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Jocteur T, Figueiredo S, Martens K, Bertin E, Mari R. Yielding Is an Absorbing Phase Transition with Vanishing Critical Fluctuations. PHYSICAL REVIEW LETTERS 2024; 132:268203. [PMID: 38996301 DOI: 10.1103/physrevlett.132.268203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/22/2024] [Accepted: 05/21/2024] [Indexed: 07/14/2024]
Abstract
The yielding transition in athermal complex fluids can be interpreted as an absorbing phase transition between an elastic, absorbing state with high mesoscopic degeneracy and a flowing, active state. We characterize quantitatively this phase transition in an elastoplastic model under fixed applied shear stress, using a finite-size scaling analysis. We find vanishing critical fluctuations of the order parameter (i.e., the shear rate), and relate this property to the convex character of the phase transition (β>1). We locate yielding within a family of models akin to fixed-energy sandpile (FES) models, only with long-range redistribution kernels with zero modes that result from mechanical equilibrium. For redistribution kernels with sufficiently fast decay, this family of models belongs to a short-range universality class distinct from the conserved directed percolation class of usual FES, which is induced by zero modes.
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2
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Shekh Alshabab S, Markert B, Bamer F. Criticality in the fracture of silica glass: Insights from molecular mechanics. Phys Rev E 2024; 109:034110. [PMID: 38632794 DOI: 10.1103/physreve.109.034110] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2023] [Accepted: 02/02/2024] [Indexed: 04/19/2024]
Abstract
The universality of avalanches characterizing the inelastic response of disordered materials has the potential to bridge the gap from micro to macroscale. In this study, we explore the statistics and the scaling behavior of avalanches occurring during the fracture process in silica glass using molecular mechanics. We introduce a robust method for capturing and quantifying these avalanches, allowing us to perform rigorous statistical analyses, revealing universal power laws associated with critical phenomena. The influence of an initial crack is explored, observing deviations from mean-field predictions while maintaining the property of criticality. However, the avalanche exponents in the unnotched samples are predicted correctly by the mean-field depinning model. Furthermore, we investigate the strain-dependent probability density function, its cutoff function, and the interrelation between the critical exponents. Finally, we unveil distinct scaling behavior for small and large avalanches of the crack growth, shedding light on the underlying fracture mechanisms in silica glass.
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Affiliation(s)
| | - Bernd Markert
- Institute of General Mechanics, RWTH Aachen University, 52062 Aachen, Germany
| | - Franz Bamer
- Institute of General Mechanics, RWTH Aachen University, 52062 Aachen, Germany
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3
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Zhu W, Li Z, Shu H, Gao H, Wei X. Amorphous alloys surpass E/10 strength limit at extreme strain rates. Nat Commun 2024; 15:1717. [PMID: 38403631 PMCID: PMC10894860 DOI: 10.1038/s41467-024-45472-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2022] [Accepted: 01/23/2024] [Indexed: 02/27/2024] Open
Abstract
Theoretical predictions of the ideal strength of materials range from E/30 to E/10 (E is Young's modulus). However, despite intense interest over the last decade, the value of the ideal strength achievable through experiments for metals remains a mystery. This study showcases the remarkable spall strength of Cu50Zr50 amorphous alloy that exceeds the E/10 limit at strain rates greater than 107 s-1 through laser-induced shock experiments. The material exhibits a spall strength of 11.5 GPa, approximately E/6 or 1/13 of its P-wave modulus, which sets a record for the elastic limit of metals. Electron microscopy and large-scale molecular dynamics simulations reveal that the primary failure mechanism at extreme strain rates is void nucleation and growth, rather than shear-banding. The rate dependence of material strength is explained by a void kinetic model controlled by surface energy. These findings help advance our understanding on the mechanical behavior of amorphous alloys under extreme strain rates.
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Affiliation(s)
- Wenqing Zhu
- State Key Laboratory for Turbulence and Complex System, Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing, 100871, China
| | - Zhi Li
- Institute of High Performance Computing, Agency for Science, Technology and Research (A*STAR), Singapore, 138632, Republic of Singapore
| | - Hua Shu
- Shanghai Institute of Laser Plasma, China Academy of Engineering Physics, Shanghai, 201800, China
| | - Huajian Gao
- Institute of High Performance Computing, Agency for Science, Technology and Research (A*STAR), Singapore, 138632, Republic of Singapore.
- School of Mechanical and Aerospace Engineering, College of Engineering, Nanyang Technological University, 70 Nanyang Drive, 637457, Singapore, Republic of Singapore.
- Center for Advanced Mechanics and Materials, Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing, 100084, China.
| | - Xiaoding Wei
- State Key Laboratory for Turbulence and Complex System, Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing, 100871, China.
- Peking University Nanchang Innovation Institute, Nanchang, 330000, China.
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4
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Ozawa M, Biroli G. Elasticity, Facilitation, and Dynamic Heterogeneity in Glass-Forming Liquids. PHYSICAL REVIEW LETTERS 2023; 130:138201. [PMID: 37067329 DOI: 10.1103/physrevlett.130.138201] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2022] [Accepted: 03/02/2023] [Indexed: 06/19/2023]
Abstract
We study the role of elasticity-induced facilitation on the dynamics of glass-forming liquids by a coarse-grained two-dimensional model in which local relaxation events, taking place by thermal activation, can trigger new relaxations by long-range elastically mediated interactions. By simulations and an analytical theory, we show that the model reproduces the main salient facts associated with dynamic heterogeneity and offers a mechanism to explain the emergence of dynamical correlations at the glass transition. We also discuss how it can be generalized and combined with current theories.
