Session A45: Understanding Glasses and Disordered Systems Through Computational Models I

Predicting failure in disordered solids from structural metrics

Under applied shear, amorphous solids flow via a succession of plastic rearrangements of localized particles. Numerous numerical and experimental studies have shown that plastic instabilities in glasses are triggered by spatially localized soft spots in direct analogy with dislocations present in crystalline solids, although the population and microscopic structure of the former are significantly different from the latter. In addition, many research groups have developed methods for identifying such defects, although these methods have not been systematically compared. Here we use a swap Monte Carlo algorithm to prepare equilibrium amorphous configurations with very different stabilities that exhibit a range of behaviors under shear, from ductile flow to brittle failure. We compute various structural indicators ranging from purely structural to highly non-linear metrics that require the knowledge of the interactions between constituents. We compare these metrics on the same data sets, quantifying how well these metrics perform in predicting plastic deformation across this range of glass stabilities. Moreover, we use these structural metrics to quantify the spatial distribution of plastic defects for different preparation protocols, as well as the evolution of these defects across the yielding transition, allowing us to precisely characterize how the microscopic structure encodes the differences between ductile and brittle materials.   

Yielding of Ultrastable Computer Glasses

We study mechanical yielding of ultrastable computer glasses generated by optimized swap Monte-Carlo simulations for polydisperse particles [1,2] as well as more realistic multi-component metallic glass models [3]. We observe brittle yielding associated with a sharp system-spanning shearband in various rheological settings, such as uniform shear and oscillatory deformation in two and three dimensions [4,5,6]. The observed behaviors are qualitatively different from the standard computer glasses that have been studied previously. Thus, our computational scheme opens up new opportunities to investigate the mechanical behaviors of metallic glasses in experimentally relevant conditions. As an application, we numerically test the scenario of shearband nucleation by artificially inserting a soft spot into a stable glass sample. We argue that brittle yielding in macroscopic samples is triggered by rare droplets of the soft spot [4].

[1] Berthier, Coslovich, Ninarello, and Ozawa, Phys. Rev. Lett., 116, 238002 (2018)
[2] Ozawa, Berthier, Biroli, Rosso, and Tarjus, PNAS, 115, 6656 (2018)
[3] Parmar, Ozawa, and Berthier
[4] Ozawa, Berthier, Biroli, and Tarjus
[5] Singh, Ozawa, and Berthier
[6] Yeh, Ozawa, Miyazaki, Kawasaki, and Berthier   

When does local structure play a role in sheared jammed packings?

In jammed packings, it is usually assumed that local structure only plays a significant role in specific regimes. For instance, it is known that in jammed packings the variance of the relative excess coordination, δΖ/Ζ_c, decays like 1/d, so that local structure should play no role at high spatial dimensions. Furthermore, in any fixed dimension d >= 2, lowering the pressure results in a diverging length scale, again suggesting that local structure should not be sufficient to describe response. Here we address the validity of the assumption that local structure does not matter in these cases. Focusing on jammed packings under athermal, quasistatic shear, we utilize machine learning to identify a local structural variable, softness, that has been shown to be strongly predictive of rearrangements in many disordered systems. We apply the softness analysis to plastic events in jammed packings across many dimensions and pressures, and find that local structure is perhaps more predictive than one might have guessed.   

Connecting thermal relaxation to local yield stress in glassy systems

We study a binary Lennard-Jones mixture in the supercooled regime using molecular dynamic simulations. At low temperatures, thermal relaxation proceeds in a series of activated jumps between inherent structures, i.e. local minima of the potential energy landscape. From these inherent dynamics we recover information about the location of thermally activated rearrangements. We observe a strong connection between the thermal relaxation and areas where the structure has been previously identified as being soft using a local, direct probing of shear stress thresholds. Using the probability distribution of local shear stresses we are able to capture features of the system's dynamical relaxation processes. We thus can establish a link between structural and dynamical properties of the supercooled liquid. Furthermore, we extend our analysis to out of equilibrium dynamics by studying the effects of rejuvenation and aging on the local yield stress distribution in both glasses and liquids at different temperatures.   

Correlation between local structural order and ductility of glasses

Bulk metallic glasses (BMGs) are amorphous metallic alloys with desirable material properties such as high yield strength and superior corrosion resistance compared to conventional crystalline alloys. However, their use as structural materials has been limited because of their brittle behavior, especially in tension. In this work, we identify atomic-scale structural signatures in undeformed metallic glasses that are able to predict their mechanical response to tension or pure shear tests. In particular, we employ molecular dynamics simulations to prepare different types of glasses using a range of cooling rates and interaction potentials, including highly polydisperse soft-repulsive spheres, binary Lennard-Jones spheres, atomic systems that interact via the Stillinger-Weber potential, and binary and ternary alloys described by the embedded atom method. We then perform quasi-static tension or pure shear tests on the glassy samples, and measure the shear stress and local structural order as a function of strain. For each model system, we find a strong correlation between the measure of local structural order in the undeformed sample and the mechanical response at finite strain.   

Understanding shear bands characteristics and formation in model glasses through the measure of the local yield stress.

Many phenomena remain poorly understood in amorphous materials such as plasticity and shear banding, their brittleness and disordered structure making it difficult to study them experimentally. As a consequence, we employ a two-dimensional Lennard-Jones numerical model of glasses and measure their local yield stress, a measure of the local softness presented in [1]. This method is nonperturbative and gives access to a quantitative property on a well-controlled length scale. Applying it on deeply quench glasses under simple shear loading, we show that the plastic events create a local yield stress [2] decrease in the material which cause the emergence of a shear band [3]. We finally focus on the shear bands formation by looking for a relevant localization criterion to understand the influence of the system size and quench protocol.


[1] A. Barbot et al., Phys. Rev. E, 97, 033001 (2018)
[2] S. Patinet et al., arXiv::cond-mat/1906.09818 (2019)
[3] A. Barbot et al., arXiv::cond-mat/1906.09663 (2019)   

Atomic nonaffinity as structural indicator of protocol-dependent plasticity in amorphous solids

Structural heterogeneity of amorphous solids challenges the prediction of plastic events which is intimately connected to their mechanical behaviors. Here we report the atomic nonaffinity, as a structural indicator with intrinsic orientation, which is derived from the total nonaffine modulus based on a perturbation analysis of the potential energy landscape. We find that the atomic nonaffinity can efficiently characterize the locations of plastic events, which is comparable to other indicators. More importantly, it can accurately predict the protocol-dependent response of plastic events by quantitatively analyzing the relation between its softest direction and shear loading direction. These results shed light on the characterization and prediction of the mechanical response of amorphous solids.   

Unveiling the predictive power of static structure in glassy systems

Despite decades of theoretical studies, the nature of the glass transition remains elusive and debated, while the existence of structural predictors of the dynamics is a major open question. Recent approaches propose inferring predictors from a variety of human-defined features using machine learning. We learn the long time evolution of a glassy system solely from the initial particle positions and without any hand-crafted features, using a powerful model: graph neural networks. We show that this method strongly outperforms state-of-the-art methods, generalizing over a wide range of temperatures, pressures, and densities. In shear experiments, it predicts the location of rearranging particles. The structural predictors learned by our network exhibit a correlation length which increases with larger timescales to reach the size of our system. Beyond glasses, our method could apply to many other physical systems that map to a graph of local interactions.   

Identifying flow units by machine learning in a model metallic glass

Characterizing and predicting the flow units directly from the atomic structure are longstanding challenges in metallic glasses. We report the successful identification of flow units in the model Zr₅₀Cu₅₀ metallic glass above and below its glass transition temperature by machine learning methods. We find that the differences of the structural characteristics between flow units and the rest of the system are beyond short-range order, and further confirmed by the local structural entropy. Our study demonstrates that machine learning provides an unconventional tool to understand the intrinsic heterogeneities in metallic glasses, and sheds light on the structural indicator of heterogeneous dynamic behaviors in amorphous solids.   

Residual stress distributions and mechanical noise in athermally deformed amorphous solids from atomistic simulations

The distribution P(x) of local residual stresses in amorphous packings governs the statistical properties of global collective failure events at the yielding transition. We reveal the evolution of P(x) upon deformation by combining atomistic simulations with the frozen matrix approach. A pseudogap form P(x) ~ x^Θ is observed in the freshly quenched state and in the early stages of deformation. After a few percent strain, however, P(x) starts to develop a plateau p₀ in the small x-limit, where p₀ ~ L^-p with L the system size. A direct comparison with the system size scaling of the stress drops shows that the distribution of avalanche sizes are controlled by Θ in the transient regime and the plateau exponent p in the steady state flow. The broad distribution of mechanical noise P(|Δx|) ~ |Δx|^-1-µ is characterized by a Levy-exponent μ and can be related to the behavior of P(x) via a mean-field description.   

Interplay between rearrangements, strain, and softness and during avalanche propagation

Disordered solids yield at a common shear strain of about 3%, but the behavior beyond yield is different for different systems and for systems with different histories. Foams can deform indefinitely without fracturing, many systems exhibit crackling noise or avalanche behavior, and still others exhibit shear banding and brittle fracture. Here we study an athermal, jammed packing of Hertzian particles that is sheared quasistatically. We identify the stress drops associated with rearrangements and then use steepest descent dynamics to study the evolution of the avalanches. We find that the avalanches consist of localized events that appear sequentially in well-separated locations of the sample. To understand this behavior, we study the interplay between rearrangements, strain, and softness, a machine-learned structural descriptor that predicts the propensity of a particle to rearrange. We find that each rearrangement gives rise to a shear strain field that can immediately trigger other rearrangements, while also causing an isotropic strain field that changes the softness of other particles; this may affect subsequent rearrangements over a much longer time scale. We compare our results to elasto-plastic and mean-field models of avalanches.   

Structural evolution of amorphous systems during avalanches

Under applied shear strain, granular and amorphous materials deform. At zero temperature, the deformation can be separated into elastic branches where the particles do not change neighbors and rearrangements where they do. Some rearrangement events are small and localized, while others involve large or system-spanning avalanches. Using numerical simulations of soft spheres, we find that avalanches can be decomposed into a series of localized excitations, and we develop an extension of persistent homology to isolate these excitations. Next, we develop a method to study the linear response of unstable systems during an avalanche, by extending existing tools for identifying structural defects using the Hessian and study how the population of structural defects evolves during an avalanche. We find that localized excitations in the avalanche correlate strongly with localized excitations in the linear spectrum, and investigate how these excitations are created and coupled during the avalanche. These data should help to constrain elastoplastic models for glasses and granular matter.   

The behavior of jammed packings under correlated random forces

Mean-field calculations suggest that the response of a system to global shear and random forces are essentially equivalent in infinite dimensions. However, it remains an open question whether this is true for systems in lower dimensions. To address this, Morse and collaborators have recently developed a method for driving 2D jammed packings of disks quasti-statically, with random, infinitely-persistent, active forces, and found striking similarities and differences between sheared and actively forced systems. Here, we extend that previous work by studying how changing correlation length of the random forcing affects the mechanical response. We find that both the effective modulus with respect to the random forcing direction, as well as the average effective strain between rearrangements or saddle points, does change systematically with correlation length. This paves the way for a deeper understanding of the connection between shear and active driving in lower dimensions.