ORIGINAL RESEARCH article
Sec. Mechanics of Materials
Volume 10 - 2023 | https://doi.org/10.3389/fmats.2023.1272355
Identifying a machine-learning structural descriptor linked to the creep behavior of Kob-Andersen glasses
- Computational Nanomaterials Laboratory, Department of Civil and Architectural Engineering, University of Miami, Coral Gables, FL, United States
A wide variety of materials, ranging from metals to concrete, experience, typically at high-temperatures or over long time scales, permanent deformations when subjected to sustained loads below their yield stress—a phenomenon known as creep. While theories grounded on defects such as vacancies, dislocations, or grain boundaries can explain creep in crystalline materials, our understanding of creep in disordered solids remains incomplete due to the lack of analogous structural descriptors. In this study, we use molecular dynamics to simulate the creep response of a Kob-Andersen glass model system under constant, uniaxial, compressive stress at finite temperature. We leverage that data to derive, using a machine-learning classification model, a structural descriptor termed looseness,
Certain materials, when exposed to sustained loads below their yielding point, and typically over long time scales and/or high temperatures, exhibit permanent deformations—a phenomenon known as creep. Creep occurs in metals under high-temperature conditions, such as those found in turbine blades (McLean, 1966), in ice causing glaciers to flow (Weertman, 1983), or in amorphous materials such as polymers (Brinson and Gates, 1995), metallic glasses (Castellero et al., 2008), or even concrete (Bazant and Wittmann, 1982), the most used man-made material worldwide. While several mechanisms responsible for creep of crystalline solids have been proposed, which include the diffusion of vacancies (Nabarro, 1948; Herring, 2004), dislocation dynamics (Harper and Dorn, 1957), or grain boundary sliding (Bell and Langdon, 1967; Langdon, 2006), all these mechanisms are based on structural defects that break the long-range order of the crystal lattice and therefore can be trivially identified. Analogous knowledge for disordered solids is understandably lacking, as what constitutes as a structural defect in these systems remains an open question. For example, intuitive structural descriptors, such as free volume or bond orientational order, have been shown to be poor predictors of the plasticity of glasses (Richard et al., 2020). Other more successful indicators have also been proposed such as soft-modes (Widmer-Cooper et al., 2008; Tanguy et al., 2010), or rattling amplitude (Larini et al., 2008), but those rely on the dynamics of the system and thus are not strictly structural.
Motivated by this challenge and the tremendous power of machine learning (ML) techniques to find patterns within complex datasets, when human intuition falls short (Bishop and Nasrabadi, 2006), (Cubuk et al., 2015) pioneered the use of ML techniques to identify potentially complex structural signatures that are predictive of the particle dynamics in glassy systems. In this context and given the challenge of collecting experimental data at the needed time and length scales, molecular dynamics (MD) simulations have become indispensable in generating high-quality, comprehensive data sets essential for the successful implementation of ML models. Despite the remarkable advancements made in this field over the past few years (Schoenholz et al., 2016; Wang and Jain, 2019; Bapst et al., 2020; Boattini et al., 2020; Fan et al., 2020; Wang et al., 2020; Liu et al., 2021; Peng et al., 2021; Wang and Zhang, 2021; Xiao et al., 2021; Wu et al., 2023), prior studies have tackled thermally-driven and stress-driven relaxation events independently. Studies focused on understanding structural signatures underlying the glass transition are based on simulations of stress-free glasses near the glass transition temperature. In contrast, those focused on predicting plastic rearrangements in disordered solids under stress rely, almost exclusively, on simulations of the glass under athermal, quasistatic shear conditions. Moreover, to the best of our knowledge, the recent work by Liu et al. (2021) stands alone in its focus on creep. Interestingly, they demonstrated, for shear strains up to approximately 1%, a strong correlation between the macroscopic creep rate and a structural descriptor derived through ML based on the initial undeformed structure of the disordered colloidal gel (Liu et al., 2021). Their simulations, however, were conducted in the quasistatic athermal regime and under oscillatory shear, which is a condition more closely related to fatigue behavior than to creep. Deriving ML structural descriptors that can predict the creep response of disordered solids under sustained loads at finite temperatures remains a largely unexplored area, and it is extremely relevant in the context, for example, of bulk metallic glasses operating at high temperatures (Li et al., 2019).
