Vibrational modes identify soft spots in a sheared disordered packing

Analyzing QCM Data Using a New Transfer-Matrix Model: Long-Ranged Asymmetric Gradient in Shear Modulus Identified Across Immiscible Glassy-Rubbery Polymer Interface

A new approach to analyzing quartz crystal microbalance (QCM) data using an acoustic transfer-matrix model is presented that enables determining a local depth-dependent shear modulus G̃(z) profile. A strong decrease in dissipation upon annealing is observed for immiscible polymer bilayer films of rubbery polybutadiene (PB) atop glassy polystyrene (PS), reflecting large viscoelastic changes in the sample corresponding to the emergence of a broad gradient in modulus G̃(z) when the ≈5 nm compositional interface is formed. Using a new transfer-matrix form of our continuum mechanics model that matches boundary conditions of shear waves between discrete modeled layers, we computationally fit these changes in frequency Δf(n) and dissipation ΔΓ(n) shifts over a range of harmonics n to the evolution of a modulus gradient. The G̃(z) gradient across the PS/PB bilayer, treated as a hyperbolic tangent, is observed to be broad (230 nm) and strongly asymmetric (200 nm) toward the glassy PS side, consistent with the general trends of local glass transition T g(z) previously reported. Surprisingly, the G̃(z) gradient is found to be symmetric on a log G scale, with the value of G at the interface equivalent to the geometric mean that optimizes acoustic energy transmission.

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.

Sampling the large-dimensional energy landscape of a 2D granular system with the hydra string method

In this work, I improve upon the existing hydra string method [C. Moakler and K. A. Newhall, Granular Matter, 2021, 24, 24] to systematically sample the energy landscape of a low friction 2D granular system. This method climbs in random directions out of a minimum energy state, finding unique saddle transition points and the neighboring minimum energy states only to repeat the process from the newly found minima. The data is saved as a network with nodes representing the energy-minimizing states and edges representing transition pathways that are parallel to the gradient of the energy at each point along the path. I show how the hydra string method is able to produce a better sample of transition pathways between stable states compared to just randomly sampling the system. The method is also modified to take into account energy minima that are not points caused by non-mechanically stable individual particles and skip past entire configurations that are not mechanically stable. The samples reveal that the energy of the states correlates with the size of the energy barriers between them. Neighboring state energies are also correlated, with correlations decreasing with distance as measured by path length on the network.

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.

Comparison of Physical Aging and Glass Transition in Glassy-Rubbery Polymer Bilayer Films

In the present work, we use ellipsometry to extract the physical aging response of thin glassy polystyrene (PS) layers from rubbery-glassy bilayer films of poly(n-butyl methacrylate) (PnBMA) atop PS. How the soft interface between rubbery and glassy polymer domains can impact the physical aging response of glassy domains is unclear. Measurements in the literature have shown that the local glass transition temperature Tg of PS is strongly reduced near a PnBMA/PS interface with a magnitude twice as large compared to that imparted by a free surface. As the free surface is known to reduce physical aging, we anticipated large changes in the physical aging response of PS within PnBMA/PS bilayer films. However, surprisingly the aging response remained equivalent to bulk down to 75 nm PS layer thicknesses that were the thinnest we found could be accurately measured given the optical limits of dispersion. With complementary fluorescence measurements, we show that the average Tg(hPS) of such PS layers within 150 nm PnBMA/75 nm PS bilayer films are also still bulk. These findings demonstrate that films with finite domain sizes have interfacial dynamical gradients that are significantly altered from those previously measured in systems with semi-infinite domain sizes.

Multiple and transforming vibrational identities of atoms in amorphous solids

Identifying the diverse roles of disorderly packed atoms inside an amorphous solid has been a highly pursued but daunting task in glass physics. By analyzing the full-frequency vibrational modes of a model Cu50Zr50 glass, here, we classify the internal atoms into low-, subhigh-, and high-frequency ones that have different tendencies for rearrangements upon excitations. We find that low-frequency atoms are structurally unfavored and tend to aggregate. High-frequency atoms originating from compressed atomic pairs are also mechanically unstable. As yield approaches, shear-transformation rearrangements shift from low-frequency to high-frequency atoms. Subhigh-frequency atoms play the role of stable backbones. Given that atoms can have different identities, multiple identities are observed to overlap in space. Atoms with one vibrational identity often transform to another one, showing different preferences in transformation routes. Our results deepen the understanding of atomic structures for amorphous plasticity beyond the simplified picture of soft vs hard spots.

Is the Future of Materials Amorphous? Challenges and Opportunities in Simulations of Amorphous Materials

Amorphous solids form an enormous and underutilized class of materials. In order to drive the discovery of new useful amorphous materials further we need to achieve a closer convergence between computational and experimental methods. In this review, we highlight some of the important gaps between computational simulations and experiments, discuss popular state-of-the-art computational techniques such as the Activation Relaxation Technique nouveau (ARTn) and Reverse Monte Carlo (RMC), and introduce more recent advances: machine learning interatomic potentials (MLIPs) and generative machine learning for simulations of amorphous matter (e.g., MAP). Examples are drawn from amorphous silicon and silica literature as well as from molecular glasses. Our outlook stresses the need for new computational methods to extend the time- and length-scales accessible through numerical simulations.

Experimental identification of topological defects in 2D colloidal glass

Topological defects are singularities within a field that cannot be removed by continuous transformations. The definition of these irregularities requires an ordered reference configuration, calling into question whether they exist in disordered materials, such as glasses. However, recent work suggests that well-defined topological defects emerge in the dynamics of glasses, even if they are not evident in the static configuration. In this study, we reveal the presence of topological defects in the vibrational eigenspace of a two-dimensional experimental colloidal glass. These defects strongly correlate with the vibrational features and spatially correlate with each other and structural "soft spots", more prone to plastic flow. This work experimentally confirms the existence of topological defects in disordered systems revealing the complex interplay between topology, disorder, and dynamics.

Selecting relevant structural features for glassy dynamics by information imbalance

We numerically investigate the identification of relevant structural features that contribute to the dynamical heterogeneity in a model glass-forming liquid. By employing the recently proposed information imbalance technique, we select these features from a range of physically motivated descriptors. This selection process is performed in a supervised manner (using both dynamical and structural data) and an unsupervised manner (using only structural data). We then apply the selected features to predict future dynamics using a machine learning technique. One of the advantages of the information imbalance technique is that it does not assume any model a priori, i.e., it is a non-parametric method. Finally, we discuss the potential applications of this approach in identifying the dominant mechanisms governing the glassy slow dynamics.

Medium-Range Structural Order as the Driver of Activated Dynamics and Complexity Reduction in Glass-Forming Liquids

We analyze in depth the Elastically Collective Nonlinear Langevin Equation theory of activated dynamics in metastable liquids to establish that the predicted inter-relationships between the alpha relaxation time, local cage and collective elastic barriers, dynamic localization length, and shear modulus are causally related within the theory to the medium range order (MRO) static correlation length. The latter grows exponentially with density for metastable hard sphere fluids and as a nonuniversal inverse power law with temperature for supercooled liquids under isobaric conditions. The physical origin of predicted connections between the alpha time and other metrics of cage order and the thermodynamic inverse dimensionless compressibility is fully established. It is discovered that although kinetic constraints from the real space first coordination shell are important for the alpha time, they are of secondary importance compared to the consequences of the more universal MRO correlations in both the modestly and deeply metastable regimes. This understanding sheds new light on the theoretical basis for, and prior successes of, the predictive mapping of chemically complex thermal liquids to effective hard sphere fluids based on matching their dimensionless compressibilities, a scheme we call "complexity reduction". In essence, the latter is equivalent to the physical requirement that the thermal liquid MRO correlation equals that of its effective hard sphere analog. The mapping alone is shown to provide a remarkable level of quantitative predictive power for the glass transition temperature Tg of 21 molecular and polymer liquids. Predictions for the chemically specific absolute magnitude and growth with cooling of the MRO correlation length are obtained and lie in the window of 2-6 nm at Tg. Dynamic heterogeneity, elastic facilitation, and beyond pair structure issues are briefly discussed. Future opportunities to theoretically analyze the equilibrated deep glass regime are outlined.

Tuning collective actuation of active solids by optimizing activity localization

Active solids, more specifically elastic lattices embedded with polar active units, exhibit collective actuation when the elasto-active feedback, generically present in such systems, exceeds some critical value. The dynamics then condensates on a small fraction of the vibrational modes, the selection of which obeys non trivial rules rooted in the nonlinear part of the dynamics. So far, the complexity of the selection mechanism has limited the design of specific actuation. Here, we investigate numerically how localizing activity to a fraction of modes enables the selection of non-trivial collective actuation. We perform numerical simulations of an agent-based model on triangular and disordered lattices and vary the concentration and the localization of the active agents on the lattice nodes. Both contribute to the distribution of the elastic energy across the modes. We then introduce an algorithm, which, for a given fraction of active nodes, evolves the localization of the activity in such a way that the energy distribution on a few targeted modes is maximized - or minimized. We illustrate on a specific targeted actuation, how the algorithm performs as compared to manually chosen localization of the activity. While, in the case of the ordered lattice, a well-educated guess performs better than the algorithm, and the latter outperform the manual trials in the case of the disordered lattice. Finally, the analysis of the results in the case of the ordered lattice leads us to introduce a design principle based on a measure of the susceptibility of the modes to be activated along certain activation paths.

