1
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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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2
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Amiri A, Duclut C, Jülicher F, Popović M. Random Traction Yielding Transition in Epithelial Tissues. PHYSICAL REVIEW LETTERS 2023; 131:188401. [PMID: 37977637 DOI: 10.1103/physrevlett.131.188401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/03/2022] [Accepted: 10/04/2023] [Indexed: 11/19/2023]
Abstract
We investigate how randomly oriented cell traction forces lead to fluidization in a vertex model of epithelial tissues. We find that the fluidization occurs at a critical value of the traction force magnitude F_{c}. We show that this transition exhibits critical behavior, similar to the yielding transition of sheared amorphous solids. However, we find that it belongs to a different universality class, even though it satisfies the same scaling relations between critical exponents established in the yielding transition of sheared amorphous solids. Our work provides a fluidization mechanism through active force generation that could be relevant in biological tissues.
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Affiliation(s)
- Aboutaleb Amiri
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany
| | - Charlie Duclut
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany
- Université Paris Cité, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, Paris, France
- Laboratoire Physico-Chimie Curie, CNRS UMR 168, Institut Curie, Université PSL, Sorbonne Université, 75005 Paris, France
| | - Frank Jülicher
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany
- Cluster of Excellence Physics of Life, Technical University of Dresden, 01307 Dresden, Germany
- Center for Systems Biology Dresden, Pfotenhauerstrasse 108, 01307 Dresden, Germany
| | - Marko Popović
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany
- Cluster of Excellence Physics of Life, Technical University of Dresden, 01307 Dresden, Germany
- Center for Systems Biology Dresden, Pfotenhauerstrasse 108, 01307 Dresden, Germany
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3
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Xiao H, Zhang G, Yang E, Ivancic R, Ridout S, Riggleman R, Durian DJ, Liu AJ. Identifying microscopic factors that influence ductility in disordered solids. Proc Natl Acad Sci U S A 2023; 120:e2307552120. [PMID: 37812709 PMCID: PMC10589640 DOI: 10.1073/pnas.2307552120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2023] [Accepted: 08/16/2023] [Indexed: 10/11/2023] Open
Abstract
There are empirical strategies for tuning the degree of strain localization in disordered solids, but they are system-specific and no theoretical framework explains their effectiveness or limitations. Here, we study three model disordered solids: a simulated atomic glass, an experimental granular packing, and a simulated polymer glass. We tune each system using a different strategy to exhibit two different degrees of strain localization. In tandem, we construct structuro-elastoplastic (StEP) models, which reduce descriptions of the systems to a few microscopic features that control strain localization, using a machine learning-based descriptor, softness, to represent the stability of the disordered local structure. The models are based on calculated correlations of softness and rearrangements. Without additional parameters, the models exhibit semiquantitative agreement with observed stress-strain curves and softness statistics for all systems studied. Moreover, the StEP models reveal that initial structure, the near-field effect of rearrangements on local structure, and rearrangement size, respectively, are responsible for the changes in ductility observed in the three systems. Thus, StEP models provide microscopic understanding of how strain localization depends on the interplay of structure, plasticity, and elasticity.
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Affiliation(s)
- Hongyi Xiao
- Department of Physics, University of Pennsylvania, Philadelphia, PA19104
- Chemical and Biological Engineering, Institute for Multiscale Simulation, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen91058, Germany
- Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI48109
| | - Ge Zhang
- Department of Physics, University of Pennsylvania, Philadelphia, PA19104
- Department of Physics, City University of Hong Kong, Hong Kong999077, China
| | - Entao Yang
- Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, PA19104
| | - Robert Ivancic
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, MD20899
| | - Sean Ridout
- Department of Physics, University of Pennsylvania, Philadelphia, PA19104
- Department of Physics, Emory University, Atlanta, GA30322
| | - Robert Riggleman
- Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, PA19104
| | - Douglas J. Durian
- Department of Physics, University of Pennsylvania, Philadelphia, PA19104
- Center for Computational Biology, Flatiron Institute, Simons Foundation, New York, NY10010
| | - Andrea J. Liu
- Department of Physics, University of Pennsylvania, Philadelphia, PA19104
- Center for Computational Biology, Flatiron Institute, Simons Foundation, New York, NY10010
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4
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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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5
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Wiese KJ. Theory and experiments for disordered elastic manifolds, depinning, avalanches, and sandpiles. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2022; 85:086502. [PMID: 35943081 DOI: 10.1088/1361-6633/ac4648] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2021] [Accepted: 12/23/2021] [Indexed: 06/15/2023]
Abstract
Domain walls in magnets, vortex lattices in superconductors, contact lines at depinning, and many other systems can be modeled as an elastic system subject to quenched disorder. The ensuing field theory possesses a well-controlled perturbative expansion around its upper critical dimension. Contrary to standard field theory, the renormalization group (RG) flow involves a function, the disorder correlator Δ(w), and is therefore termed the functional RG. Δ(w) is a physical observable, the auto-correlation function of the center of mass of the elastic manifold. In this review, we give a pedagogical introduction into its phenomenology and techniques. This allows us to treat both equilibrium (statics), and depinning (dynamics). Building on these techniques, avalanche observables are accessible: distributions of size, duration, and velocity, as well as the spatial and temporal shape. Various equivalences between disordered elastic manifolds, and sandpile models exist: an elastic string driven at a point and the Oslo model; disordered elastic manifolds and Manna sandpiles; charge density waves and Abelian sandpiles or loop-erased random walks. Each of the mappings between these systems requires specific techniques, which we develop, including modeling of discrete stochastic systems via coarse-grained stochastic equations of motion, super-symmetry techniques, and cellular automata. Stronger than quadratic nearest-neighbor interactions lead to directed percolation, and non-linear surface growth with additional Kardar-Parisi-Zhang (KPZ) terms. On the other hand, KPZ without disorder can be mapped back to disordered elastic manifolds, either on the directed polymer for its steady state, or a single particle for its decay. Other topics covered are the relation between functional RG and replica symmetry breaking, and random-field magnets. Emphasis is given to numerical and experimental tests of the theory.
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Affiliation(s)
- Kay Jörg Wiese
- Laboratoire de physique, Département de physique de l'ENS, École normale supérieure, UPMC Univ. Paris 06, CNRS, PSL Research University, 75005 Paris, France
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6
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Villarroel C, Düring G. Critical yielding rheology: from externally deformed glasses to active systems. SOFT MATTER 2021; 17:9944-9949. [PMID: 34693958 DOI: 10.1039/d1sm00948f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
We use extensive computer simulations to study the yielding transition under two different loading schemes: standard simple shear dynamics and self-propelled dense active systems. In the active systems, a yielding transition toward an out-of-equilibrium flowing state known as the liquid phase is observed when self-propulsion is increased. The range of self-propulsions in which this pure liquid regime exists appears to vanish upon approaching the so-called 'jamming point' at which the solidity of soft-sphere packings is lost. Such an 'active yielding' transition shares similarities with the generic yielding transition for shear flows. A Herschel-Bulkley law is observed along the liquid regime in both loading scenarios, with a clear difference in the critical scaling exponents between the two, suggesting the existence of different universality classes for the yielding transition under different driving conditions. In addition, we present the direct measurements of growing length and time scales for both driving scenarios. A comparison with theoretical predictions from the recent literature reveals poor agreement with our numerical results.
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Affiliation(s)
- