Predicting plasticity with soft vibrational modes: from dislocations to glasses

Origin of yield stress and mechanical plasticity in model biological tissues

During development and under normal physiological conditions, biological tissues are continuously subjected to substantial mechanical stresses. In response to large deformations, cells in a tissue must undergo multicellular rearrangements to maintain integrity and robustness. However, how these events are connected in time and space remains unknown. Here, using theoretical modeling, we study the mechanical plasticity of cell monolayers under large deformations. Our results suggest that the jamming-unjamming (solid-fluid) transition can vary significantly depending on the degree of deformation, implying that tissues are highly unconventional materials. We elucidate the origins of this behavior. We also demonstrate how large deformations are accommodated through a series of cellular rearrangements, similar to avalanches in non-living materials. We find that these 'tissue avalanches' are governed by stress redistribution and the spatial distribution of "soft" or vulnerable spots, which are more prone to undergo rearrangements. Finally, we propose a simple and experimentally accessible framework to infer tissue-level stress and predict avalanches based on static images.

Emergent marginality in frustrated multistable networks

We study disordered networks of coupled bistable elastic elements, representing a coarse-grained view of amorphous solids. We find that such networks self-organize to a marginally stable state, in which the barrier for local activations becomes vanishingly small. The model provides unique access to both local and global properties associated with marginal stability. We directly measure pseudo-gaps in the spectrum of local excitations, as well as diverging fluctuations under shear. Crucially, the dynamics are dominated by a small population of bonds that are locally unstable, which give rise to quasi-localized, low-frequency vibrational modes and scale-free avalanches of instabilities. We propose a correction to the scaling between the pseudo-gap exponent and avalanche statistics based on diverging length fluctuations. Our model combines a coarse-grained view with a continuous, real-space implementation, providing novel insights to a wide class of amorphous solids.

Topology of vibrational modes predicts plastic events in glasses

The plastic deformation of crystalline materials can be understood by considering their structural defects such as disclinations and dislocations. Although also glasses are solids, their structure resembles closely the one of a liquid and hence the concept of structural defects becomes ill-defined. As a consequence it is very challenging to rationalize on a microscopic level the mechanical properties of glasses close to the yielding point and to relate plastic events to structural properties. Here we investigate the topological characteristics of the eigenvector field of the vibrational excitations of a two-dimensional glass model, notably the geometric arrangement of the topological defects as a function of vibrational frequency. We find that if the system is subjected to a quasistatic shear, the location of the resulting plastic events correlate strongly with the topological defects that have a negative charge. Our results provide thus a direct link between the structure of glasses prior their deformation and the plastic events during deformation.

Avalanche dynamics in sheared athermal particle packings occurs via localized bursts predicted by unstable linear response

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 eigenvalue dynamics are highly complex during such events, and that the most unstable eigenvector is a poor predictor of avalanche dynamics. Instead, we modify existing tools that identify localized excitations in stable systems, and apply them to these unstable systems with non-positive definite Hessians, quantifying the evolution of such excitations during avalanches. We find that bursts of localized deformations in the avalanche almost always occur at localized excitations identified using the linear spectrum. These new tools will provide an improved framework for validating and extending mesoscale elastoplastic models that are commonly used to explain avalanche statistics in glasses and granular matter.

Friction and Adhesion Govern Yielding of Disordered Nanoparticle Packings: A Multiscale Adhesive Discrete Element Method Study

Recent studies have demonstrated that amorphous materials, from granular packings to atomic glasses, share multiple striking similarities, including a universal onset strain level for yield. This is despite vast differences in length scales and in the constituent particles' interactions. However, the nature of localized particle rearrangements is not well understood, and how local interactions affect overall performance remains unknown. Here, we introduce a multiscale adhesive discrete element method to simulate recent novel experiments of disordered nanoparticle packings indented and imaged with single nanoparticle resolution. The simulations exhibit multiple behaviors matching the experiments. By directly monitoring spatial rearrangements and interparticle bonding/debonding under the packing's surface, we uncover the mechanisms of the yielding and hardening phenomena observed in experiments. Interparticle friction and adhesion synergistically toughen the packings and retard plastic deformation. Moreover, plasticity can result from bond switching without particle rearrangements. These results furnish insights for understanding yielding in amorphous materials generally.

