Heterogeneous relaxation dynamics in amorphous materials under cyclic loading

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.

Mechanical annealing and memories in a disordered solid

Shearing a disordered or amorphous solid for many cycles with a constant strain amplitude can anneal it, relaxing a sample to a steady state that encodes a memory of that amplitude. This steady state also features a remarkable stability to amplitude variations that allows one to read the memory. Here, we shed light on both annealing and memory by considering how to mechanically anneal a sample to have as little memory content as possible. In experiments, we show that a "ring-down" protocol reaches a comparable steady state but with no discernible memories and minimal structural anisotropy. We introduce a method to characterize the population of rearrangements within a sample and show how it connects with the response to amplitude variation and the size of annealing steps. These techniques can be generalized to other forms of glassy matter and a wide array of disordered solids, especially those that yield by flowing homogeneously.

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.

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.

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.

Yielding in an Integer Automaton Model for Amorphous Solids under Cyclic Shear

We present results on an automaton model of an amorphous solid under cyclic shear. After a transient, the steady state falls into one of three cases in order of increasing strain amplitude: (i) pure elastic behavior with no plastic activity, (ii) limit cycles where the state recurs after an integer period of strain cycles, and (iii) irreversible plasticity with longtime diffusion. The number of cycles N required for the system to reach a periodic orbit diverges as the amplitude approaches the yielding transition between regimes (ii) and (iii) from below, while the effective diffusivity D of the plastic strain field vanishes on approach from above. Both of these divergences can be described by a power law. We further show that the average period T of the limit cycles increases on approach to yielding.

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.

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.

Quantification of plasticity via particle dynamics above and below yield in a 2D jammed suspension

The yield transition of amorphous materials is characterized by a swift increase of energy dissipation. The connection between particle dynamics, dissipation, and overall material rheology, however, has still not been elucidated. Here, we take a new approach relating trajectories to yielding, using a custom built interfacial stress rheometer, which allows for measurement of shear moduli (G',G'') of a dense athermal suspension's microstructure while simultaneously tracking particle trajectories undergoing cyclic shear. We find an increase in total area traced by particle trajectories as the system is stressed well below to well above yield. Trajectories may be placed into three categories: reversibly elastic paths; reversibly plastic paths, associated with smooth limit cycles; and irreversibly plastic paths, in which particles do not return to their original position. We find that above yield, reversibly plastic trajectories are predominantly found near to the shearing surface, whereas reversibly elastic paths are more prominent near the stationary wall. This spatial transition between particles acting as liquids to those acting as solids is characteristic of a 'melting front', which is observed to shift closer to the wall with increasing strain. We introduce a non-dimensional measure of plastic dissipation based on particle trajectories that scales linearly with strain amplitude both above and below yield, and that is unity at the rheological yield point. Surprisingly, this relation collapses for three systems of varying degrees of disorder.

Unified phase diagram of reversible-irreversible, jamming, and yielding transitions in cyclically sheared soft-sphere packings

Self-organization, and transitions from reversible to irreversible behavior, of interacting particle assemblies driven by externally imposed stresses or deformation is of interest in comprehending diverse phenomena in soft matter. They have been investigated in a wide range of systems, such as colloidal suspensions, glasses, and granular matter. In different density and driving regimes, such behavior is related to yielding of amorphous solids, jamming, memory formation, etc. How these phenomena are related to each other has not, however, been much studied. In order to obtain a unified view of the different regimes of behavior, and transitions between them, we investigate computationally the response of soft-sphere assemblies to athermal cyclic-shear deformation over a wide range of densities and amplitudes of shear deformation. Cyclic-shear deformation induces transitions from reversible to irreversible behavior in both unjammed and jammed soft-sphere packings. Well above the minimum isotropic jamming density ([Formula: see text]), this transition corresponds to yielding. In the vicinity of the jamming point, up to a higher-density limit, we designate [Formula: see text], an unjammed phase emerges between a localized, absorbing phase and a diffusive, irreversible, phase. The emergence of the unjammed phase signals the shifting of the jamming point to higher densities as a result of annealing and opens a window where shear jamming becomes possible for frictionless packings. Below [Formula: see text], two distinct localized states, termed point- and loop-reversible, are observed. We characterize in detail the different regimes and transitions between them and obtain a unified density-shear amplitude phase diagram.

Shear Band Formation in Amorphous Materials under Oscillatory Shear Deformation

The effect of periodic shear on strain localization in disordered solids is investigated using molecular dynamics simulations. We consider a binary mixture of one million atoms annealed to a low temperature with different cooling rates and then subjected to oscillatory shear deformation with a strain amplitude slightly above the critical value. It is found that the yielding transition occurs during one cycle but the accumulation of irreversible displacements and initiation of the shear band proceed over larger number of cycles for more slowly annealed glasses. The spatial distribution and correlation function of nonaffine displacements reveal that their collective dynamics changes from homogeneously distributed small clusters to a system-spanning shear band. The analysis of spatially averaged profiles of nonaffine displacements indicates that the location of a shear band in periodically loaded glasses can be identified at least several cycles before yielding. These insights are important for the development of novel processing methods and prediction of the fatigue lifetime of metallic glasses.

Classification of the reversible-irreversible transitions in particle trajectories across the jamming transition point

The reversible-irreversible (RI) transition of particle trajectories in athermal colloidal suspensions under cyclic shear deformation is an archetypal nonequilibrium phase transition which has attracted much attention recently. Most studies of the RI transitions have focused on either dilute limit or very high densities well above the jamming transition point. The transition between the two limiting cases is largely unexplored. In this paper, we study the RI transition of athermal frictionless colloidal particles over a wide range of densities, with emphasis on the region below φ_J, by using oscillatory sheared molecular dynamics simulation. We reveal that the nature of the RI transitions in the intermediate densities is very rich. As demonstrated by the previous work by Schreck et al. [Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2013, 88, 052205], there exist the point-reversible and the loop-reversible phases depending on the density and the shear strain amplitude. We find that, between the two reversible phases, a quasi-irreversible phase where the particles' trajectories are highly non-affine and diffusive. The averaged number of contacts of particles is found to characterize the phase boundaries. We also find that the system undergoes the yielding transition below but in the vicinity of φ_J when the strain with a small but finite strain rate is applied. This yielding transition line matches with the RI transition line separating the loop-reversible from the irreversible phases. Surprisingly, the nonlinear rheological response called "softening" has been observed even below φ_J. These findings imply that geometrical properties encoded in the sheared configurations control the dynamical transitions.

Memory formation in cyclically deformed amorphous solids and sphere assemblies

We study a model amorphous solid that is subjected to repeated athermal cyclic shear deformation. It has previously been demonstrated that the memory of the amplitudes of shear deformation the system is subjected to (or trained at) is encoded, and can be retrieved by subsequent deformation cycles that serve as read operations. Here we consider different read protocols and measurements and show that single and multiple memories can be robustly retrieved through these different protocols. We also show that shear deformation by a larger amplitude always erases the stored memories. These observations are similar to those in experiments with non-Brownian colloidal suspensions and corresponding models, but differ in the possibility of storing multiple memories non-transiently. Such a possibility has been associated with the presence of cycles of transitions that take place in the model amorphous solids, between local energy minima. Here, we also study low-density sphere assemblies which serve as models for non-Brownian colloidal suspensions, under athermal deformation, and identify a regime where the signatures of memory encoding are similar to the model glass, even when transition between local energy minima are absent. We show that such a regime corresponds to the presence of loop reversibility, rather than point reversibility of configurations under cyclic deformation.

The yielding transition in amorphous solids under oscillatory shear deformation

Amorphous solids are ubiquitous among natural and man-made materials. Often used as structural materials for their attractive mechanical properties, their utility depends critically on their response to applied stresses. Processes underlying such mechanical response, and in particular the yielding behaviour of amorphous solids, are not satisfactorily understood. Although studied extensively, observed yielding behaviour can be gradual and depend significantly on conditions of study, making it difficult to convincingly validate existing theoretical descriptions of a sharp yielding transition. Here we employ oscillatory deformation as a reliable probe of the yielding transition. Through extensive computer simulations for a wide range of system sizes, we demonstrate that cyclically deformed model glasses exhibit a sharply defined yielding transition with characteristics that are independent of preparation history. In contrast to prevailing expectations, the statistics of avalanches reveals no signature of the impending transition, but exhibit dramatic, qualitative, changes in character across the transition.

The onset of yielding can be difficult to define unambiguously for amorphous materials. Here the authors undertake computer simulations of model glasses of varying system sizes and show that, under oscillatory shear, they exhibit a sharp transition independent of preparation history.

Collective nonaffine displacements in amorphous materials during large-amplitude oscillatory shear

Using molecular dynamics simulations, we study the transient response of a binary Lennard-Jones glass subjected to periodic shear deformation. The amorphous solid is modeled as a three-dimensional Kob-Andersen binary mixture at a low temperature. The cyclic loading is applied to slowly annealed, quiescent samples, which induces irreversible particle rearrangements at large strain amplitudes, leading to stress-strain hysteresis and a drift of the potential energy towards higher values. We find that the initial response to cyclic shear near the critical strain amplitude involves disconnected clusters of atoms with large nonaffine displacements. In contrast, the amplitude of shear stress oscillations decreases after a certain number of cycles, which is accompanied by the initiation and subsequent growth of a shear band.

Colloidal polycrystalline monolayers under oscillatory shear

In this paper we probe the structural response to oscillatory shear deformations of polycrystalline monolayers of soft repulsive colloids with varying area fraction over a broad range of frequencies and amplitudes. The particles are confined at a fluid interface, sheared using a magnetic microdisk, and imaged through optical microscopy. The structural and mechanical response of soft materials is highly dependent on their microstructure. If crystals are well understood and deform through the creation and mobilization of specific defects, the situation is much more complex for disordered jammed materials, where identifying structural motifs defining plastically rearranging regions remains an elusive task. Our materials fall between these two classes and allow the identification of clear pathways for structural evolution. In particular, we demonstrate that large enough strains are able to fluidize the system, identifying critical strains that fulfill a local Lindemann criterion. Conversely, smaller strains lead to localized and erratic irreversible particle rearrangements due to the motion of structural defects. In this regime, oscillatory shear promotes defect annealing and leads to the growth of large crystalline domains. Numerical simulations help identify the population of rearranging particles with those exhibiting the largest deviatoric stresses and indicate that structural evolution proceeds towards the minimization of the stress stored in the system. The particles showing high deviatoric stresses are localized around grain boundaries and defects, providing a simple criterion to spot regions likely to rearrange plastically under oscillatory shear.

The fractal correlation between relaxation dynamics and atomic-level structures observed in metallic glasses by computer simulation

Hierarchical clustering analysis shows that the activating atoms are excited in a cooperative and avalanche-like model to form activating units. Interestingly, a fractal correlation is found between the number and size of the activating units.

Comparatively studying the local atomic structures of metallic glasses upon cyclic-loading by computer simulations

Through a variety of local structural analysis methods, it is revealed that the NixZr_100–xMGs exhibit a combination of the icosahedral-, fcc- and hcp-like configurations, while the icosahedra or distorted icosahedra cover a dominant fraction.

Macroscopic yielding in jammed solids is accompanied by a nonequilibrium first-order transition in particle trajectories

We use computer simulations to analyze the yielding transition during large-amplitude oscillatory shear of a simple model for soft jammed solids. Simultaneous analysis of global mechanical response and particle-scale motion demonstrates that macroscopic yielding, revealed by a smooth crossover in mechanical properties, is accompanied by a sudden change in the particle dynamics, which evolves from nondiffusive motion to irreversible diffusion as the amplitude of the shear is increased. We provide numerical evidence that this sharp change corresponds to a nonequilibrium first-order dynamic phase transition, thus establishing the existence of a well-defined microscopic dynamic signature of the yielding transition in amorphous materials in oscillatory shear.

Nonaffine rearrangements of atoms in deformed and quiescent binary glasses

The influence of periodic shear deformation on nonaffine atomic displacements in an amorphous solid is examined via molecular dynamics simulations. We study the three-dimensional Kob-Andersen binary mixture model at a finite temperature. It is found that when the material is periodically strained, most of the atoms undergo repetitive nonaffine displacements with amplitudes that are broadly distributed. We show that particles with large amplitudes of nonaffine displacements are organized into compact clusters. With increasing strain amplitude, spatial correlations of nonaffine displacements become increasingly long-ranged, although they remain present even in a quiescent system due to thermal fluctuations.

Reversible plastic events during oscillatory deformation of amorphous solids

The effect of oscillatory shear strain on nonaffine rearrangements of individual particles in a three-dimensional binary glass is investigated using molecular dynamics simulations. The amorphous material is represented by the Kob-Andersen mixture at the temperature well below the glass transition. We find that during periodic shear deformation of the material, some particles undergo reversible nonaffine displacements with amplitudes that are approximately power-law distributed. Our simulations show that particles with large amplitudes of nonaffine displacement exhibit a collective behavior; namely, they tend to aggregate into relatively compact clusters that become comparable with the system size near the yield strain. Along with reversible displacements there exist a number of irreversible ones. With increasing strain amplitude, the probability of irreversible displacements during one cycle increases, which leads to permanent structural relaxation of the material.

Reversibility and criticality in amorphous solids

The physical processes governing the onset of yield, where a material changes its shape permanently under external deformation, are not yet understood for amorphous solids that are intrinsically disordered. Here, using molecular dynamics simulations and mean-field theory, we show that at a critical strain amplitude the sizes of clusters of atoms undergoing cooperative rearrangements of displacements (avalanches) diverges. We compare this non-equilibrium critical behaviour to the prevailing concept of a 'front depinning' transition that has been used to describe steady-state avalanche behaviour in different materials. We explain why a depinning-like process can result in a transition from periodic to chaotic behaviour and why chaotic motion is not possible in pinned systems. These findings suggest that, at least for highly jammed amorphous systems, the irreversibility transition may be a side effect of depinning that occurs in systems where the disorder is not quenched.

The effect of a reversible shear transformation on plastic deformation of an amorphous solid

Langevin dynamics simulations are performed to investigate the plastic response of a model glass to a local shear transformation in a quiescent system. The deformation of the material is induced by a spherical inclusion that is gradually strained into an ellipsoid of the same volume and then reverted back into the sphere. We show that the number of cage-breaking events increases with increasing strain amplitude of the shear transformation. The results of numerical simulations indicate that the density of cage jumps is larger in the cases of weak damping or slow shear transformation. Remarkably, we also found that, for a given strain amplitude, the peak value of the density profiles is a function of the ratio of the damping coefficient and the time scale of the shear transformation.

Stretched Exponential Relaxation of Glasses at Low Temperature

The question of whether glass continues to relax at low temperature is of fundamental and practical interest. Here, we report a novel atomistic simulation method allowing us to directly access the long-term dynamics of glass relaxation at room temperature. We find that the potential energy relaxation follows a stretched exponential decay, with a stretching exponent β=3/5, as predicted by Phillips's diffusion-trap model. Interestingly, volume relaxation is also found. However, it is not correlated to the energy relaxation, but it is rather a manifestation of the mixed alkali effect.

Memory effects in schematic models of glasses subjected to oscillatory deformation

We consider two schematic models of glasses subjected to oscillatory shear deformation, motivated by the observations, in computer simulations of a model glass, of a nonequilibrium transition from a localized to a diffusive regime as the shear amplitude is increased, and of persistent memory effects in the localized regime. The first of these schematic models is the NK model, a spin model with disordered multi-spin interactions previously studied as a model for sheared amorphous solids. The second model, a transition matrix model, is an abstract formulation of the manner in which occupancy of local energy minima evolves under oscillatory deformation cycles. In both of these models, we find a behavior similar to that of an atomic model glass studied earlier. We discuss possible further extensions of the approaches outlined.

Plastic deformation of a model glass induced by a local shear transformation

The effect of a local shear transformation on plastic deformation of a three-dimensional amorphous solid is studied using molecular dynamics simulations. We consider a spherical inclusion, which is gradually transformed into an ellipsoid of the same volume and then converted back into the sphere. It is shown that at sufficiently large strain amplitudes, the deformation of the material involves localized plastic events that are identified based on the relative displacement of atoms before and after the shear transformation. We find that the density profiles of cage jumps decay away from the inclusion, which correlates well with the radial dependence of the local deformation of the material. At the same strain amplitude, the plastic deformation becomes more pronounced in the cases of weakly damped dynamics or large time scales of the shear transformation. We show that the density profiles can be characterized by the universal function of the radial distance multiplied by a dimensionless factor that depends on the friction coefficient and the time scale of the shear event.