Here, we employ MD simulations to investigate the creep response of a Kob-Andersen (KA) glass (Kob and Andersen, 1995) under sustained uniaxial compressive stress at finite temperature. We provide a detailed analysis of how the macroscopic creep response of the glass is affected by the level of applied stress and temperature, as well as characterize the statistical evolution during creep of the microscopic deformations, which we characterize by the non-affine squared displacements of individual particles in the glass,
2 Materials and methods
2.1 Molecular dynamics simulations
We performed MD simulations using the program LAMMPS (Thompson et al., 2022) to study the creep response of a KA glass under a sustained compressive stress at finite temperature. The KA model is a two-component Lennard-Jones (LJ) system, which has been extensively used to study the dynamics of supercooled liquids and the glass transition, due to being relatively simple and computationally efficient while still being able to capture many of the key behaviors of real glasses (Kob and Andersen, 1995). All the simulated systems here contained 10,000 particles, where 80% and 20% of them were type A and type B, respectively. The parameters of the LJ interactions are:
We generated initial glass configurations as follows. First, we generated a random configuration of particles in a simulation box at density
Starting from each of those ten glass configurations, we performed simulations in the NPT ensemble where the KA glasses were instantaneously placed under a constant uniaxial compressive stress at
2.2 Analysis of non-affine displacements
We calculated the non-affine squared displacement of particle
2.3 Machine learning
2.3.1 Problem statement
Our ultimate goal is to train a ML model that can predict whether or not a particle will undergo a plastic rearrangement (
Each particle in each of the configurations outputted during the MD simulations at
2.3.3 Feature engineering
Inspired by the work by Wang and Jain (2019), we created features that encompass easily interpretable and straightforward structural quantities that capture the interstitial environments of each particle short- and medium-range length scales. The short-range features (SRFs) are derived from the free distances, areas, and volumes between a given particle and its neighbors. The distances, areas, and volumes, determined by pairs, triplets, and groups of four particles, respectively, are corrected for the spherical particle sizes (proportional to
FIGURE 1. Short-Range Features (SRFs) and Medium-Range Features (MRFs). (A) Particle O, surrounded by particles a, b, c, … , f which are neighbors according to a Voronoi construction depicted by black, dashed lines. A distance (green), an area (red), and a volume (yellow) element are illustrated in the sketch. (B) SRFs are calculated based on the summary statistics (mean, maximum, minimum, and standard deviation) of the distances, areas, and volumes defined by the particle O and its neighbors The numbers shown in the arrays correspond to the indexes of the corresponding features (1–12 are SRF, and 13 to 60 MRF). (C) The MRFs assigned to particle O comprise the summary statistics of the SRFs corresponding to the neighboring particles.
2.3.4 Workflow design
All the ML tasks in this paper were executed using Python scripts with the Scikit-Learn (Pedregosa et al., 2011) and Imbalanced-learn (Lemaître et al., 2017) packages. To evaluate and assess the ML models, we utilized balanced accuracy as our evaluation metric, which is the arithmetic mean of sensitivity,
To investigate the influence of
We used RFE, once established
2.4 Fluctuations, space, and time autocorrelation functions
We calculated the space autocorrelation function of looseness,
To characterize the temporal autocorrelation, we require a fixed reference space frame. To that end, we map each configuration of the glass to a cube of side 1, discretize that space into 15 × 15 × 15 voxels, and map the looseness of individual particles to each voxel in the normalized cube. That transformation allows us to track the time correlations of a looseness field,
We quantify the fluctuations of the looseness field as a function of system size,
3 Results and discussion
3.1 Macroscopic and microscopic creep response of the KA glass from MD simulations
We use the term macroscopic response, to denote the response at the system level, as our simulations are conducted on bulk glasses. Conversely, microscopic response pertains to the dynamics of individual particles. Figure 2A shows the uniaxial strain evolution of the KA glass under a uniaxial compressive stress of
FIGURE 2. Macroscopic creep response of the KA glass from MD simulations. (A) Time evolution of the average strain over ten independent runs,
To characterize the microscopic response of the glasses during creep at
FIGURE 3. Microscopic creep response of the KA glass from MD simulations. (A) The probability distribution of non-affine squared displacements,
3.2 Understanding the effect of
and on accuracy of the ML predictions
Two key parameters,
Figure 4 shows the validation accuracy for each class of classification models trained as described in the Section 2. Both Figures 4A, B show that the model performs slightly better on the majority class, which is expected given a series of factors including information richness and sampling quality. It is worth noting that the datasets used for training and validation, but not testing, were balanced using random undersampling. In Figure 4A, we see that the accuracy of the models increases monotonically with the threshold
FIGURE 4. Validation accuracy for each class as a function of: (A)
Figure 4B shows a logarithmic decay of the model accuracy with increasing
3.3 Feature selection and physical interpretation of the most important features
Before training the final classification ML model used to predict plastic rearrangements, we carry out RFE to identify and select the most important of the 60 features in the dataset. To this end, we use the data from the ten simulations at
FIGURE 5. (A) Average testing balanced accuracy versus the number of top n ranked features selected via RFE. Each point corresponds to the average of five model predictions trained each on independent balanced samples generated through random undersampling. (B) Top 10 ranked features by RFE. (C) Confusion matrix corresponding to the model trained using the top 10 ranked features by RFE, evaluated on the test set.