Using delaunay triangularization to characterize non-affine displacement fields during athermal, quasistatic deformation of amorphous solids

We investigate the non-affine displacement fields that occur in two-dimensional Lennard-Jones models of metallic glasses subjected to athermal, quasistatic simple shear (AQS). During AQS, the shear stress versus strain displays continuous quasi-elastic segments punctuated by rapid drops in shear stress, which correspond to atomic rearrangement events. We capture all information concerning the atomic motion during the quasi-elastic segments and shear stress drops by performing Delaunay triangularizations and tracking the deformation gradient tensor F_α associated with each triangle α. To understand the spatio-temporal evolution of the displacement fields during shear stress drops, we calculate F_α along minimal energy paths from the mechanically stable configuration immediately before to that after the stress drop. We find that quadrupolar displacement fields form and dissipate both during the quasi-elastic segments and shear stress drops. We then perform local perturbations (rotation, dilation, simple and pure shear) to single triangles and measure the resulting displacement fields. We find that local pure shear deformations of single triangles give rise to mostly quadrupolar displacement fields, and thus pure shear strain is the primary type of local strain that is activated by bulk, athermal quasistatic simple shear. Other local perturbations, e.g. rotations, dilations, and simple shear of single triangles, give rise to vortex-like and dipolar displacement fields that are not frequently activated by bulk AQS. These results provide fundamental insights into the non-affine atomic motion that occurs in driven, glassy materials.

Structural and short-time vibrational properties of colloidal glasses and supercooled liquids in the vicinity of the re-entrant glass transition

We investigate the short-time vibrational properties and structure of two-dimensional, bidisperse, colloidal glasses and supercooled liquids in the vicinity of the re-entrant glass transition, as a function of interparticle depletion attraction strength. The long-time spatiotemporal dynamics of the samples are measured to be non-monotonic, confirming that the suspensions evolve from repulsive glass to supercooled liquid to attractive glass with increasing depletion attraction. Here, we search for vibrational signatures of the re-entrant behavior in the short-time spatiotemporal dynamics, i.e., dynamics associated with particle motion inside its nearest-neighbor cage. Interestingly, we observe that the anharmonicity of these in-cage vibrations varies non-monotonically with increasing attraction strength, consistent with the non-monotonic long-time structural relaxation dynamics of the re-entrant glass. We also extract effective spring constants between neighboring particles; we find that spring stiffness involving small particles also varies non-monotonically with increasing attraction strength, while stiffness between large particles increases monotonically. Last, from study of depletion-dependent local structure and vibration participation fractions, we gain microscopic insight into the particle-size-dependent contributions to short-time vibrational modes in the glass and supercooled liquid states.

Crystalline shielding mitigates structural rearrangement and localizes memory in jammed systems under oscillatory shear

The nature of yield in amorphous materials under stress has yet to be fully elucidated. In particular, understanding how microscopic rearrangement gives rise to macroscopic structural and rheological signatures in disordered systems is vital for the prediction and characterization of yield and the study of how memory is stored in disordered materials. Here, we investigate the evolution of local structural homogeneity on an individual particle level in amorphous jammed two-dimensional (athermal) systems under oscillatory shear and relate this evolution to rearrangement, memory, and macroscale rheological measurements. We define the structural metric crystalline shielding, and show that it is predictive of rearrangement propensity and structural volatility of individual particles under shear. We use this metric to identify localized regions of the system in which the material's memory of its preparation is preserved. Our results contribute to a growing understanding of how local structure relates to dynamic response and memory in disordered systems.

A structural approach to vibrational properties ranging from crystals to disordered systems

Many scientists generally attribute the vibrational anomalies of disordered solids to the structural disorder, which, however, is still under intense debate. Here we conduct simulations on two-dimensional packings with a finite temperature, whose structure is tuned from a crystalline configuration to an amorphous one, then the amorphous from very dense state to a relatively loose state. By measuring the vibrational density of states and the reduced density of states, we clearly observe the evolution of the boson peak with the change of the disorder and volume fractions. Meanwhile, to understand the structural origin of this anomaly, we identify the soft regimes of all systems with a novel machine-learning method, where the "softness", a local structural quantity, is defined. Interestingly, we find a strong monotonic relationship between the shape of the boson peak and the softness as well as its spatial heterogeneity, suggesting that the softness of a system may be a new structural approach to the anomalous vibrational properties of amorphous solids.

Inferring the particle-wise dynamics of amorphous solids from the local structure at the jamming point

Jamming is a phenomenon shared by a wide variety of systems, such as granular materials, foams, and glasses in their high density regime. This has motivated the development of a theoretical framework capable of explaining many of their static critical properties with a unified approach. However, the dynamics occurring in the vicinity of the jamming point has received little attention and the problem of finding a connection with the local structure of the configuration remains unexplored. Here we address this issue by constructing physically well defined structural variables using the information contained in the network of contacts of jammed configurations, and then showing that such variables yield a resilient statistical description of the particle-wise dynamics near this critical point. Our results are based on extensive numerical simulations of systems of spherical particles that allow us to statistically characterize the trajectories of individual particles in terms of their first two moments. We first demonstrate that, besides displaying a broad distribution of mobilities, particles may also have preferential directions of motion. Next, we associate each of these features with a structural variable computed uniquely in terms of the contact vectors at jamming, obtaining considerably high statistical correlations. The robustness of our approach is confirmed by testing two types of dynamical protocols, namely molecular dynamics and Monte Carlo, with different types of interaction. We also provide evidence that the dynamical regime we study here is dominated by anharmonic effects and therefore it cannot be described properly in terms of vibrational modes. Finally, we show that correlations decay slowly and in an interaction-independent fashion, suggesting a universal rate of information loss.

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.

Complexity of plastic instability in amorphous solids: Insights from spatiotemporal evolution of vibrational modes

It has been accepted that low-frequency vibrational modes are causally correlated to fundamental plastic rearrangement events in amorphous solids, irrespective of the structural details. But the mode-event relationship is far from clear. In this work, we carry out case studies using atomistic simulations of a three-dimensional Cu₅₀Zr₅₀ model glass under athermal, quasistatic shear. We focus on the first four plastic events, and carefully trace the spatiotemporal evolution of the associated low-frequency normal modes with applied shear strain. We reveal that these low-frequency modes get highly entangled with each other, from which the critical mode emerges spontaneously to predict a shear transformation event. But the detailed emergence picture is event by event and shear-protocol dependent, even for the first plastic event. This demonstrates that the instability of a plastic event is a result of extremely complex multiple-path choice or competition, and there is a strong, elastic interaction among neighboring instability events. At last, the generality of the present findings is shown to be applicable to covalent-bonded glasses.

Statistical mechanics of local force dipole responses in computer glasses

Soft quasilocalized modes (QLMs) are universally featured by structural glasses quenched from a melt, and are involved in several glassy anomalies such as the low-temperature scaling of their thermal conductivity and specific heat, and sound attenuation at intermediate frequencies. In computer glasses, QLMs may assume the form of harmonic vibrational modes under a narrow set of circumstances; however, direct access to their full distribution over frequency is hindered by hybridizations of QLMs with other low-frequency modes (e.g., phonons). Previous studies to overcome this issue have demonstrated that the response of a glass to local force dipoles serves as a good proxy for its QLMs; we, therefore, study here the statistical-mechanical properties of these responses in computer glasses, over a large range of glass stabilities and in various spatial dimensions, with the goal of revealing properties of the yet-inaccessible full distribution of QLMs' frequencies. We find that as opposed to the spatial-dimension-independent universal distribution of QLMs' frequencies ω (and, consequently, also of their stiffness κ = ω²), the distribution of stiffnesses associated with responses to local force dipoles features a (weak) dependence on spatial dimension. We rationalize this dependence by introducing a lattice model that incorporates both the real-space profiles of QLMs-associated with dimension-dependent long-range elastic fields-and the universal statistical properties of their frequencies. Based on our findings, we propose a conjecture about the form of the full distribution of QLMs' frequencies and its protocol-dependence. Finally, we discuss possible connections of our findings to basic aspects of glass formation and deformation.

Pinching a glass reveals key properties of its soft spots

It is now well established that glasses feature quasilocalized nonphononic excitations-coined "soft spots"-, which follow a universal [Formula: see text] density of states in the limit of low frequencies ω. All glass-specific properties, such as the dependence on the preparation protocol or composition, are encapsulated in the nonuniversal prefactor of the universal [Formula: see text] law. The prefactor, however, is a composite quantity that incorporates information both about the number of quasilocalized nonphononic excitations and their characteristic stiffness, in an apparently inseparable manner. We show that by pinching a glass-i.e., by probing its response to force dipoles-one can disentangle and independently extract these two fundamental pieces of physical information. This analysis reveals that the number of quasilocalized nonphononic excitations follows a Boltzmann-like law in terms of the parent temperature from which the glass is quenched. The latter, sometimes termed the fictive (or effective) temperature, plays important roles in nonequilibrium thermodynamic approaches to the relaxation, flow, and deformation of glasses. The analysis also shows that the characteristic stiffness of quasilocalized nonphononic excitations can be related to their characteristic size, a long sought-for length scale. These results show that important physical information, which is relevant for various key questions in glass physics, can be obtained through pinching a glass.

Nonlinear quasilocalized excitations in glasses: True representatives of soft spots

Structural glasses formed by quenching a melt possess a population of soft quasilocalized excitations-often called "soft spots"-that are believed to play a key role in various thermodynamic, transport, and mechanical phenomena. Under a narrow set of circumstances, quasilocalized excitations assume the form of vibrational (normal) modes, that are readily obtained by a harmonic analysis of the multidimensional potential energy. In general, however, direct access to the population of quasilocalized modes via harmonic analysis is hindered by hybridizations with other low-energy excitations, e.g., phonons. In this series of papers we reintroduce and investigate the statistical-mechanical properties of a class of low-energy quasilocalized modes-coined here nonlinear quasilocalized excitations (NQEs)-that are defined via an anharmonic (nonlinear) analysis of the potential-energy landscape of a glass, and do not hybridize with other low-energy excitations. In this paper, we review the theoretical framework that embeds a micromechanical definition of NQEs. We demonstrate how harmonic quasilocalized modes hybridize with other soft excitations, whereas NQEs properly represent soft spots without hybridization. We show that NQEs' energies converge to the energies of the softest, nonhybridized harmonic quasilocalized modes, cementing their status as true representatives of soft spots in structural glasses. Finally, we perform a statistical analysis of the mechanical properties of NQEs, which results in a prediction for the distribution of potential-energy barriers that surround typical inherent states of structural glasses, as well as a prediction for the distribution of local strain thresholds to plastic instability.

Structural characteristics in deformation mechanism transformation in nanoscale metallic glasses

Deformation of metallic glasses is closely related to their microstructures which depend on the composition, processing method, and the size of the materials. This subtle structure-property relation is fairly complex and remains to be explored. Here, we scrutinize the microstructural evolution in relation to the mechanical properties in metallic glass nanowires with the same composition and size but subtle microstructural differences by controlling the preparing process using molecular dynamics simulations. The results suggest that a structural threshold exists for the transformation of deformation mechanisms in metallic glasses: when the structural feature exceeds the threshold, the deformation changes from homogeneous flow to shear localized deformation.

Anisotropic structural predictor in glassy materials

There is growing evidence that relaxation in glassy materials, both spontaneous and externally driven, is mediated by localized soft spots. Recent progress made it possible to identify the soft spots inside glassy structures and to quantify their degree of softness. These softness measures, however, are typically scalars, not taking into account the tensorial, anisotropic nature of soft spots, which implies orientation-dependent coupling to external deformation. Here, we derive from first principles the linear response coupling between the local heat capacity of glasses, previously shown to provide a measure of glassy softness, and external deformation in different directions. We first show that this linear response quantity follows an anomalous, fat-tailed distribution related to the universal ω^{4} density of states of quasilocalized, nonphononic excitations in glasses. We then construct a structural predictor as the product of the local heat capacity and its linear response to external deformation, and show that it offers an enhanced predictability of plastic rearrangements under deformation in different directions, compared to the purely scalar predictor.