Role of disorder in finite-amplitude shear of a 2D jammed material

A material's response to small but finite deformations can reveal the roots of its response to much larger deformations. Here, we identify commonalities in the responses of 2D soft jammed solids with different amounts of disorder. We cyclically shear the materials while tracking their constituent particles, in experiments that feature a stable population of repeated structural relaxations. Using bidisperse particle sizes creates a more amorphous material, while monodisperse sizes yield a more polycrystalline one. We find that the materials' responses are very similar, both at the macroscopic, mechanical level and in the microscopic motions of individual particles. However, both locally and in bulk, crystalline arrangements of particles are stiffer (greater elastic modulus) and less likely to rearrange. Our work supports the idea of a common description for the responses of a wide array of materials.

Echoes in x-ray speckles track nanometer-scale plastic events in colloidal gels under shear

We report x-ray photon correlation spectroscopy experiments on a concentrated nanocolloidal gel subject to in situ oscillatory shear strain. The strain causes periodic echoes in the speckle pattern that lead to peaks in the intensity autocorrelation function. Above a threshold strain that is near the first yield point of the gel, the peak amplitude decays exponentially with the number of shear cycles, signaling irreversible particle rearrangements. The wave-vector dependence of the decay rate reveals a power-law distribution in the size of regions undergoing shear-induced rearrangement. The gel also displays strain softening well below the threshold, indicating a range of strains at which the rheology is nonlinear but the microscopic deformations are reversible.

A microscopic view of the yielding transition in concentrated emulsions

We use a custom shear cell coupled to an optical microscope to investigate at the particle level the yielding transition in concentrated emulsions subjected to an oscillatory shear deformation. By performing experiments lasting thousands of cycles on samples at several volume fractions and for a variety of applied strain amplitudes, we obtain a comprehensive, microscopic picture of the yielding transition. We find that irreversible particle motion sharply increases beyond a volume-fraction dependent critical strain, which is found to be in close agreement with the strain beyond which the stress-strain relation probed in rheology experiments significantly departs from linearity. The shear-induced dynamics are very heterogenous: quiescent particles coexist with two distinct populations of mobile and 'supermobile' particles. Dynamic activity exhibits spatial and temporal correlations, with rearrangements events organized in bursts of motion affecting localized regions of the sample. Analogies with other sheared soft materials and with recent work on the transition to irreversibility in sheared complex fluids are briefly discussed.

Plasticity of a colloidal polycrystal under cyclic shear

We use confocal microscopy and time-resolved light scattering to investigate plasticity in a colloidal polycrystal, following the evolution of the network of grain boundaries as the sample is submitted to thousands of shear deformation cycles. The grain boundary motion is found to be ballistic, with a velocity distribution function exhibiting nontrivial power law tails. The shear-induced dynamics initially slow down, similarly to the aging of the spontaneous dynamics in glassy materials, but eventually reach a steady state. Surprisingly, the crossover time between the initial aging regime and the steady state decreases with increasing probed length scale, hinting at a hierarchical organization of the grain boundary dynamics.

Variable-amplitude oscillatory shear response of amorphous materials

Variable-amplitude oscillatory shear tests are emerging as powerful tools to investigate and quantify the nonlinear rheology of amorphous solids, complex fluids, and biological materials. Quite a few recent experimental and atomistic simulation studies demonstrated that at low shear amplitudes, an amorphous solid settles into an amplitude- and initial-conditions-dependent dissipative limit cycle, in which back-and-forth localized particle rearrangements periodically bring the system to the same state. At sufficiently large shear amplitudes, the amorphous system loses memory of the initial conditions, exhibits chaotic particle motions accompanied by diffusive behavior, and settles into a stochastic steady state. The two regimes are separated by a transition amplitude, possibly characterized by some critical-like features. Here we argue that these observations support some of the physical assumptions embodied in the nonequilibrium thermodynamic, internal-variables based, shear-transformation-zone model of amorphous viscoplasticity; most notably that "flow defects" in amorphous solids are characterized by internal states between which they can make transitions, and that structural evolution is driven by dissipation associated with plastic deformation. We present a rather extensive theoretical analysis of the thermodynamic shear-transformation-zone model for a variable-amplitude oscillatory shear protocol, highlighting its success in accounting for various experimental and simulational observations, as well as its limitations. Our results offer a continuum-level theoretical framework for interpreting the variable-amplitude oscillatory shear response of amorphous solids and may promote additional developments.