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Affiliation(s)
- Misaki Ozawa
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | - Giulio Biroli
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
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5
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Richard D, Elgailani A, Vandembroucq D, Manning ML, Maloney CE. Mechanical excitation and marginal triggering during avalanches in sheared amorphous solids. Phys Rev E 2023; 107:034902. [PMID: 37072969 DOI: 10.1103/physreve.107.034902] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2022] [Accepted: 02/26/2023] [Indexed: 04/20/2023]
Abstract
We study plastic strain during individual avalanches in overdamped particle-scale molecular dynamics (MD) and mesoscale elastoplastic models (EPM) for amorphous solids sheared in the athermal quasistatic limit. We show that the spatial correlations in plastic activity exhibit a short length scale that grows as t^{3/4} in MD and ballistically in EPM, which is generated by mechanical excitation of nearby sites not necessarily close to their stability thresholds, and a longer lengthscale that grows diffusively for both models and is associated with remote marginally stable sites. These similarities in spatial correlations explain why simple EPMs accurately capture the size distribution of avalanches observed in MD, though the temporal profiles and dynamical critical exponents are quite different.
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Affiliation(s)
- D Richard
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, Amsterdam, Netherlands
- Department of Physics and BioInspired Institute, Syracuse University, Syracuse, New York 13244, USA
- Univiversité Grenoble Alpes, CNRS, LIPhy, 38000 Grenoble, France
| | - A Elgailani
- Northeastern University, Boston, Massachusetts 02115, USA
| | - D Vandembroucq
- PMMH, CNRS UMR 7636, ESPCI Paris, PSL University, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | - M L Manning
- Department of Physics and BioInspired Institute, Syracuse University, Syracuse, New York 13244, USA
| | - C E Maloney
- Northeastern University, Boston, Massachusetts 02115, USA
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6
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Korchinski D, Rottler J. Dynamic phase diagram of plastically deformed amorphous solids at finite temperature. Phys Rev E 2022; 106:034103. [PMID: 36266895 DOI: 10.1103/physreve.106.034103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2022] [Accepted: 07/27/2022] [Indexed: 06/16/2023]
Abstract
The yielding transition that occurs in amorphous solids under athermal quasistatic deformation has been the subject of many theoretical and computational studies. Here, we extend this analysis to include thermal effects at finite shear rate, focusing on how temperature alters avalanches. We derive a nonequilibrium phase diagram capturing how temperature and strain rate effects compete, when avalanches overlap, and whether finite-size effects dominate over temperature effects. The predictions are tested through simulations of an elastoplastic model in two dimensions and in a mean-field approximation. We find a scaling for temperature-dependent softening in the low-strain rate regime when avalanches do not overlap, and a temperature-dependent Herschel-Bulkley exponent in the high-strain rate regime when avalanches do overlap.
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Affiliation(s)
- Daniel Korchinski
- Department of Physics and Astronomy and Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver BC V6T 1Z1, Canada
| | - Jörg Rottler
- Department of Physics and Astronomy and Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver BC V6T 1Z1, Canada
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7
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Vasisht VV, Chaudhuri P, Martens K. Residual stress in athermal soft disordered solids: insights from microscopic and mesoscale models. SOFT MATTER 2022; 18:6426-6436. [PMID: 35980086 DOI: 10.1039/d2sm00615d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
In soft amorphous materials, shear cessation after large shear deformation leads to configurations having residual shear stress. The origin of these states and the distribution of the local shear stresses within the material is not well understood, despite its importance for the change in material properties and consequent applications. In this work, we use molecular dynamics simulations of a model dense non-Brownian soft amorphous material to probe the non-trivial relaxation process towards a residual stress state. We find that, similar to thermal glasses, an increase in shear rate prior to the shear cessation leads to lower residual stress states. We rationalise our findings using a mesoscopic elasto-plastic description that explicitly includes a long range elastic response to local shear transformations. We find that after flow cessation the initial stress relaxation indeed depends on the pre-sheared stress state, but the final residual stress is majorly determined by newly activated plastic events occurring during the relaxation process, a scenario consistent with the phenomenology of avalanche dynamics in the low shear rate limit of steadily sheared amorphous solids. Our simplified coarse grained description not only allows capturing the phenomenology of residual stress states but also rationalising the altered material properties that are probed using small and large deformation protocols applied to the relaxed material.
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Affiliation(s)
- Vishwas V Vasisht
- Department of Physics, Indian Institute of Technology, Palakkad 678557, India.
| | | | - Kirsten Martens
- The Institute of Mathematical Sciences, Taramani, Chennai 600113, India
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8
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Abstract
Arrested soft materials such as gels and glasses exhibit a slow stress relaxation with a broad distribution of relaxation times in response to linear mechanical perturbations. Although this macroscopic stress relaxation is an essential feature in the application of arrested systems as structural materials, consumer products, foods, and biological materials, the microscopic origins of this relaxation remain poorly understood. Here, we elucidate the microscopic dynamics underlying the stress relaxation of such arrested soft materials under both quiescent and mechanically perturbed conditions through X-ray photon correlation spectroscopy. By studying the dynamics of a model associative gel system that undergoes dynamical arrest in the absence of aging effects, we show that the mean stress relaxation time measured from linear rheometry is directly correlated to the quiescent superdiffusive dynamics of the microscopic clusters, which are governed by a buildup of internal stresses during arrest. We also show that perturbing the system via small mechanical deformations can result in large intermittent fluctuations in the form of avalanches, which give rise to a broad non-Gaussian spectrum of relaxation modes at short times that is observed in stress relaxation measurements. These findings suggest that the linear viscoelastic stress relaxation in arrested soft materials may be governed by nonlinear phenomena involving an interplay of internal stress relaxations and perturbation-induced intermittent avalanches.