Machine learning determination of atomic dynamics at grain boundaries

In polycrystalline materials, grain boundaries are sites of enhanced atomic motion, but the complexity of the atomic structures within a grain boundary network makes it difficult to link the structure and atomic dynamics. Here, we use a machine learning technique to establish a connection between local structure and dynamics of these materials. Following previous work on bulk glassy materials, we define a purely structural quantity (softness) that captures the propensity of an atom to rearrange. This approach correctly identifies crystalline regions, stacking faults, and twin boundaries as having low likelihood of atomic rearrangements while finding a large variability within high-energy grain boundaries. As has been found in glasses, the probability that atoms of a given softness will rearrange is nearly Arrhenius. This indicates a well-defined energy barrier as well as a well-defined prefactor for the Arrhenius form for atoms of a given softness. The decrease in the prefactor for low-softness atoms indicates that variations in entropy exhibit a dominant influence on the atomic dynamics in grain boundaries.

Yielding of a model glass former: An interpretation with an effective system of icosahedra

We consider the yielding under simple shear of a binary Lennard-Jones glass former whose super-Arrhenius dynamics are correlated with the formation of icosahedral structures. We recast this glass former as an effective system of icosahedra [Pinney et al., J. Chem. Phys. 143, 244507 (2015)JCPSA60021-960610.1063/1.4938424]. Looking at the small-strain region of sheared simulations, we observe that shear rates affect the shear localization behavior particularly at temperatures below the glass transition as defined with a fit to the Vogel-Fulcher-Tamman equation. At higher temperature, shear localization starts immediately on shearing for all shear rates. At lower temperatures, faster shear rates can result in a delayed start in shear localization, which begins close to the yield stress. Building from a previous work which considered steady-state shear [Pinney et al., J. Chem. Phys. 143, 244507 (2015)JCPSA60021-960610.1063/1.4938424], we interpret the response to shear and the shear localization in terms of a local effective temperature with our system of icosahedra. We find that the effective temperatures of the regions undergoing shear localization increase significantly with increasing strain (before reaching a steady-state plateau).

Structure-property relationships from universal signatures of plasticity in disordered solids

When deformed beyond their elastic limits, crystalline solids flow plastically via particle rearrangements localized around structural defects. Disordered solids also flow, but without obvious structural defects. We link structure to plasticity in disordered solids via a microscopic structural quantity, "softness," designed by machine learning to be maximally predictive of rearrangements. Experimental results and computations enabled us to measure the spatial correlations and strain response of softness, as well as two measures of plasticity: the size of rearrangements and the yield strain. All four quantities maintained remarkable commonality in their values for disordered packings of objects ranging from atoms to grains, spanning seven orders of magnitude in diameter and 13 orders of magnitude in elastic modulus. These commonalities link the spatial correlations and strain response of softness to rearrangement size and yield strain, respectively.

Local yield stress statistics in model amorphous solids

We develop and extend a method presented by Patinet, Vandembroucq, and Falk [Phys. Rev. Lett. 117, 045501 (2016)PRLTAO0031-900710.1103/PhysRevLett.117.045501] to compute the local yield stresses at the atomic scale in model two-dimensional Lennard-Jones glasses produced via differing quench protocols. This technique allows us to sample the plastic rearrangements in a nonperturbative manner for different loading directions on a well-controlled length scale. Plastic activity upon shearing correlates strongly with the locations of low yield stresses in the quenched states. This correlation is higher in more structurally relaxed systems. The distribution of local yield stresses is also shown to strongly depend on the quench protocol: the more relaxed the glass, the higher the local plastic thresholds. Analysis of the magnitude of local plastic relaxations reveals that stress drops follow exponential distributions, justifying the hypothesis of an average characteristic amplitude often conjectured in mesoscopic or continuum models. The amplitude of the local plastic rearrangements increases on average with the yield stress, regardless of the system preparation. The local yield stress varies with the shear orientation tested and strongly correlates with the plastic rearrangement locations when the system is sheared correspondingly. It is thus argued that plastic rearrangements are the consequence of shear transformation zones encoded in the glass structure that possess weak slip planes along different orientations. Finally, we justify the length scale employed in this work and extract the yield threshold statistics as a function of the size of the probing zones. This method makes it possible to derive physically grounded models of plasticity for amorphous materials by directly revealing the relevant details of the shear transformation zones that mediate this process.

Disentangling defects and sound modes in disordered solids

We develop a new method to isolate localized defects from extended vibrational modes in disordered solids. This method augments particle interactions with an artificial potential that acts as a high-pass filter: it preserves small-scale structures while pushing extended vibrational modes to higher frequencies. The low-frequency modes that remain are "bare" defects; they are exponentially localized without the quadrupolar tails associated with elastic interactions. We demonstrate that these localized excitations are excellent predictors of plastic rearrangements in the solid. We characterize several of the properties of these defects that appear in mesoscopic theory of plasticity, including their distribution of energy barriers, number density, and size, which is a first step in testing and revising continuum models for plasticity in disordered solids.

Local thermal energy as a structural indicator in glasses

Identifying heterogeneous structures in glasses-such as localized soft spots-and understanding structure-dynamics relations in these systems remain major scientific challenges. Here, we derive an exact expression for the local thermal energy of interacting particles (the mean local potential energy change caused by thermal fluctuations) in glassy systems by a systematic low-temperature expansion. We show that the local thermal energy can attain anomalously large values, inversely related to the degree of softness of localized structures in a glass, determined by a coupling between internal stresses-an intrinsic signature of glassy frustration-anharmonicity and low-frequency vibrational modes. These anomalously large values follow a fat-tailed distribution, with a universal exponent related to the recently observed universal [Formula: see text] density of states of quasilocalized low-frequency vibrational modes. When the spatial thermal energy field-a "softness field"-is considered, this power law tail manifests itself by highly localized spots, which are significantly softer than their surroundings. These soft spots are shown to be susceptible to plastic rearrangements under external driving forces, having predictive powers that surpass those of the normal modes-based approach. These results offer a general, system/model-independent, physical/observable-based approach to identify structural properties of quiescent glasses and relate them to glassy dynamics.

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.

Structure in sheared supercooled liquids: Dynamical rearrangements of an effective system of icosahedra

We consider a binary Lennard-Jones glassformer whose super-Arrhenius dynamics are correlated with the formation of particles organized into icosahedra under simple steady state shear. We recast this glassformer as an effective system of icosahedra [Pinney et al., J. Chem. Phys. 143, 244507 (2015)]. From the observed population of icosahedra in each steady state, we obtain an effective temperature which is linearly dependent on the shear rate in the range considered. Upon shear banding, the system separates into a region of high shear rate and a region of low shear rate. The effective temperatures obtained in each case show that the low shear regions correspond to a significantly lower temperature than the high shear regions. Taking a weighted average of the effective temperature of these regions (weight determined by region size) yields an estimate of the effective temperature which compares well with an effective temperature based on the global mesocluster population of the whole system.

Connecting Local Yield Stresses with Plastic Activity in Amorphous Solids

In model amorphous solids produced via differing quench protocols, a strong correlation is established between local yield stress measured by direct local probing of shear stress thresholds and the plastic rearrangements observed during remote loading in shear. This purely local measure shows a higher predictive power for identifying sites of plastic activity when compared with more conventional structural properties. Most importantly, the sites of low local yield stress, thus defined, are shown to be persistent, remaining predictive of deformation events even after fifty or more such plastic rearrangements. This direct and nonperturbative approach gives access to relevant transition pathways that control the stability of amorphous solids. Our results reinforce the relevance of modeling plasticity in amorphous solids based on a gradually evolving population of discrete and local zones preexisting in the structure.

Heterogeneity in the Small-Scale Deformation Behavior of Disordered Nanoparticle Packings

Atomic force microscopy-based nanoindentation is used to image and probe the local mechanical properties of thin disordered nanoparticle packings. The probed region is limited to the size of a few particles, and an individual particle can be loaded and displaced to a fraction of a single particle radius. The results demonstrate heterogeneous mechanical response that is location-dependent. The weak locations may be analogous to the "soft spots" previously predicted in glasses and other disordered packings.

