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Wu ZW, Chen Y, Wang WH, Kob W, Xu L. Topology of vibrational modes predicts plastic events in glasses. Nat Commun 2023; 14:2955. [PMID: 37225717 DOI: 10.1038/s41467-023-38547-w] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2022] [Accepted: 05/02/2023] [Indexed: 05/26/2023] Open
Abstract
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.
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Affiliation(s)
- Zhen Wei Wu
- Institute of Nonequilibrium Systems, School of Systems Science, Beijing Normal University, 100875, Beijing, China.
- International Center for Quantum Materials, School of Physics, Peking University, Beijing, 100871, China.
| | - Yixiao Chen
- Yuanpei College, Peking University, 100871, Beijing, China
| | - Wei-Hua Wang
- Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
| | - Walter Kob
- Department of Physics, University of Montpellier and CNRS, 34095, Montpellier, France.
| | - Limei Xu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing, 100871, China.
- Collaborative Innovation Center of Quantum Matter, Beijing, 100871, China.
- Interdisciplinary Institute of Light-Element Quantum Materials and Research Center for Light-Element Advanced Materials, Peking University, Beijing, 100871, China.
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2
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Ishima D, Saitoh K, Otsuki M, Hayakawa H. Theory of rigidity and numerical analysis of density of states of two-dimensional amorphous solids with dispersed frictional grains in the linear response regime. Phys Rev E 2023; 107:054902. [PMID: 37328994 DOI: 10.1103/physreve.107.054902] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2022] [Accepted: 03/23/2023] [Indexed: 06/18/2023]
Abstract
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}.
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Affiliation(s)
- Daisuke Ishima
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa-oiwake cho, Sakyo-ku, Kyoto 606-8502, Japan
| | - Kuniyasu Saitoh
- Department of Physics, Faculty of Science, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-ku, Kyoto 603-8555, Japan
| | - Michio Otsuki
- Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Hisao Hayakawa
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa-oiwake cho, Sakyo-ku, Kyoto 606-8502, Japan
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3
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Ishima D, Saitoh K, Otsuki M, Hayakawa H. Eigenvalue analysis of stress-strain curve of two-dimensional amorphous solids of dispersed frictional grains with finite shear strain. Phys Rev E 2023; 107:034904. [PMID: 37073050 DOI: 10.1103/physreve.107.034904] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2022] [Accepted: 03/05/2023] [Indexed: 04/20/2023]
Abstract
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.
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Affiliation(s)
- Daisuke Ishima
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa-oiwake cho, Sakyo-ku, Kyoto 606-8502, Japan
| | - Kuniyasu Saitoh
- Department of Physics, Faculty of Science, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-ku, Kyoto 603-8555, Japan
| | - Michio Otsuki
- Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Hisao Hayakawa
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa-oiwake cho, Sakyo-ku, Kyoto 606-8502, Japan
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4
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Font-Clos F, Zanchi M, Hiemer S, Bonfanti S, Guerra R, Zaiser M, Zapperi S. Predicting the failure of two-dimensional silica glasses. Nat Commun 2022; 13:2820. [PMID: 35595727 PMCID: PMC9122924 DOI: 10.1038/s41467-022-30530-1] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2021] [Accepted: 04/29/2022] [Indexed: 11/09/2022] Open
Abstract
Being able to predict the failure of materials based on structural information is a fundamental issue with enormous practical and industrial relevance for the monitoring of devices and components. Thanks to recent advances in deep learning, accurate failure predictions are becoming possible even for strongly disordered solids, but the sheer number of parameters used in the process renders a physical interpretation of the results impossible. Here we address this issue and use machine learning methods to predict the failure of simulated two dimensional silica glasses from their initial undeformed structure. We then exploit Gradient-weighted Class Activation Mapping (Grad-CAM) to build attention maps associated with the predictions, and we demonstrate that these maps are amenable to physical interpretation in terms of topological defects and local potential energies. We show that our predictions can be transferred to samples with different shape or size than those used in training, as well as to experimental images. Our strategy illustrates how artificial neural networks trained with numerical simulation results can provide interpretable predictions of the behavior of experimentally measured structures. The sheer number of parameters in deep learning makes the physical interpretation of failure predictions in glasses challenging. Here the authors use Grad-CAM to reveal the role of topological defects and local potential energies in failure predictions.
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Affiliation(s)
- Francesc Font-Clos
- Center for Complexity and Biosystems, Department of Physics, University of Milan, via Celoria 16, 20133, Milan, Italy
| | - Marco Zanchi
- Center for Complexity and Biosystems, Department of Physics, University of Milan, via Celoria 16, 20133, Milan, Italy
| | - Stefan Hiemer
- Institute of Materials Simulation, Department of Materials Science Science and Engineering, Friedrich-Alexander-University Erlangen-Nuremberg, Dr.-Mack-Str. 77, 90762, Fürth, Germany
| | - Silvia Bonfanti
- Center for Complexity and Biosystems, Department of Physics, University of Milan, via Celoria 16, 20133, Milan, Italy.,CNR - Consiglio Nazionale delle Ricerche, Istituto di Chimica della Materia Condensata e di Tecnologie per l'Energia Via R. Cozzi 53, 20125, Milan, Italy
| | - Roberto Guerra
- Center for Complexity and Biosystems, Department of Physics, University of Milan, via Celoria 16, 20133, Milan, Italy
| | - Michael Zaiser
- Institute of Materials Simulation, Department of Materials Science Science and Engineering, Friedrich-Alexander-University Erlangen-Nuremberg, Dr.-Mack-Str. 77, 90762, Fürth, Germany
| | - Stefano Zapperi
- Center for Complexity and Biosystems, Department of Physics, University of Milan, via Celoria 16, 20133, Milan, Italy. .,Institute of Materials Simulation, Department of Materials Science Science and Engineering, Friedrich-Alexander-University Erlangen-Nuremberg, Dr.-Mack-Str. 77, 90762, Fürth, Germany. .,CNR - Consiglio Nazionale delle Ricerche, Istituto di Chimica della Materia Condensata e di Tecnologie per l'Energia Via R. Cozzi 53, 20125, Milan, Italy.
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5
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Guerra R, Bonfanti S, Procaccia I, Zapperi S. Universal density of low-frequency states in silica glass at finite temperatures. Phys Rev E 2022; 105:054104. [PMID: 35706171 DOI: 10.1103/physreve.105.054104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2021] [Accepted: 04/13/2022] [Indexed: 06/15/2023]
Abstract
The theoretical understanding of the low-frequency modes in amorphous solids at finite temperature is still incomplete. The study of the relevant modes is obscured by the dressing of interparticle forces by collision-induced momentum transfer that is unavoidable at finite temperatures. Recently, it was proposed that low-frequency modes of vibrations around the thermally averaged configurations deserve special attention. In simple model glasses with bare binary interactions, these included quasilocalized modes whose density of states appears to be universal, depending on the frequencies as D(ω)∼ω^{4}, in agreement with the similar law that is obtained with bare forces at zero temperature. In this paper, we report investigations of a model of silica glass at finite temperature; here the bare forces include binary and ternary interactions. Nevertheless, we can establish the validity of the universal law of the density of quasilocalized modes also in this richer and more realistic model glass.