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9
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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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10
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Korchinski D, Ruscher C, Rottler J. Signatures of the spatial extent of plastic events in the yielding transition in amorphous solids. Phys Rev E 2021; 104:034603. [PMID: 34654138 DOI: 10.1103/physreve.104.034603] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2021] [Accepted: 08/06/2021] [Indexed: 11/07/2022]
Abstract
Amorphous solids are yield stress materials that flow when a sufficient load is applied. Their flow consists of periods of elastic loading interrupted by rapid stress drops, or avalanches, coming from microscopic rearrangements known as shear transformations (STs). Here we show that the spatial extent of avalanches in a steadily sheared amorphous solid has a profound effect on the distribution of local residual stresses that in turn determines the stress drop statistics. As reported earlier, the most unstable sites are located in a flat "plateau" region that decreases with system size. While the entrance into the plateau is set by the lower cutoff of the mechanical noise produced by individual STs, the departure from the usually assumed power-law (pseudogap) form of the residual stress distribution comes from far field effects related to spatially extended rearrangements. Interestingly, we observe that the average residual stress of the weakest sites is located in an intermediate power-law regime between the pseudogap and the plateau regimes, whose exponent decreases with system size. Our findings imply a new scaling relation linking the exponents characterizing the avalanche size and residual stress distributions.
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Affiliation(s)
- Daniel Korchinski
- Department of Physics and Astronomy and Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver BC V6T 1Z1, Canada
| | - Céline Ruscher
- Institut Charles Sadron - CNRS - UPR22, 23 rue du Loess, F-67034 Strasbourg, France
| | - Jörg Rottler
- Department of Physics and Astronomy and Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver BC V6T 1Z1, Canada
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11
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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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12
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Oyama N, Mizuno H, Ikeda A. Unified view of avalanche criticality in sheared glasses. Phys Rev E 2021; 104:015002. [PMID: 34412287 DOI: 10.1103/physreve.104.015002] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2020] [Accepted: 06/14/2021] [Indexed: 11/07/2022]
Abstract
Plastic events in sheared glasses are considered an example of so-called avalanches, whose sizes obey a power-law probability distribution with the avalanche critical exponent τ. Although the so-called mean-field depinning (MFD) theory predicts a universal value of this exponent, τ_{MFD}=1.5, such a simplification is now known to connote qualitative disagreement with realistic systems. Numerically and experimentally, different values of τ have been reported depending on the literature. Moreover, in the elastic regime, it has been noted that the critical exponent can be different from that in the steady state, and even criticality itself is a matter of debate. Because these confusingly varying results have been reported under different setups, our knowledge of avalanche criticality in sheared glasses is greatly limited. To gain a unified understanding, in this work, we conduct a comprehensive numerical investigation of avalanches in Lennard-Jones glasses under athermal quasistatic shear. In particular, by excluding the ambiguity and arbitrariness that has crept into the conventional measurement schemes, we achieve high-precision measurement and demonstrate that the exponent τ in the steady state follows the prediction of MFD theory, τ_{MFD}=1.5. Our results also suggest that there are two qualitatively different avalanche events. This binariness leads to the nonuniversal behavior of the avalanche size distribution and is likely to be the cause of the varying values of τ reported thus far. To investigate the dependence of criticality and universality on applied shear, we further study the statistics of avalanches in the elastic regime and the ensemble of the first avalanche event in different samples, which provide information about the unperturbed system. We show that while the unperturbed system is indeed off-critical, criticality gradually develops as shear is applied. The degree of criticality is encoded in the fractal dimension of the avalanches, which starts from zero in the off-critical unperturbed state and saturates in the steady state. Moreover, the critical exponent τ is consistent with the prediction of the MFD τ_{MFD} universally, regardless of the amount of applied shear, once the system becomes critical.
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Affiliation(s)
- Norihiro Oyama
- Graduate School of Arts and Sciences, The University of Tokyo, Komaba, Tokyo 153-8902, Japan.,Mathematics for Advanced Materials-OIL, AIST, Sendai 980-8577, Japan
| | - Hideyuki Mizuno
- Graduate School of Arts and Sciences, The University of Tokyo, Komaba, Tokyo 153-8902, Japan
| | - Atsushi Ikeda
- Graduate School of Arts and Sciences, The University of Tokyo, Komaba, Tokyo 153-8902, Japan.,Research Center for Complex Systems Biology, Universal Biology Institute, The University of Tokyo, Komaba, Tokyo 153-8902, Japan
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13
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Chacko RN, Landes FP, Biroli G, Dauchot O, Liu AJ, Reichman DR. Elastoplasticity Mediates Dynamical Heterogeneity Below the Mode Coupling Temperature. PHYSICAL REVIEW LETTERS 2021; 127:048002. [PMID: 34355934 DOI: 10.1103/physrevlett.127.048002] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/04/2021] [Revised: 05/14/2021] [Accepted: 06/10/2021] [Indexed: 05/23/2023]
Abstract
As liquids approach the glass transition temperature, dynamical heterogeneity emerges as a crucial universal feature of their behavior. Dynamic facilitation, where local motion triggers further motion nearby, plays a major role in this phenomenon. Here we show that long-ranged, elastically mediated facilitation appears below the mode coupling temperature, adding to the short-range component present at all temperatures. Our results suggest deep connections between the supercooled liquid and glass states, and pave the way for a deeper understanding of dynamical heterogeneity in glassy systems.
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Affiliation(s)
- Rahul N Chacko
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
- James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
| | - François P Landes
- Université Paris-Saclay, CNRS, Laboratoire Interdisciplinaire des Sciences du Numérique, Orsay 91400, France
| | - Giulio Biroli
- Laboratoire de Physique de l'École normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris F-75005 Paris, France
| | - Olivier Dauchot
- UMR Gulliver 7083 CNRS, ESPCI, PSL Research University, 10 rue Vauquelin, Paris 75005, France
| | - Andrea J Liu
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - David R Reichman
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA
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14
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Jovković D, Janićević S, Mijatović S, Laurson L, Spasojević D. Effects of external noise on threshold-induced correlations in ferromagnetic systems. Phys Rev E 2021; 103:062114. [PMID: 34271613 DOI: 10.1103/physreve.103.062114] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2020] [Accepted: 05/17/2021] [Indexed: 11/07/2022]
Abstract
In the present paper we investigate the impact of the external noise and detection threshold level on the simulation data for the systems that evolve through metastable states. As a representative model of such systems we chose the nonequilibrium athermal random-field Ising model with two types of the external noise, uniform white noise and Gaussian white noise with various different standard deviations, imposed on the original response signal obtained in model simulations. We applied a wide range of detection threshold levels in analysis of the signal and show how these quantities affect the values of exponent γ_{S/T} (describing the scaling of the average avalanche size with duration), the shift of waiting time between the avalanches, and finally the collapses of the waiting time distributions. The results are obtained via extensive numerical simulations on the equilateral three-dimensional cubic lattices of various sizes and disorders.
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Affiliation(s)
- Dragutin Jovković
- Faculty of Mining and Geology, University of Belgrade, P.O. Box 162, 11000 Belgrade, Serbia
| | - Sanja Janićević
- Faculty of Science, University of Kragujevac, P.O. Box 60, 34000 Kragujevac, Serbia
| | - Svetislav Mijatović
- Faculty of Physics, University of Belgrade, P.O. Box 44, 11001 Belgrade, Serbia
| | - Lasse Laurson
- Computational Physics Laboratory, Tampere University, P.O. Box 692, FI-33014 Tampere, Finland
| | - Djordje Spasojević
- Faculty of Physics, University of Belgrade, P.O. Box 44, 11001 Belgrade, Serbia
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15
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Khirallah K, Tyukodi B, Vandembroucq D, Maloney CE. Yielding in an Integer Automaton Model for Amorphous Solids under Cyclic Shear. PHYSICAL REVIEW LETTERS 2021; 126:218005. [PMID: 34114864 DOI: 10.1103/physrevlett.126.218005] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/11/2020] [Accepted: 04/06/2021] [Indexed: 06/12/2023]
Abstract
We present results on an automaton model of an amorphous solid under cyclic shear. After a transient, the steady state falls into one of three cases in order of increasing strain amplitude: (i) pure elastic behavior with no plastic activity, (ii) limit cycles where the state recurs after an integer period of strain cycles, and (iii) irreversible plasticity with longtime diffusion. The number of cycles N required for the system to reach a periodic orbit diverges as the amplitude approaches the yielding transition between regimes (ii) and (iii) from below, while the effective diffusivity D of the plastic strain field vanishes on approach from above. Both of these divergences can be described by a power law. We further show that the average period T of the limit cycles increases on approach to yielding.
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Affiliation(s)
| | - Botond Tyukodi
- Northeastern University, Boston, Massachusetts 02115, USA
- Department of Physics, Brandeis University, Waltham, Massachusetts 02454, USA
| | - Damien Vandembroucq
- PMMH, CNRS, ESPCI Paris, Université PSL, Sorbonne Université, Université de Paris, F-75005 Paris, France
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16
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Johari MAF, Mazlan SA, Nasef MM, Ubaidillah U, Nordin NA, Aziz SAA, Johari N, Nazmi N. Microstructural behavior of magnetorheological elastomer undergoing durability evaluation by stress relaxation. Sci Rep 2021; 11:10936. [PMID: 34035434 PMCID: PMC8149425 DOI: 10.1038/s41598-021-90484-0] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2021] [Accepted: 04/20/2021] [Indexed: 11/28/2022] Open
Abstract
The widespread use of magnetorheological elastomer (MRE) materials in various applications has yet to be limited due to the fact that there are substantial deficiencies in current experimental and theoretical research on its microstructural durability behavior. In this study, MRE composed of silicon rubber (SR) and 70 wt% of micron-sized carbonyl iron particles (CIP) was prepared and subjected to stress relaxation evaluation by torsional shear load. The microstructure and particle distribution of the obtained MRE was evaluated by a field emission scanning electron microscopy (FESEM). The influence of constant low strain at 0.01% is the continuing concern within the linear viscoelastic (LVE) region of MRE. Stress relaxation plays a significant role in the life cycle of MRE and revealed that storage modulus was reduced by 8.7%, normal force has weakened by 27%, and stress performance was reduced by 6.88% along approximately 84,000 s test duration time. This time scale was the longest ever reported being undertaken in the MRE stress relaxation study. Novel micro-mechanisms that responsible for the depleted performance of MRE was obtained by microstructurally observation using FESEM and in-phase mode of atomic force microscope (AFM). Attempts have been made to correlate strain localization produced by stress relaxation, with molecular deformation in MRE amorphous matrix. Exceptional attention was focused on the development of molecular slippage, disentanglement, microplasticity, microphase separation, and shear bands. The relation between these microstructural phenomena and the viscoelastic properties of MRE was diffusely defined and discussed. The presented MRE is homogeneous with uniform distribution of CIP. The most significant recent developments of systematic correlation between the effects of microstructural deformation and durability performance of MRE under stress relaxation has been observed and evaluated.
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Affiliation(s)
- Mohd Aidy Faizal Johari
- Engineering Materials and Structures (eMast) ikhoza, Malaysia-Japan, International Institute of Technology (MJIIT), Universiti Teknologi Malaysia, 54100, Kuala Lumpur, Malaysia
| | - Saiful Amri Mazlan
- Engineering Materials and Structures (eMast) ikhoza, Malaysia-Japan, International Institute of Technology (MJIIT), Universiti Teknologi Malaysia, 54100, Kuala Lumpur, Malaysia.
| | - Mohamed Mahmoud Nasef
- Advanced Materials Research Group, Centre of Hydrogen Energy, Institute of Future Energy, Universiti Teknologi Malaysia, 54100, Kuala Lumpur, Malaysia
| | - U Ubaidillah
- Mechanical Engineering Department, Faculty of Engineering, Universitas Sebelas Maret, J1. Ir. Sutami 36A, Ketingan, Surakarta, 57126, Central Java, Indonesia.