Mechanical and microscopic properties of the reversible plastic regime in a 2D jammed material

At the microscopic level, plastic flow of a jammed, disordered material consists of a series of particle rearrangements that cannot be reversed by subsequent deformation. An infinitesimal deformation of the same material has no rearrangements. Yet between these limits, there may be a self-organized plastic regime with rearrangements, but with no net change upon reversing a deformation. We measure the oscillatory response of a jammed interfacial material, and directly observe rearrangements that couple to bulk stress and dissipate energy, but do not always give rise to global irreversibility.

Dynamical heterogeneity in periodically deformed polymer glasses

The dynamics of structural relaxation in a model polymer glass subject to spatially homogeneous, time-periodic shear deformation is investigated using molecular dynamics simulations. We study a coarse-grained bead-spring model of short polymer chains below the glass transition temperature. It is found that at small strain amplitudes, the segmental dynamics is nearly reversible over about 10^{4} cycles, while at strain amplitudes above a few percent, polymer chains become fully relaxed after a hundred cycles. At the critical strain amplitude, the transition from slow to fast relaxation dynamics is associated with the largest number of dynamically correlated monomers as indicated by the peak value of the dynamical susceptibility. The analysis of individual monomer trajectories showed that mobile monomers tend to assist their neighbors to become mobile and aggregate into relatively compact transient clusters.

Onset of irreversibility and chaos in amorphous solids under periodic shear

A fundamental problem in the physics of amorphous materials is understanding the transition from reversible to irreversible plastic behavior and its connection to yield. Currently, continuum material modeling relies on phenomenological yield thresholds, however in many cases the transition from elastic to plastic behavior is gradual, which makes it difficult to identify an exact yield criterion. Here we show that under periodic shear, amorphous solids undergo a transition from repetitive, predictable behavior to chaotic, irregular behavior as a function of the strain amplitude. In both the periodic and chaotic regimes, localized particle rearrangements are observed. We associate the point of transition from repetitive to chaotic behavior with the yield strain and suggest that at least for oscillatory shear, yield in amorphous solids is a result of a "transition to chaos."

Oscillatory athermal quasistatic deformation of a model glass

We report computer simulations of oscillatory athermal quasistatic shear deformation of dense amorphous samples of a three-dimensional model glass former. A dynamical transition is observed as the amplitude of the deformation is varied: For large values of the amplitude the system exhibits diffusive behavior and loss of memory of the initial conditions, whereas localization is observed for small amplitudes. Our results suggest that the same kind of transition found in driven colloidal systems is present in the case of amorphous solids (e.g., metallic glasses). The onset of the transition is shown to be related to the onset of energy dissipation. Shear banding is observed for large system sizes, without, however, affecting qualitative aspects of the transition.

Distribution of local relaxation events in an aging three-dimensional glass: spatiotemporal correlation and dynamical heterogeneity

We investigate the spatiotemporal distribution of microscopic relaxation events, defined through particle hops, in a model polymer glass using molecular dynamics simulations. We introduce an efficient algorithm to directly identify hops during the simulation, which allows the creation of a map of relaxation events for the whole system. Based on this map, we present density-density correlations between hops and directly extract correlation scales. These scales define collaboratively rearranging groups of particles and their size distributions are presented as a function of temperature and age. Dynamical heterogeneity is spatially resolved as the aggregation of hops into clusters, and we analyze their volume distribution and growth during aging. A direct comparison with the four-point dynamical susceptibility χ(4) reveals the formation of a single dominating cluster prior to the χ(4) peak, which indicates maximally correlated dynamics. An analysis of the fractal dimension of the hop clusters finds slightly noncompact shapes in excellent agreement with independent estimates from four-point correlations.