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Affiliation(s)
- Roberto Guerra
- Center for Complexity and Biosystems, Department of Physics, University of Milan, via Celoria 16, 20133 Milano, Italy
| | - Silvia Bonfanti
- Center for Complexity and Biosystems, Department of Physics, University of Milan, via Celoria 16, 20133 Milano, Italy
| | - Itamar Procaccia
- Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
- Center for OPTical IMagery Analysis and Learning, Northwestern Polytechnical University, Xi'an, 710072 China
| | - Stefano Zapperi
- Center for Complexity and Biosystems, Department of Physics, University of Milan, via Celoria 16, 20133 Milano, Italy
- CNR-Consiglio Nazionale delle Ricerche, Istituto di Chimica della Materia Condensata e di Tecnologie per l'Energia, Via R. Cozzi 53, 20125 Milano, Italy
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6
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Bhaumik H, Foffi G, Sastry S. Avalanches, Clusters, and Structural Change in Cyclically Sheared Silica Glass. PHYSICAL REVIEW LETTERS 2022; 128:098001. [PMID: 35302798 DOI: 10.1103/physrevlett.128.098001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/17/2021] [Revised: 01/14/2022] [Accepted: 02/09/2022] [Indexed: 06/14/2023]
Abstract
We investigate avalanches and clusters associated with plastic rearrangements and the nature of structural change in the prototypical strong glass, silica, computationally. We perform a detailed analysis of avalanches, and of spatially disconnected clusters that constitute them, for a wide range of system sizes. Although qualitative aspects of yielding in silica are similar to other glasses, the statistics of clusters exhibits significant differences, which we associate with differences in local structure. Across the yielding transition, anomalous structural change and densification, associated with a suppression of tetrahedral order, is observed to accompany strain localization.
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Affiliation(s)
- Himangsu Bhaumik
- Jawaharlal Nehru Center for Advanced Scientific Research, Jakkur Campus, Bengaluru 560064, India
| | - Giuseppe Foffi
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
| | - Srikanth Sastry
- Jawaharlal Nehru Center for Advanced Scientific Research, Jakkur Campus, Bengaluru 560064, India
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7
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Bhaumik H, Foffi G, Sastry S. Yielding transition of a two dimensional glass former under athermal cyclic sheardeformation. J Chem Phys 2022; 156:064502. [DOI: 10.1063/5.0085064] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
| | - Giuseppe Foffi
- Laboratoire de Physique des Solides, Laboratoire de Physique des Solides, France
| | - Srikanth Sastry
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, India
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8
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Baró J, Pouragha M, Wan R, Davidsen J. Quasistatic kinetic avalanches and self-organized criticality in deviatorically loaded granular media. Phys Rev E 2021; 104:024901. [PMID: 34525539 DOI: 10.1103/physreve.104.024901] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2021] [Accepted: 07/08/2021] [Indexed: 11/07/2022]
Abstract
The behavior of granular media under quasistatic loading has recently been shown to attain a stable evolution state corresponding to a manifold in the space of micromechanical variables. This state is characterized by sudden transitions between metastable jammed states, involving the partial micromechanical rearrangement of the granular medium. Using numerical simulations of two-dimensional granular media under quasistatic biaxial compression, we show that the dynamics in the stable evolution state is characterized by scale-free avalanches well before the macromechanical stationary flow regime traditionally linked to a self-organized critical state. This, together with the nonuniqueness and the nonmonotony of macroscopic deformation curves, suggests that the statistical avalanche properties and the susceptibilities of the system cannot be reduced to a function of the macromechanical state. The associated scaling exponents are nonuniversal and depend on the interactions between particles. For stiffer particles (or samples at low confining pressure) we find distributions of avalanche properties compatible with the predictions of mean-field theory. The scaling exponents decrease below the mean-field values for softer interactions between particles. These lower exponents are consistent with observations for amorphous solids at their critical point. We specifically discuss the relationship between microscopic and macroscopic variables, including the relation between the external stress drop and the internal potential energy released during kinetic avalanches.