| | - Nur Azmah Nordin
- Engineering Materials and Structures (eMast) ikhoza, Malaysia-Japan, International Institute of Technology (MJIIT), Universiti Teknologi Malaysia, 54100, Kuala Lumpur, Malaysia
| | - Siti Aishah Abdul Aziz
- Engineering Materials and Structures (eMast) ikhoza, Malaysia-Japan, International Institute of Technology (MJIIT), Universiti Teknologi Malaysia, 54100, Kuala Lumpur, Malaysia
| | - Norhasnidawani Johari
- Engineering Materials and Structures (eMast) ikhoza, Malaysia-Japan, International Institute of Technology (MJIIT), Universiti Teknologi Malaysia, 54100, Kuala Lumpur, Malaysia
| | - Nurhazimah Nazmi
- Engineering Materials and Structures (eMast) ikhoza, Malaysia-Japan, International Institute of Technology (MJIIT), Universiti Teknologi Malaysia, 54100, Kuala Lumpur, Malaysia
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17
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Clemmer JT, Salerno KM, Robbins MO. Criticality in sheared, disordered solids. I. Rate effects in stress and diffusion. Phys Rev E 2021; 103:042605. [PMID: 34005889 DOI: 10.1103/physreve.103.042605] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/30/2020] [Accepted: 03/16/2021] [Indexed: 11/07/2022]
Abstract
Rate effects in sheared disordered solids are studied using molecular dynamics simulations of binary Lennard-Jones glasses in two and three dimensions. In the quasistatic (QS) regime, systems exhibit critical behavior: the magnitudes of avalanches are power-law distributed with a maximum cutoff that diverges with increasing system size L. With increasing rate, systems move away from the critical yielding point and the average flow stress rises as a power of the strain rate with exponent 1/β, the Herschel-Bulkley exponent. Finite-size scaling collapses of the stress are used to measure β as well as the exponent ν which characterizes the divergence of the correlation length. The stress and kinetic energy per particle experience fluctuations with strain that scale as L^{-d/2}. As the largest avalanche in a system scales as L^{α}, this implies α<d/2. The diffusion rate of particles diverges as a power of decreasing rate before saturating in the QS regime. A scaling theory for the diffusion is derived using the QS avalanche rate distribution and generalized to the finite strain rate regime. This theory is used to collapse curves for different system sizes and confirm β/ν.
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Affiliation(s)
- Joel T Clemmer
- Sandia National Laboratories, Albuquerque, New Mexico 87123, USA
| | | | - Mark O Robbins
- Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA
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18
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Ferrero EE, Jagla EA. Properties of the density of shear transformations in driven amorphous solids. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:124001. [PMID: 33393487 DOI: 10.1088/1361-648x/abd73a] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2020] [Accepted: 12/29/2020] [Indexed: 06/12/2023]
Abstract
The strain load Δγthat triggers consecutive avalanches is a key observable in the slow deformation of amorphous solids. Its temporally averaged value ⟨Δγ⟩ displays a non-trivial system-size dependence that constitutes one of the distinguishing features of the yielding transition. Details of this dependence are not yet fully understood. We address this problem by means of theoretical analysis and simulations of elastoplastic models for amorphous solids. An accurate determination of the size dependence of ⟨Δγ⟩ leads to a precise evaluation of the steady-state distribution of local distances to instabilityx. We find that the usually assumed formP(x) ∼xθ(withθbeing the so-called pseudo-gap exponent) is not accurate at lowxand that in generalP(x) tends to a system-size-dependentfinitelimit asx→ 0. We work out the consequences of this finite-size dependence standing on exact results for random-walks and disclosing an alternative interpretation of the mechanical noise felt by a reference site. We test our predictions in two- and three-dimensional elastoplastic models, showing the crucial influence of the saturation ofP(x) at smallxon the size dependence of ⟨Δγ⟩ and related scalings.
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Affiliation(s)
- Ezequiel E Ferrero
- Instituto de Nanociencia y Nanotecnología, CNEA-CONICET, Centro Atómico Bariloche, (R8402AGP) San Carlos de Bariloche, Río Negro, Argentina
| | - Eduardo A Jagla
- Centro Atómico Bariloche, Instituto Balseiro, Comisión Nacional de Energía Atómica, CNEA, CONICET, UNCUYO, Av E Bustillo 9500 R8402AGP S C de Bariloche, Río Negro, Argentina
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19
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Biswas S, Fernandez Castellanos D, Zaiser M. Prediction of creep failure time using machine learning. Sci Rep 2020; 10:16910. [PMID: 33037259 PMCID: PMC7547726 DOI: 10.1038/s41598-020-72969-6] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2020] [Accepted: 07/27/2020] [Indexed: 11/12/2022] Open
Abstract
A subcritical load on a disordered material can induce creep damage. The creep rate in this case exhibits three temporal regimes viz. an initial decelerating regime followed by a steady-state regime and a stage of accelerating creep that ultimately leads to catastrophic breakdown. Due to the statistical regularities in the creep rate, the time evolution of creep rate has often been used to predict residual lifetime until catastrophic breakdown. However, in disordered samples, these efforts met with limited success. Nevertheless, it is clear that as the failure is approached, the damage become increasingly spatially correlated, and the spatio-temporal patterns of acoustic emission, which serve as a proxy for damage accumulation activity, are likely to mirror such correlations. However, due to the high dimensionality of the data and the complex nature of the correlations it is not straightforward to identify the said correlations and thereby the precursory signals of failure. Here we use supervised machine learning to estimate the remaining time to failure of samples of disordered materials. The machine learning algorithm uses as input the temporal signal provided by a mesoscale elastoplastic model for the evolution of creep damage in disordered solids. Machine learning algorithms are well-suited for assessing the proximity to failure from the time series of the acoustic emissions of sheared samples. We show that materials are relatively more predictable for higher disorder while are relatively less predictable for larger system sizes. We find that machine learning predictions, in the vast majority of cases, perform substantially better than other prediction approaches proposed in the literature.
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Affiliation(s)
- Soumyajyoti Biswas
- WW8-Materials Simulation, Department of Materials Science, Friedrich-Alexander-Universität Erlangen-Nürnberg, Dr.-Mack-Str. 77, 90762, Fürth, Germany.,Department of Physics, SRM University - AP, Guntur, Andhra Pradesh, 522502, India
| | - David Fernandez Castellanos
- PMMH, CNRS-UMR 7636, ESPCI Paris, PSL University, Sorbonne Universite, Universite de Paris, 75005, Paris, France
| | - Michael Zaiser
- WW8-Materials Simulation, Department of Materials Science, Friedrich-Alexander-Universität Erlangen-Nürnberg, Dr.-Mack-Str. 77, 90762, Fürth, Germany.
