and in simulations results in serious difficulties to prepare deeply quenched, well annealed, glassy material. Recently, methods to achieve such deep quenching were proposed, including vapor deposition on the experimental side and "swap Monte Carlo" and oscillatory shearing on the simulation side. The relation between the resulting glasses under different protocols remains unclear. Here we show that oscillatory shear and swap Monte Carlo result in thermodynamically equivalent glasses sharing the same statistical mechanics and similar mechanical responses under external strain.

State transition graph of the Preisach model and the role of return-point memory

The Preisach model has been useful as a null model for understanding memory formation in periodically driven disordered systems. In amorphous solids, for example, the athermal response to shear is due to localized plastic events (soft spots). As shown recently by Mungan et al. [Phys. Rev. Lett. 123, 178002 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.178002], the plastic response to applied shear can be rigorously described in terms of a directed network whose transitions correspond to one or more soft spots changing states. The topology of this graph depends on the interactions between soft spots and when such interactions are negligible, the resulting description becomes that of the Preisach model. A first step in linking transition graph topology with the underlying soft-spot interactions is therefore to determine the structure of such graphs in the absence of interactions. Here we perform a detailed analysis of the transition graph of the Preisach model. We highlight the important role played by return-point memory in organizing the graph into a hierarchy of loops and subloops. Our analysis reveals that the topology of a large portion of this graph is actually not governed by the values of the switching fields that describe the hysteretic behavior of the individual elements but by a coarser parameter, a permutation ρ which prescribes the sequence in which the individual hysteretic elements change their states as the main hysteresis loop is traversed. This in turn allows us to derive combinatorial properties, such as the number of major loops in the transition graph as well as the number of states |R| constituting the main hysteresis loop and its nested subloops. We find that |R| is equal to the number of increasing subsequences contained in the permutation ρ.