Structural origin of relaxation in dense colloidal suspensions

Amorphous solids relax via slow molecular rearrangement induced by thermal fluctuations or applied stress. Microscopic structural signatures predicting these structural relaxations have been long searched for but have so far only been found in dynamic quantities such as vibrational quasi-localized soft modes or with structurally trained neural networks. A physically meaningful structural quantity remains elusive. Here, we introduce a structural order parameter derived from the mean-field caging potential experienced by the particles due to their neighbors, which reliably predicts the occurrence of structural relaxations. The structural parameter, derived from density functional theory, provides a measure of susceptibility to particle rearrangements that can effectively identify weak or defect-like regions in disordered systems. Using experiments on dense colloidal suspensions, we demonstrate a strong correlation between this order parameter and the structural relaxations of the amorphous solid. In quiescent suspensions, this correlation increases with density, when particle rearrangements become rarer and more localized. In sheared suspensions, the order parameter reliably pinpoints shear transformations; the applied shear weakens the caging potential due to shear-induced structural distortions, causing the proliferation of plastic deformation at structurally weak regions. Our work paves the way to a structural understanding of the relaxation of a wide range of amorphous solids, from suspensions to metallic glasses.

Exploring the unfolding pathways of protein families using Elastic Network Model

We explore how a protein's native structure determines its unfolding process. We examine how the local structural features, like shear, and the global structural properties, like the number of soft modes, change during unfolding. Simulations are performed using a Gaussian Network Model (GNM) with bond breaking for both thermal and force-induced unfolding scenarios. We find that unfolding starts in areas of high shear in the native structure and progressively spreads to the low shear regions. Interestingly, analysis of single domain protein families (Chymotrypsin inhibitor and Barnase) reveal that proteins with distinct unfolding pathways exhibit divergent behavior of the number of soft modes during unfolding. This suggests that the number of soft modes might be a valuable tool for understanding thermal unfolding pathways. Additionally, we found a strong link between a protein's overall structural similarity (TM-score) and its unfolding pathways, highlighting the importance of the native structure in determining how a protein unfolds.

Structural rejuvenation of a well-aged metallic glass

Rejuvenation of glassy structures in general is characterized by the exothermic enthalpy prior to the glass transition. In the present work, we find that this situation is not applicable to a heavily-aged Zr-based metallic glass that rejuvenates by anelastic deformation before yield. Instead, its rejuvenation can be precisely captured by the low-temperature boson heat capacity peak as well as the effective enthalpy change with the glass-to-liquid transition. These results demonstrate that a structurally stable glass could rejuvenate by decreasing mechanical stability of its basin of potential energy landscape, but without changing the basin's energy level. The underlying mechanism points toward the redistribution of the atomic free volume with a constant system-averaged value. We further find that the rejuvenation limit of this glass is its steady-flow state with self-similar inherent structures at both short- and long-time scales. Our findings refresh the understanding of glass rejuvenation and suggest that the boson peak is a better probe for the structural rejuvenation of glasses.

Clustering of negative topological charges precedes plastic failure in 3D glasses

The deformation mechanism in amorphous solids subjected to external shear remains poorly understood because of the absence of well-defined topological defects mediating the plastic deformation. The notion of soft spots has emerged as a useful tool to characterize the onset of irreversible rearrangements and plastic flow, but these entities are not clearly defined in terms of geometry and topology. In this study, we unveil the phenomenology of recently discovered, precisely defined topological defects governing the microscopic mechanical and yielding behavior of a model 3D glass under shear deformation. We identify the existence of vortex-like and antivortex-like topological defects within the 3D nonaffine displacement field. The number density of these defects exhibits a significant anticorrelation with the plastic events, with defect proliferation-annihilation cycles matching the alternation of elastic-like segments and catastrophic plastic drops, respectively. Furthermore, we observe collective annihilation of these point-like defects via plastic events, with large local topological charge fluctuations in the vicinity of regions that feature strong nonaffine displacements. We reveal that plastic yielding is driven by several large sized clusters of net negative topological charge, the massive annihilation of which triggers the onset of plastic flow. These findings suggest a geometric and topological characterization of soft spots and pave the way for the mechanistic understanding of topological defects as mediators of plastic deformation in glassy materials.

The yielding of granular matter is marginally stable and critical

Amorphous materials undergo a transition from liquid-like to solid-like states through processes like rapid quenching or densification. Under external loads, they exhibit yielding, with minimal structural changes compared to crystals. However, these universal characteristics are rarely explored comprehensively in a single granular experiment due to the added complexity of inherent friction. The discernible differences between static configurations before and after yielding are largely unaddressed, and a comprehensive examination from both statistical physics and mechanical perspectives is lacking. To address these gaps, we conducted experiments using photoelastic disks, simultaneously tracking particles and measuring forces. Our findings reveal that the yielding transition demonstrates critical behavior from a statistical physics standpoint and marginal stability from a mechanical perspective, akin to the isotropic jamming transition. This criticality differs significantly from spinodal criticality in frictionless amorphous solids, highlighting unique characteristics of granular yielding. Furthermore, our analysis confirms the marginal stability of granular yielding by assessing the contact number and evaluating the balance between weak forces and small gaps. These factors serve as structural indicators for configurations before and after yielding. Our results not only contribute to advancing our understanding of the fundamental physics of granular materials but also bear significant implications for practical applications in various fields.