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20
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Zhang P, Salman OU, Weiss J, Truskinovsky L. Variety of scaling behaviors in nanocrystalline plasticity. Phys Rev E 2020; 102:023006. [PMID: 32942484 DOI: 10.1103/physreve.102.023006] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2020] [Accepted: 08/03/2020] [Indexed: 11/07/2022]
Abstract
We address the question of why larger, high-symmetry crystals are mostly weak, ductile, and statistically subcritical, while smaller crystals with the same symmetry are strong, brittle and supercritical. We link it to another question of why intermittent elasto-plastic deformation of submicron crystals features highly unusual size sensitivity of scaling exponents. We use a minimal integer-valued automaton model of crystal plasticity to show that with growing variance of quenched disorder, which can serve in this case as a proxy for increasing size, submicron crystals undergo a crossover from spin-glass marginality to criticality characterizing the second order brittle-to-ductile (BD) transition. We argue that this crossover is behind the nonuniversality of scaling exponents observed in physical and numerical experiments. The nonuniversality emerges only if the quenched disorder is elastically incompatible, and it disappears if the disorder is compatible.
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Affiliation(s)
- P Zhang
- State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, Xi'an, 710049, China
| | - O U Salman
- CNRS, LSPM UPR3407, Paris Nord Sorbonne Université, 93430, Villetaneuse, France
| | - J Weiss
- IsTerre, CNRS/Université Grenoble Alpes, 38401 Grenoble, France
| | - L Truskinovsky
- PMMH, CNRS UMR 7636, ESPCI ParisTech, 10 Rue Vauquelin, 75005, Paris, France
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21
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Jagla EA. Tensorial description of the plasticity of amorphous composites. Phys Rev E 2020; 101:043004. [PMID: 32422834 DOI: 10.1103/physreve.101.043004] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2019] [Accepted: 04/06/2020] [Indexed: 11/07/2022]
Abstract
We use a continuous mesoscopic model to address the yielding properties of plastic composites, formed by a host material and inclusions with different elastic and/or plastic properties. We investigate the flow properties of the composed material under a uniform externally applied deviatoric stress. We show that due to the heterogeneities induced by the inclusions, a scalar modeling in terms of a single deviatoric strain of the same symmetry as the externally applied deformation gives inaccurate results. A realistic modeling must include all possible shear deformations. Implementing this model in a two-dimensional system, we show that the effect of harder inclusions is very weak to relatively high concentrations. For softer inclusions instead, the effect is much stronger; even a small concentration of inclusions affecting the form of the flow curve and the critical stress. We also present the details of a full three-dimensional simulation scheme and obtain the corresponding results for harder and softer inclusions.
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Affiliation(s)
- E A Jagla
- Centro Atómico Bariloche, Instituto Balseiro, Comisión Nacional de Energía Atómica, CNEA, CONICET, UNCUYO, and Av. E. Bustillo 9500 (R8402AGP) San Carlos de Bariloche, Río Negro, Argentina
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22
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Abstract
We present a high-throughput nanoindentation study of in situ bending effects on incipient plastic deformation behavior of polycrystalline and single-crystalline pure aluminum and pure copper at ultranano depths (< 200 nm). We find that hardness displays a statistically inverse dependence on in-plane stress for indentation depths smaller than 10 nm, and the dependence disappears for larger indentation depths. In contrast, plastic noise in the nanoindentation force and displacement displays statistically robust noise features, independently of applied stresses. Our experimental results suggest the existence of a regime in Face Centered Cubic (FCC) crystals where ultranano hardness is sensitive to residual applied stresses, but plasticity pop-in noise is insensitive to it.
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23
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Bonfanti S, Guerra R, Mondal C, Procaccia I, Zapperi S. Elementary plastic events in amorphous silica. Phys Rev E 2019; 100:060602. [PMID: 31962406 DOI: 10.1103/physreve.100.060602] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2019] [Indexed: 06/10/2023]
Abstract
Plastic instabilities in amorphous materials are often studied using idealized models of binary mixtures that do not capture accurately molecular interactions and bonding present in real glasses. Here we study atomic-scale plastic instabilities in a three-dimensional molecular dynamics model of silica glass under quasistatic shear. We identify two distinct types of elementary plastic events, one is a standard quasilocalized atomic rearrangement while the second is a bond-breaking event that is absent in simplified models of fragile glass formers. Our results show that both plastic events can be predicted by a drop of the lowest nonzero eigenvalue of the Hessian matrix that vanishes at a critical strain. Remarkably, we find very high correlation between the associated eigenvectors and the nonaffine displacement fields accompanying the bond-breaking event, predicting the locus of structural failure. Both eigenvectors and nonaffine displacement fields display an Eshelby-like quadrupolar structure for both failure modes, rearrangement, and bond breaking. Our results thus clarify the nature of atomic-scale plastic instabilities in silica glasses, providing useful information for the development of mesoscale models of amorphous plasticity.
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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, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Itamar Procaccia
- Department of Chemical Physics, 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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24
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Ferrero EE, Jagla EA. Criticality in elastoplastic models of amorphous solids with stress-dependent yielding rates. SOFT MATTER 2019; 15:9041-9055. [PMID: 31647078 DOI: 10.1039/c9sm01073d] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We analyze the behavior of different elastoplastic models approaching the yielding transition. We propose two kinds of rules for the local yielding events: yielding occurs above the local threshold either at a constant rate or with a rate that increases as the square root of the stress excess. We establish a family of "static" universal critical exponents which do not depend on this dynamic detail of the model rules: in particular, the exponents for the avalanche size distribution P(S) ∼S-τSf(S/Ldf) and the exponents describing the density of sites at the verge of yielding, which we find to be of the form P(x) ≃P(0) + xθ with P(0) ∼L-a controlling the extremal statistics. On the other hand, we discuss "dynamical" exponents that are sensitive to the local yielding rule. We find that, apart form the dynamical exponent z controlling the duration of avalanches, also the flowcurve's (inverse) Herschel-Bulkley exponent β ([small gamma, Greek, dot above]∼ (σ-σc)β) enters in this category, and is seen to differ in ½ between the two yielding rate cases. We give analytical support to this numerical observation by calculating the exponent variation in the Hébraud-Lequeux model and finding an identical shift. We further discuss an alternative mean-field approximation to yielding only based on the so-called Hurst exponent of the accumulated mechanical noise signal, which gives good predictions for the exponents extracted from simulations of fully spatial models.
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Affiliation(s)
- E E Ferrero
- Instituto de Nanociencia y Nanotecnología, CNEA-CONICET, Centro Atómico Bariloche, (R8402AGP) San Carlos de Bariloche, Río Negro, Argentina.
| | - E A Jagla
- Centro Atómico Bariloche, Instituto Balseiro, Comisión Nacional de Energía Atómica, CNEA, CONICET, UNCUYO, Av. E. Bustillo 9500 (R8402AGP), San Carlos de Bariloche Río Negro, Argentina
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25
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Ferrero EE, Jagla EA. Elastic Interfaces on Disordered Substrates: From Mean-Field Depinning to Yielding. PHYSICAL REVIEW LETTERS 2019; 123:218002. [PMID: 31809180 DOI: 10.1103/physrevlett.123.218002] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2019] [Indexed: 06/10/2023]
Abstract
We consider a model of an elastic manifold driven on a disordered energy landscape, with generalized long range elasticity. Varying the form of the elastic kernel by progressively allowing for the existence of zero modes, the model interpolates smoothly between mean-field depinning and finite dimensional yielding. We find that the critical exponents of the model change smoothly in this process. Also, we show that in all cases the Herschel-Buckley exponent of the flow curve depends on the analytical form of the microscopic pinning potential. Within the present elastoplastic description, all this suggests that yielding in finite dimensions is a mean-field transition.
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Affiliation(s)
- E E Ferrero
- Instituto de Nanociencia y Nanotecnología, CNEA-CONICET, Centro Atómico Bariloche, (R8402AGP) San Carlos de Bariloche, Río Negro, Argentina
| | - E A Jagla
- Centro Atómico Bariloche, Instituto Balseiro, Comisión Nacional de Energía Atómica, CNEA, CONICET, UNCUYO, Av. E. Bustillo 9500 (R8402AGP) San Carlos de Bariloche, Río Negro, Argentina
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26
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Tyukodi B, Vandembroucq D, Maloney CE. Avalanches, thresholds, and diffusion in mesoscale amorphous plasticity. Phys Rev E 2019; 100:043003. [PMID: 31770912 DOI: 10.1103/physreve.100.043003] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2019] [Indexed: 06/10/2023]
Abstract
We present results on a mesoscale model for amorphous matter in athermal, quasistatic (a-AQS), steady-state shear flow. In particular, we perform a careful analysis of the scaling with the lateral system size L of (i) statistics of individual relaxation events in terms of stress relaxation S, and individual event mean-squared displacement M, and the subsequent load increments Δγ, required to initiate the next event; (ii) static properties of the system encoded by x=σ_{y}-σ, the distance of local stress values from threshold; and (iii) long-time correlations and the emergence of diffusive behavior. For the event statistics, we find that the distribution of S is similar to, but distinct from, the distribution of M. We find a strong correlation between S and M for any particular event, with S∼M^{q} with q≈0.65. The exponent q completely determines the scaling exponents for P(M) given those for P(S). For the distribution of local thresholds, we find P(x) is analytic at x=0, and has a value P(x)|_{x=0}=p_{0} which scales with lateral system length as p_{0}∝L^{-0.6}. The size dependence of the average load increment 〈Δγ〉 appears to be asymptotically controlled by the plateau behavior of P(x) rather than by a subsequent apparent power-law behavior. Extreme value statistics arguments lead thus to a scaling relation between the exponents governing P(x) and those governing P(S). Finally, we study the long-time correlations via single-particle tracer statistics. The value of the diffusion coefficient is completely determined by 〈Δγ〉 and the scaling properties of P(M) (in particular from 〈M〉) rather than directly from P(S) as one might have naively guessed. Our results (i) further define the a-AQS universality class, (ii) clarify the relation between avalanches of stress relaxation and diffusive behavior, and (iii) clarify the relation between local threshold distributions and event statistics.
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Affiliation(s)
- Botond Tyukodi
- Department of Mechanical and Industrial Engineering, Northeastern University, Boston, Massachusetts 02115, USA
| | - Damien Vandembroucq
- PMMH, CNRS, ESPCI Paris, PSL University, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | - Craig E Maloney
- Department of Mechanical and Industrial Engineering, Northeastern University, Boston, Massachusetts 02115, USA
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27
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Tyukodi B, Vandembroucq D, Maloney CE. Diffusion in Mesoscopic Lattice Models of Amorphous Plasticity. PHYSICAL REVIEW LETTERS 2018; 121:145501. [PMID: 30339423 DOI: 10.1103/physrevlett.121.145501] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2018] [Revised: 05/21/2018] [Indexed: 06/08/2023]
Abstract
We present results on tagged particle diffusion in a mesoscale lattice model for sheared amorphous material in athermal quasistatic conditions. We find a short time diffusive regime and a long time diffusive regime whose diffusion coefficients depend on system size in dramatically different ways. At short time, we find that the diffusion coefficient, D, scales roughly linearly with system length, D∼L^{1.05}. This short time behavior is consistent with particle-based simulations. The long-time diffusion coefficient scales like D∼L^{1.6}, close to previous studies which found D∼L^{1.5}. Furthermore, we show that the near-field details of the interaction kernel do not affect the short time behavior but qualitatively and dramatically affect the long time behavior, potentially causing a saturation of the mean-squared displacement at long times. Our finding of a D∼L^{1.05} short time scaling resolves a long standing puzzle about the disagreement between the diffusion coefficient measured in particle-based models and mesoscale lattice models of amorphous plasticity.