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Affiliation(s)
- Jordi Baró
- Department of Physics and Astronomy, University of Calgary, 2500 University Drive NW Calgary, Alberta, Canada T2N 1N4.,Centre for Mathematical Research, Campus de Bellaterra, Edifici C, 08193 Bellaterra, Barcelona, Spain
| | - Mehdi Pouragha
- Civil Engineering Department, University of Calgary, 2500 University Drive NW Calgary, Alberta, Canada T2N 1N4.,Department of Civil and Environmental Engineering, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario, Canada K1S 5B6
| | - Richard Wan
- Civil Engineering Department, University of Calgary, 2500 University Drive NW Calgary, Alberta, Canada T2N 1N4
| | - Jörn Davidsen
- Department of Physics and Astronomy, University of Calgary, 2500 University Drive NW Calgary, Alberta, Canada T2N 1N4.,Hotchkiss Brain Institute, University of Calgary, 3330 Hospital Drive NW, Calgary, Alberta, Canada T2N 4N1
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9
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Ebrahem F, Bamer F, Markert B. Origin of reversible and irreversible atomic-scale rearrangements in a model two-dimensional network glass. Phys Rev E 2020; 102:033006. [PMID: 33076029 DOI: 10.1103/physreve.102.033006] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2020] [Accepted: 09/09/2020] [Indexed: 01/08/2023]
Abstract
In this contribution, we investigate the fundamental mechanism of plasticity in a model two-dimensional network glass. The glass is generated by using a Monte Carlo bond-switching algorithm and subjected to athermal simple shear deformation, followed by subsequent unloading at selected deformation states. This enables us to investigate the topological origin of reversible and irreversible atomic-scale rearrangements. It is shown that some events that are triggered during loading recover during unloading, while some do not. Thus, two kinds of elementary plastic events are observed, which can be linked to the network topology of the model glass.
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Affiliation(s)
- Firaz Ebrahem
- Institute of General Mechanics, RWTH Aachen University, 52062 Aachen, Germany
| | - Franz Bamer
- Institute of General Mechanics, RWTH Aachen University, 52062 Aachen, Germany
| | - Bernd Markert
- Institute of General Mechanics, RWTH Aachen University, 52062 Aachen, Germany
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10
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Bonfanti S, Guerra R, Mondal C, Procaccia I, Zapperi S. Universal Low-Frequency Vibrational Modes in Silica Glasses. PHYSICAL REVIEW LETTERS 2020; 125:085501. [PMID: 32909803 DOI: 10.1103/physrevlett.125.085501] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/12/2020] [Revised: 07/09/2020] [Accepted: 07/21/2020] [Indexed: 06/11/2023]
Abstract
It was recently shown that different simple models of glass formers with binary interactions define a universality class in terms of the density of states of their quasilocalized low-frequency modes. Explicitly, once the hybridization with standard Debye (extended) modes is avoided, a number of such models exhibit a universal density of states, depending on the mode frequencies as D(ω)∼ω^{4}. It is unknown, however, how wide this universality class is, and whether it also pertains to more realistic models of glass formers. To address this issue we present analysis of the quasilocalized modes in silica, a network glass that has both binary and ternary interactions. We conclude that in three dimensions silica exhibits the very same frequency dependence at low frequencies, suggesting that this universal form is a generic consequence of amorphous glassiness.
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Affiliation(s)
- Silvia Bonfanti
- Center for Complexity and Biosystems, Department of Physics, University of Milan, via Celoria 16, 20133 Milano, Italy
| | - Roberto Guerra
- Center for Complexity and Biosystems, Department of Physics, University of Milan, via Celoria 16, 20133 Milano, Italy
| | - Chandana Mondal
- Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
| | - Itamar Procaccia
- Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
- Center for OPTical IMagery Analysis and Learning, Northwestern Polytechnical University, Xi'an, 710072 China
| | - Stefano Zapperi
- Center for Complexity and Biosystems, Department of Physics, University of Milan, via Celoria 16, 20133 Milano, Italy
- CNR-Consiglio Nazionale delle Ricerche, Istituto di Chimica della Materia Condensata e di Tecnologie per l'Energia, Via R. Cozzi 53, 20125 Milano, Italy
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