Long-range correlations in elastic moduli and local stresses at the unjamming transition

We explore the behaviour of spatially heterogeneous elastic moduli as well as the correlations between local moduli in model solids with short-range repulsive potentials. We show through numerical simulations that local elastic moduli exhibit long-range correlations, similar to correlations in the local stresses. Specifically, the correlations in local shear moduli exhibit anisotropic behavior at large lengthscales characterized by pinch-point singularities in Fourier space, displaying a structural pattern akin to shear stress correlations. Focussing on two-dimensional jammed solids approaching the unjamming transition, we show that stress correlations exhibit universal properties, characterized by a quadratic p2 dependence of the correlations as the pressure p approaches zero, independent of the details of the model. In contrast, the modulus correlations exhibit a power-law dependence with different exponents depending on the specific interaction potential. Furthermore, we illustrate that while affine responses lack long-range correlations, the total modulus, which encompasses non-affine behavior, exhibits long-range correlations.

Predicting the pathways of string-like motions in metallic glasses via path-featurizing graph neural networks

String-like motions (SLMs)-cooperative, "snake"-like movements of particles-are crucial for dynamics in diverse glass formers. Despite their ubiquity, questions persist: Do SLMs prefer specific paths? If so, can we predict these paths? Here, in Al-Sm glasses, our isoconfigurational ensemble simulations reveal that SLMs do follow certain paths. By designing a graph neural network (GNN) to featurize the environment around directional paths, we achieve a high-fidelity prediction of likely SLM pathways, solely based on the static structure. GNN gauges a structural measure to assess each path's propensity to engage in SLMs, akin to a "softness" metric, but for paths rather than for atoms. Our GNN interpretation reveals the critical role of the bottleneck zone along a path in steering SLMs. By monitoring "path softness," we elucidate that SLM-favored paths transit from fragmented to interconnected upon glass transition. Our findings reveal that, beyond atoms or clusters, glasses have another dimension of structural heterogeneity: "paths."

Information decomposition in complex systems via machine learning

One of the fundamental steps toward understanding a complex system is identifying variation at the scale of the system's components that is most relevant to behavior on a macroscopic scale. Mutual information provides a natural means of linking variation across scales of a system due to its independence of functional relationship between observables. However, characterizing the manner in which information is distributed across a set of observables is computationally challenging and generally infeasible beyond a handful of measurements. Here, we propose a practical and general methodology that uses machine learning to decompose the information contained in a set of measurements by jointly optimizing a lossy compression of each measurement. Guided by the distributed information bottleneck as a learning objective, the information decomposition identifies the variation in the measurements of the system state most relevant to specified macroscale behavior. We focus our analysis on two paradigmatic complex systems: a Boolean circuit and an amorphous material undergoing plastic deformation. In both examples, the large amount of entropy of the system state is decomposed, bit by bit, in terms of what is most related to macroscale behavior. The identification of meaningful variation in data, with the full generality brought by information theory, is made practical for studying the connection between micro- and macroscale structure in complex systems.

Rearrangements during slow compression of a jammed two-dimensional emulsion

As amorphous materials get jammed, both geometric and dynamic heterogeneity are observed. We investigate the correlation between the local geometric heterogeneity and local rearrangements in a slowly compressed bidisperse quasi-two-dimensional emulsion system. The compression is driven by evaporation of the continuous phase and causes the area packing fraction to increase from 0.88 to 0.99. We quantify the structural heterogeneity of the system using the radical Voronoi tessellation following the method of Rieser et al. [Phys. Rev. Lett. 116, 088001 (2016)]0031-900710.1103/PhysRevLett.116.088001. We define two structural quantities characterizing local structure, the first of which considers nearest neighbors and the second of which includes information from second-nearest neighbors. We find that droplets in heterogeneous local regions are more likely to have local rearrangements. These rearrangements are generally T1 events where two droplets converge toward a void, and two droplets move away from the void to make room for the converging droplets. Thus, the presence of the voids tends to orient the T1 events. The presence of a correlation between the structural quantities and the rearrangement dynamics remains qualitatively unchanged over the entire range of packing fractions observed.

Low-frequency vibrational density of states of ordinary and ultra-stable glasses

A remarkable feature of disordered solids distinct from crystals is the violation of the Debye scaling law of the low-frequency vibrational density of states. Because the low-frequency vibration is responsible for many properties of solids, it is crucial to elucidate it for disordered solids. Numerous recent studies have suggested power-law scalings of the low-frequency vibrational density of states, but the scaling exponent is currently under intensive debate. Here, by classifying disordered solids into stable and unstable ones, we find two distinct and robust scaling exponents for non-phononic modes at low frequencies. Using the competition of these two scalings, we clarify the variation of the scaling exponent and hence reconcile the debate. Via the study of both ordinary and ultra-stable glasses, our work reveals a comprehensive picture of the low-frequency vibration of disordered solids and sheds light on the low-frequency vibrational features of ultra-stable glasses on approaching the ideal glass.