In Figure 5B, we show the top 10 ranked features by RFE, which will be used later to train the final model. The distribution between SRFs and MRFs is 4 to 6, suggesting that the medium-range order, which in the context of our work captures the interstitial environments of a particle’s neighbors (as determined by a Voronoi construction), plays a substantial role in determining plastic rearrangements. Interestingly, none of the selected SRFs—
3.4 Predicting creep using the ML derived structural indicator looseness
As detailed in the Section 2, we apply the EasyEnsemble algorithm with logistic regression as the estimator, using random under-sampling to balance the dataset, to train a ML model that predicts the probability of a particle to be classified as loose or class 1 within the system. We refer to this prediction metric as looseness,
Figure 6A shows the probability density of particles as a function of the squared non-affine displacements,
FIGURE 6. Probability distributions of looseness,
The time evolution of the average looseness in the glass,
FIGURE 7. Time evolution of (A) the average looseness, and (B) the macroscopic strain response of the KA glass. Each point and its corresponding error bars represent the average and standard deviation, respectively, at each time, over the ten independent MD runs.
3.5 Fluctuations, and spatial and temporal autocorrelations of looseness
We characterize the scaling of the fluctuations of the looseness field as a function of system size,
FIGURE 8. (A) Fluctuations of looseness field,
As described in the Section 2, in order to characterize the temporal autocorrelations,
FIGURE 9. (A) Time autocorrelation function of the looseness field,
In this study, we used a machine-learning (ML) classification model based on logistic regression trained with data from molecular dynamics (MD) simulations of Kob-Andersen (KA) glasses to derive a local structural descriptor, termed looseness,
In conclusion, our research underscores the substantial predictive power of ML-derived structural indicators in systems experiencing concurrent stress and thermal excitations. Nonetheless, future research will be required to untangle the intricate interplay between thermal fluctuations and mechanical activation of structural defects in disordered solids, and how each contributes to the overall mechanical behavior of the system.
Data availability statement
The raw data supporting the conclusion of this article will be made available by the authors, without undue reservation.
MW: Methodology, Software, Visualization, Writing–Original draft. LR: Conceptualization, Methodology, Software, Supervision, Writing–Original draft.
The author(s) declare that no financial support was received for the research, authorship, and/or publication of this article.
Conflict of interest
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.
The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fmats.2023.1272355/full#supplementary-material
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Keywords: creep, molecular dynamics, machine learning, glass, disordered solid
Citation: Wu M and Ruiz Pestana L (2023) Identifying a machine-learning structural descriptor linked to the creep behavior of Kob-Andersen glasses. Front. Mater. 10:1272355. doi: 10.3389/fmats.2023.1272355
Received: 03 August 2023; Accepted: 29 August 2023;
Published: 12 September 2023.
Edited by:Reza Abedi, The University of Tennessee, Knoxville, United States
Reviewed by:Yunjiang Wang, Chinese Academy of Sciences (CAS), China
Jie Xiong, Shanghai University, China
Copyright © 2023 Wu and Ruiz Pestana. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Luis Ruiz Pestana, email@example.com