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Affiliation(s)
- Botond Tyukodi
- PMMH, ESPCI Paris, CNRS UMR 7636, Sorbonne Université, Université Paris Diderot, PSL Research University 10 rue Vauquelin, 75231 Paris cedex 05, France
- Department of Mechanical and Industrial Engineering, Northeastern University, Boston, Massachusetts 02115, USA
- Department of Physics, Babeş-Bolyai University, Cluj-Napoca 400084, Romania
| | - Damien Vandembroucq
- PMMH, ESPCI Paris, CNRS UMR 7636, Sorbonne Université, Université Paris Diderot, PSL Research University 10 rue Vauquelin, 75231 Paris cedex 05, France
| | - Craig E Maloney
- Department of Mechanical and Industrial Engineering, Northeastern University, Boston, Massachusetts 02115, USA
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28
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Castellanos DF, Zaiser M. Avalanche Behavior in Creep Failure of Disordered Materials. PHYSICAL REVIEW LETTERS 2018; 121:125501. [PMID: 30296108 DOI: 10.1103/physrevlett.121.125501] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/22/2018] [Indexed: 06/08/2023]
Abstract
We present a mesoscale elastoplastic model of creep in disordered materials, which considers temperature-dependent stochastic activation of localized deformation events that are coupled by internal stresses, leading to collective avalanche dynamics. We generalize this stochastic plasticity model by introducing damage in terms of a local strength that decreases, on statistical average, with increasing local plastic strain. The model captures failure in terms of strain localization in a catastrophic shear band concomitant with a finite-time singularity of the creep rate. The statistics of avalanches in the run-up to failure is characterized by a decreasing avalanche exponent τ that, at failure, approaches the value τ=1.5 typical of a critical branching process. The average avalanche rate exhibits an inverse Omori law as a function of time to failure. The distribution of interavalanche times turns out to be consistent with the epidemic-type aftershock sequences (ETAS) model of earthquake statistics.
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Affiliation(s)
- D F Castellanos
- Institute of Materials Simulation, Department of Materials Science, Friedrich-Alexander Universität Erlangen-Nürnberg, Dr.-Mack-Straße 77, 90762 Fürth, Germany
| | - M Zaiser
- Institute of Materials Simulation, Department of Materials Science, Friedrich-Alexander Universität Erlangen-Nürnberg, Dr.-Mack-Straße 77, 90762 Fürth, Germany and School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, China
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29
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Barbot A, Lerbinger M, Hernandez-Garcia A, García-García R, Falk ML, Vandembroucq D, Patinet S. Local yield stress statistics in model amorphous solids. Phys Rev E 2018; 97:033001. [PMID: 29776106 DOI: 10.1103/physreve.97.033001] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2017] [Indexed: 06/08/2023]
Abstract
We develop and extend a method presented by Patinet, Vandembroucq, and Falk [Phys. Rev. Lett. 117, 045501 (2016)PRLTAO0031-900710.1103/PhysRevLett.117.045501] to compute the local yield stresses at the atomic scale in model two-dimensional Lennard-Jones glasses produced via differing quench protocols. This technique allows us to sample the plastic rearrangements in a nonperturbative manner for different loading directions on a well-controlled length scale. Plastic activity upon shearing correlates strongly with the locations of low yield stresses in the quenched states. This correlation is higher in more structurally relaxed systems. The distribution of local yield stresses is also shown to strongly depend on the quench protocol: the more relaxed the glass, the higher the local plastic thresholds. Analysis of the magnitude of local plastic relaxations reveals that stress drops follow exponential distributions, justifying the hypothesis of an average characteristic amplitude often conjectured in mesoscopic or continuum models. The amplitude of the local plastic rearrangements increases on average with the yield stress, regardless of the system preparation. The local yield stress varies with the shear orientation tested and strongly correlates with the plastic rearrangement locations when the system is sheared correspondingly. It is thus argued that plastic rearrangements are the consequence of shear transformation zones encoded in the glass structure that possess weak slip planes along different orientations. Finally, we justify the length scale employed in this work and extract the yield threshold statistics as a function of the size of the probing zones. This method makes it possible to derive physically grounded models of plasticity for amorphous materials by directly revealing the relevant details of the shear transformation zones that mediate this process.
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Affiliation(s)
- Armand Barbot
- PMMH, ESPCI Paris/CNRS-UMR 7636/University Paris 6 UPMC/University Paris 7 Diderot, PSL Research University, 10 rue Vauquelin, 75231 Paris cedex 05, France
| | - Matthias Lerbinger
- PMMH, ESPCI Paris/CNRS-UMR 7636/University Paris 6 UPMC/University Paris 7 Diderot, PSL Research University, 10 rue Vauquelin, 75231 Paris cedex 05, France
| | - Anier Hernandez-Garcia
- PMMH, ESPCI Paris/CNRS-UMR 7636/University Paris 6 UPMC/University Paris 7 Diderot, PSL Research University, 10 rue Vauquelin, 75231 Paris cedex 05, France
| | - Reinaldo García-García
- PMMH, ESPCI Paris/CNRS-UMR 7636/University Paris 6 UPMC/University Paris 7 Diderot, PSL Research University, 10 rue Vauquelin, 75231 Paris cedex 05, France
| | - Michael L Falk
- Departments of Materials Science and Engineering, Mechanical Engineering, and Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Damien Vandembroucq
- PMMH, ESPCI Paris/CNRS-UMR 7636/University Paris 6 UPMC/University Paris 7 Diderot, PSL Research University, 10 rue Vauquelin, 75231 Paris cedex 05, France
| | - Sylvain Patinet
- PMMH, ESPCI Paris/CNRS-UMR 7636/University Paris 6 UPMC/University Paris 7 Diderot, PSL Research University, 10 rue Vauquelin, 75231 Paris cedex 05, France
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