Anisotropic-Isotropic Transition of Cages at the Glass Transition

Characterizing the local structural evolution is an essential step in understanding the nature of glass transition. In this work, we probe the evolution of Voronoi cell geometry in simple glass models by simulations and colloid experiments, and find that the individual particle cages deform anisotropically in supercooled liquid and isotropically in glass. We introduce an anisotropy parameter k for each Voronoi cell, whose mean value exhibits a sharp change at the mode-coupling glass transition ϕ_{c}. Moreover, a power law of packing fraction ϕ∝q_{1}^{d} is discovered in the supercooled liquid regime with d>D, in contrast to d=D in the glass regime, where q_{1} is the first peak position of structure factor, and D is the space dimension. This power law is qualitatively explained by the change of k. The active motions in supercooled liquid are spatially correlated with long axes rather than short axes of Voronoi cells. In addition, the dynamic slowing down approaching the glass transition can be well characterized through a modified free-volume model based on k. These findings reveal that the structural parameter k is effective in identifying the structure-dynamics correlations and the glass transition in these systems.

Solid-that-Flows Picture of Glass-Forming Liquids

This perspective article reviews arguments that glass-forming liquids are different from those of standard liquid-state theory, which typically have a viscosity in the mPa·s range and relaxation times on the order of picoseconds. These numbers grow dramatically and become 1012 - 1015 times larger for liquids cooled toward the glass transition. This translates into a qualitative difference, and below the "solidity length" which is roughly one micron at the glass transition, a glass-forming liquid behaves much like a solid. Recent numerical evidence for the solidity of ultraviscous liquids is reviewed, and experimental consequences are discussed in relation to dynamic heterogeneity, frequency-dependent linear-response functions, and the temperature dependence of the average relaxation time.

Instantaneous normal modes of glass-forming liquids during the athermal relaxation process of the steepest descent algorithm

Understanding glass formation by quenching remains a challenge in soft condensed matter physics. Recent numerical studies on steepest descent dynamics, which is one of the simplest models of quenching, revealed that quenched liquids undergo slow relaxation with a power law towards mechanical equilibrium and that the late stage of this process is governed by local rearrangements of particles. These advances motivate the detailed study of instantaneous normal modes during the relaxation process because the glassy dynamics is considered to be governed by stationary points of the potential energy landscape. Here, we performed a normal mode analysis of configurations during the steepest descent dynamics and found that the dynamics is driven by almost flat directions of the potential energy landscape at long times. These directions correspond to localized modes and we characterized them in terms of their statistics and structure using methods developed in the study of local minima of the potential energy landscape.

Development of broad modulus profile upon polymer-polymer interface formation between immiscible glassy-rubbery domains

Interfaces of glassy materials such as thin films, blends, and composites create strong unidirectional gradients to the local heterogeneous dynamics that can be used to elucidate the length scales and mechanisms associated with the dynamic heterogeneity of glasses. We focus on bilayer films of two different polymers with very different glass transition temperatures ([Formula: see text]) where previous work has demonstrated a long-range (∼200 nm) profile in local [Formula: see text] is established between immiscible glassy and rubbery polymer domains when the polymer-polymer interface is formed to equilibrium. Here, we demonstrate that an equally long-ranged gradient in local modulus [Formula: see text] is established when the polymer-polymer interface ([Formula: see text]5 nm) is formed between domains of glassy polystyrene (PS) and rubbery poly(butadiene) (PB), consistent with previous reports of a broad [Formula: see text] profile in this system. A continuum physics model for the shear wave propagation caused by a quartz crystal microbalance across a PB/PS bilayer film is used to measure the viscoelastic properties of the bilayer during the evolution of the PB/PS interface showing the development of a broad gradient in local modulus [Formula: see text] spanning [Formula: see text]180 nm between the glassy and rubbery domains of PS and PB. We suggest these broad profiles in [Formula: see text] and [Formula: see text] arise from a coupling of the spectrum of vibrational modes across the polymer-polymer interface as a result of acoustic impedance matching of sound waves with [Formula: see text] nm during interface broadening that can then trigger density fluctuations in the neighboring domain.

Thawed matrix method for computing local mechanical properties of amorphous solids

We present a method for computing locally varying nonlinear mechanical properties in particle simulations of amorphous solids. Plastic rearrangements outside a probed region are suppressed by introducing an external field that directly penalizes large nonaffine displacements. With increasing strength of the field, plastic deformation can be localized. We characterize the distribution of local plastic yield stresses (residual local stresses to instability) with our approach and assess the correlation of their spatial maps with plastic activity in a model two-dimensional amorphous solid. Our approach reduces artifacts inherent in a previous method known as the "frozen matrix" approach that enforces fully affine deformation and improves the prediction of plastic rearrangements from structural information.