Echoes from anharmonic normal modes in model glasses

Glasses display a wide array of nonlinear acoustic phenomena at temperatures T ≲ 1 K. This behavior has traditionally been explained by an ensemble of weakly coupled, two-level tunneling states, a theory that is also used to describe the thermodynamic properties of glasses at low temperatures. One of the most striking acoustic signatures in this regime is the existence of phonon echoes, a feature that has been associated with two-level systems with the same formalism as spin echoes in NMR. Here we report the existence of a distinctly different type of acoustic echo in classical models of glassy materials. Our simulations consist of finite-ranged, repulsive spheres and also particles with attractive forces using Lennard-Jones interactions. We show that these echoes are due to anharmonic, weakly coupled vibrational modes and perhaps provide an alternative explanation for the phonon echoes observed in glasses at low temperatures.

Glass transition of two-dimensional 80-20 Kob-Andersen model at constant pressure

We reconsider numerically the two-dimensional version of the Kob-Andersen model (KA2d) with a fraction of 80% of large spheres. A constant moderate pressure is imposed while the temperature T is systematically quenched from the liquid limit through the glass transition at [Formula: see text] down to very low temperatures. Monodisperse Lennard-Jones (mdLJ) bead systems, forming a crystal phase at low temperatures, are used to highlight several features of the KA2d model. As can be seen, e.g. from the elastic shear modulus G(T), determined using the stress-fluctuation formalism, our KA2d model is a good glass-former. A continuous cusp-singularity, [Formula: see text] with [Formula: see text], is observed in qualitative agreement with other recent numerical and theoretical work, however in striking conflict with the additive jump discontinuity predicted by mode-coupling theory.

Nonlinear plastic modes in disordered solids

We propose a theoretical framework within which a robust micromechanical definition of precursors to plastic instabilities, often termed soft spots, naturally emerges. They are shown to be collective displacements (modes) z[over ̂] that correspond to local minima of a barrier function b(z[over ̂]), which depends solely on inherent structure information. We demonstrate how some heuristic searches for local minima of b(z[over ̂]) can a priori detect the locus and geometry of imminent plastic instabilities with remarkable accuracy, at strains as large as γ_{c}-γ∼10^{-2} away from the instability strain γ_{c}. Our findings suggest that the a priori detection of the entire field of soft spots can be effectively carried out by a systematic investigation of the landscape of b(z[over ̂]).

Correlation between rearrangements and soft modes in polymer glasses during deformation and recovery

We explore the link between soft vibrational modes and local relaxation events in polymer glasses during physical aging, active deformation at constant strain rate, and subsequent recovery. A softness field is constructed out of the superposition of the amplitudes of the lowest energy normal modes, and found to predict up to 70% of the rearrangements. Overlap between softness and rearrangements increases logarithmically during aging and recovery phases as energy barriers rise due to physical aging, while yielding rapidly rejuvenates the overlap to that of a freshly prepared glass. In the strain hardening regime, correlations rise for uniaxial tensile deformation but not for simple shear. These trends can be explained by considering the differing degrees of localization of the soft modes in the two deformation protocols.

Identifying structural flow defects in disordered solids using machine-learning methods

We use machine-learning methods on local structure to identify flow defects-or particles susceptible to rearrangement-in jammed and glassy systems. We apply this method successfully to two very different systems: a two-dimensional experimental realization of a granular pillar under compression and a Lennard-Jones glass in both two and three dimensions above and below its glass transition temperature. We also identify characteristics of flow defects that differentiate them from the rest of the sample. Our results show it is possible to discern subtle structural features responsible for heterogeneous dynamics observed across a broad range of disordered materials.

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.

Structural relaxation in glassy polymers predicted by soft modes: a quantitative analysis

We present a quantitative analysis of the correlation between quasi-localized, low energy vibrational modes and structural relaxation events in computer simulations of a quiescent, thermal polymer glass. Our results extend previous studies on glass forming binary mixtures in 2D, and show that the soft modes identify regions that undergo irreversible rearrangements with up to 7 times the average probability. We study systems in the supercooled- and aging-regimes and discuss temperature- as well as age-dependence of the correlation. In addition to the location of rearrangements, we find that soft modes also predict their direction on the molecular level. The soft regions are long lived structural features, and the observed correlations vanish only after >50% of the system has undergone rearrangements.