Athermal quasistatic cavitation in amorphous solids: Effect of random pinning

Amorphous solids are known to fail catastrophically via fracture, and cavitation at nano-metric scales is known to play a significant role in such a failure process. Micro-alloying via inclusions is often used as a means to increase the fracture toughness of amorphous solids. Modeling such inclusions as randomly pinned particles that only move affinely and do not participate in plastic relaxations, we study how the pinning influences the process of cavitation-driven fracture in an amorphous solid. Using extensive numerical simulations and probing in the athermal quasistatic limit, we show that just by pinning a very small fraction of particles, the tensile strength is increased, and also the cavitation is delayed. Furthermore, the cavitation that is expected to be spatially heterogeneous becomes spatially homogeneous by forming a large number of small cavities instead of a dominant cavity. The observed behavior is rationalized in terms of screening of plastic activity via the pinning centers, characterized by a screening length extracted from the plastic-eigenmodes.

Effects of polydispersity on the plastic behaviors of dense two-dimensional granular systems under shear

We study particle-scale motion in sheared highly polydisperse amorphous materials, in which the largest particles are as much as ten times the size of the smallest. We find strikingly different behavior from the more commonly studied amorphous systems with low polydispersity. In particular, an analysis of the nonaffine motion of particles reveals qualitative differences between large and small particles: The smaller particles have dramatically more nonaffine motion, which is induced by the presence of the large particles. We characterize how the nonaffine motion changes from the low- to high-polydispersity regimes. We further demonstrate a quantitative way to distinguish between "large" and "small" particles in systems with broad distributions of particle sizes. A macroscopic consequence of the nonaffine motion is a decrease in the energy dissipation rate for highly polydisperse samples, which is due both to a geometric consequence of the changing jamming conditions for higher polydispersity and to the changing character of nonaffine motion.

Detecting low-energy quasilocalized excitations in computer glasses

Soft, quasilocalized excitations (QLEs) are known to generically emerge in a broad class of disordered solids and to govern many facets of the physics of glasses, from wave attenuation to plastic instabilities. In view of this key role of QLEs, shedding light upon several open questions in glass physics depends on the availability of computational tools that allow one to study QLEs' statistical mechanics. The latter is a formidable task since harmonic analyses are typically contaminated by hybridizations of QLEs with phononic excitations at low frequencies, obscuring a clear picture of QLEs' abundance, typical frequencies, and other important micromechanical properties. Here we present an efficient algorithm to detect the field of quasilocalized excitations in structural computer glasses. The algorithm introduced takes a computer-glass sample as input and outputs a library of QLEs embedded in that sample. We demonstrate the power of the algorithm by reporting the spectrum of glassy excitations in two-dimensional computer glasses featuring a huge range of mechanical stability, which is inaccessible using conventional harmonic analyses due to phonon hybridizations. Future applications are discussed.

Relevance of structural defects to the mechanism of mechanical deformation in metallic glasses

It is known that deformation in disordered materials such as metallic glasses and supercooled liquids occurs via the cooperative rearrangement of atoms or constituent particles at dynamical heterogeneities, commonly regarded as point-like defects. We show via molecular-dynamics simulations that there is no apparent relationship between atomic rearrangements and the local atomic environment as measured by the atomic-level stresses, kinetic and potential energies, and the per-atom Voronoi volume. In addition, there is only a weak correlation between atomic rearrangements and the largest and smallest eigenvalues of the dynamical matrix. Our results confirm the transient nature of dynamical heterogeneities and suggest that the notion of defects may be less relevant than that of a propensity for rearrangement.

Enhanced vibrational stability in glass droplets

We show through simulations of amorphous solids prepared in open-boundary conditions that they possess significantly fewer low-frequency vibrational modes compared to their periodic boundary counterparts. Specifically, using measurements of the vibrational density of states, we find that the D ( ω ) ∼ ω 4 law changes to D ( ω ) ∼ ω δ with δ ≈ 5 in two dimensions and δ ≈ 4.5 in three dimensions. Crucially, this enhanced stability is achieved when utilizing slow annealing protocols to generate solid configurations. We perform an anharmonic analysis of the minima corresponding to the lowest frequency modes in such open-boundary systems and discuss their correlation with the density of states. A study of various system sizes further reveals that small systems display a higher degree of localization in vibrations. Lastly, we confine open-boundary solids in order to introduce macroscopic stresses in the system, which are absent in the unconfined system and find that the D ( ω ) ∼ ω 4 behavior is recovered.

Designing the pressure-dependent shear modulus using tessellated granular metamaterials

Jammed packings of granular materials display complex mechanical response. For example, the ensemble-averaged shear modulus 〈G〉 increases as a power law in pressure p for static packings of soft spherical particles that can rearrange during compression. We seek to design granular materials with shear moduli that can either increase or decrease with pressure without particle rearrangements even in the large-system limit. To do this, we construct tessellated granular metamaterials by joining multiple particle-filled cells together. We focus on cells that contain a small number of bidisperse disks in two dimensions. We first study the mechanical properties of individual disk-filled cells with three types of boundaries: periodic boundary conditions (PBC), fixed-length walls (FXW), and flexible walls (FLW). Hypostatic jammed packings are found for cells with FLW, but not in cells with PBC and FXW, and they are stabilized by quartic modes of the dynamical matrix. The shear modulus of a single cell depends linearly on p. We find that the slope of the shear modulus with pressure λ_{c}<0 for all packings in single cells with PBC where the number of particles per cell N≥6. In contrast, single cells with FXW and FLW can possess λ_{c}>0, as well as λ_{c}<0, for N≤16. We show that we can force the mechanical properties of multicell granular metamaterials to possess those of single cells by constraining the end points of the outer walls and enforcing an affine shear response. These studies demonstrate that tessellated granular metamaterials provide a platform for the design of soft materials with specified mechanical properties.

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.

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}.

Local and global measures of the shear moduli of jammed disk packings

Strain-controlled isotropic compression gives rise to jammed packings of repulsive, frictionless disks with either positive or negative global shear moduli. We carry out computational studies to understand the contributions of the negative shear moduli to the mechanical response of jammed disk packings. We first decompose the ensemble-averaged, global shear modulus as 〈G〉=(1-F_{-})〈G_{+}〉+F_{-}〈G_{-}〉, where F_{-} is the fraction of jammed packings with negative shear moduli and 〈G_{+}〉 and 〈G_{-}〉 are the average values from packings with positive and negative moduli, respectively. We show that 〈G_{+}〉 and 〈|G_{-}|〉 obey different power-law scaling relations above and below pN^{2}∼1. For pN^{2}>1, both 〈G_{+}〉N and 〈|G_{-}|〉N∼(pN^{2})^{β}, where β∼0.5 for repulsive linear spring interactions. Despite this, 〈G〉N∼(pN^{2})^{β^{'}} with β^{'}≳0.5 due to the contributions from packings with negative shear moduli. We show further that the probability distribution of global shear moduli P(G) collapses at fixed pN^{2} and different values of p and N. We calculate analytically that P(G) is a Γ distribution in the pN^{2}≪1 limit. As pN^{2} increases, the skewness of P(G) decreases and P(G) becomes a skew-normal distribution with negative skewness in the pN^{2}≫1 limit. We also partition jammed disk packings into subsystems using Delaunay triangulation of the disk centers to calculate local shear moduli. We show that the local shear moduli defined from groups of adjacent triangles can be negative even when G>0. The spatial correlation function of local shear moduli C(r[over ⃗]) displays weak correlations for pn_{sub}^{2}<10^{-2}, where n_{sub} is the number of particles within each subsystem. However, C(r[over ⃗]) begins to develop long-ranged spatial correlations with fourfold angular symmetry for pn_{sub}^{2}≳10^{-2}.

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.

Gas-liquid phase separation at zero temperature: mechanical interpretation and implications for gelation

The relationship between glasses and gels has been intensely debated for decades; however, the transition between these two phases remains elusive. To investigate a gel formation process in the zero-temperature limit and its relation to the glass phase, we conducted numerical experiments on athermal quasistatic decompression. During decompression, the system experiences a cavitation event similar to phase separation and this is a gelation process at zero temperature. A normal mode analysis revealed that the phase separation is signaled by the vanishing of the lowest eigenenergy, similar to plastic events of glasses under shear. One primary difference from the shear-induced plasticity is that the vanishing mode experiences a qualitative change in its spatial energy distribution at the phase separation point. These findings enable us to define the glass-gel phase boundary based on mechanics.

Low-frequency vibrational states in ideal glasses with random pinning

Glasses exhibit spatially localized vibrations in the low-frequency regime. These localized modes emerge below the boson peak frequency ω_{BP}, and their vibrational densities of state follow g(ω)∝ω^{4} (ω is frequency). Here, we attempt to address how the localized vibrations behave through the ideal glass transition. To do this, we employ a random pinning method, which enables us to study the thermodynamic glass transition. We find that the localized vibrations survive even in equilibrium glass states. Remarkably, the localized vibrations still maintain the properties of appearance below ω_{BP} and g(ω)∝ω^{4}. Our results provide important insight into the material properties of ideal glasses.

Predicting Defects in Soft Sphere Packings near Jamming Using the Force Network Ensemble

Amorphous systems of soft particles above jamming have more contacts than are needed to achieve mechanical equilibrium. The force network of a granular system with a fixed contact network is thus underdetermined and can be characterized as a random instantiation within the space of the force network ensemble. In this Letter, we show that defect contacts that are not necessary for stability of the system can be uniquely identified by examining the boundaries of this space of allowed force networks. We further show that, for simulations in the near jamming limit, this identification is nearly always correct and that defect contacts are broken under decompression of the system.

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.

Density of states below the first sound mode in 3D glasses

Glasses feature universally low-frequency excess vibrational modes beyond Debye prediction, which could help rationalize, e.g., the glasses’ unusual temperature dependence of thermal properties compared to crystalline solids. The way the density of states of these low-frequency excess modes D( ω) depends on the frequency ω has been debated for decades. Recent simulation studies of 3D glasses suggest that D( ω) scales universally with ω4 in a low-frequency regime below the first sound mode. However, no simulation study has ever probed as low frequencies as possible to test directly whether this quartic law could work all the way to extremely low frequencies. Here, we calculated D( ω) below the first sound mode in 3D glasses over a wide range of frequencies. We find D( ω) scales with ω β with β < 4 at very low frequencies examined, while the ω4 law works only in a limited intermediate-frequency regime in some glasses. Moreover, our further analysis suggests our observation does not depend on glass models or glass stabilities examined. The ω4 law of D( ω) below the first sound mode is dominant in current simulation studies of 3D glasses, and our direct observation of the breakdown of the quartic law at very low frequencies thus leaves an open but important question that may attract more future numerical and theoretical studies.

Correlation of plastic events with local structure in jammed packings across spatial dimensions

In frictionless jammed packings, existing evidence suggests a picture in which localized physics dominates in low spatial dimensions, d = 2, 3, but quickly loses relevance as d rises, replaced by spatially extended mean-field behavior. For example, quasilocalized low-energy vibrational modes and low-coordination particles associated with deviation from mean-field behavior (rattlers and bucklers) all vanish rapidly with increasing d. These results suggest that localized rearrangements, which are associated with low-energy vibrational modes, correlated with local structure, and dominant in low dimensions, should give way in higher d to extended rearrangements uncorrelated with local structure. Here, we use machine learning to analyze simulations of jammed packings under athermal, quasistatic shear, identifying a local structural variable, softness, that correlates with rearrangements in dimensions d = 2 to d = 5. We find that softness—and even just the local coordination number Z—is essentially equally predictive of rearrangements in all d studied. This result provides direct evidence that local structure plays an important role in higher d, suggesting a modified picture for the dimensional cross-over to mean-field theory.

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.

Identifying structural signature of dynamical heterogeneity via the local softness parameter

In this work we study the relationship between the softness of a mean-field caging potential and dynamics at the local level. We first describe the local softness, which shows a distribution, thus identifying structural heterogeneity. We show that the lifetime of the softness parameter is connected to the lifetime of the well-known cage structure in supercooled liquids. Finally, our theory predicts that the local softness and the local dynamics is causal below the onset temperature where there is a decoupling between the short and long time dynamics, thus allowing a static description of the cage. With the decrease in temperature, the correlation between structure and dynamics increases. The study shows that at lower temperatures, the structural heterogeneity increases, and since the structure becomes a better predictor of the dynamics, it leads to an increase in the dynamical heterogeneity. We also find that the softness of a hard, immobile region evolves with time and becomes soft and eventually mobile due to the rearrangements in the neighborhood, confirming the well-known facilitation effect.

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.

Role of Local Structure in the Enhanced Dynamics of Deformed Glasses

External stress can accelerate molecular mobility of amorphous solids by several orders of magnitude. The changes in mobility are commonly interpreted through the Eyring model, which invokes an empirical activation volume. Here, we analyze constant-stress molecular dynamics simulations and propose a structure-dependent Eyring model, connecting activation volume to a machine-learned field, softness. We show that stress has a heterogeneous effect on the mobility that depends on local structure through softness. The barrier impeding relaxation reduces more for well-packed particles, which explains the narrower distribution of relaxation time observed under stress.

Understanding slow compression and decompression of frictionless soft granular matter by network analysis

We consider dense granular systems in three spatial dimensions exposed to slow compression and decompression, below, during, above and well above jamming. The evolution of granular systems under slow deformation is non-trivial and involves smooth, continuous, reversible (de)compression periods, interrupted by fast, discontinuous, irreversible transition events. These events are often, but not always, associated with rearrangements of particles and of the contact network. How many particles are involved in these transitions between two states can range from few to almost all in the system. An analysis of the force network that is built on top of the contact network is carried out using the tools of persistent homology. Results involve the observation that kinetic energy is correlated with the intensity of rearrangements, while the evolution of global mechanical measures, such as pressure, is strongly correlated with the evolution of the topological measures quantifying loops in the force network. Surprisingly, some transitions are clearly detected by persistent homology even though motion/rearrangement of particles is much weaker, i.e., much harder to detect or, in some cases, not observed at all.

Searching for structural predictors of plasticity in dense active packings

In amorphous solids subject to shear or thermal excitation, so-called structural indicators have been developed that predict locations of future plasticity or particle rearrangements. An open question is whether similar tools can be used in dense active materials, but a challenge is that under most circumstances, active systems do not possess well-defined solid reference configurations. We develop a computational model for a dense active crowd attracted to a point of interest, which does permit a mechanically stable reference state in the limit of infinitely persistent motion. Previous work on a similar system suggested that the collective motion of crowds could be predicted by inverting a matrix of time-averaged two-particle correlation functions. Seeking a first-principles understanding of this result, we demonstrate that this active matter system maps directly onto a granular packing in the presence of an external potential, and extend an existing structural indicator based on linear response to predict plasticity in the presence of noisy dynamics. We find that the strong pressure gradient necessitated by the directed activity, as well as a self-generated free boundary, strongly impact the linear response of the system. In low-pressure regions the linear-response-based indicator is predictive, but it does not work well in the high-pressure interior of our active packings. Our findings motivate and inform future work that could better formulate structure-dynamics predictions in systems with strong pressure gradients.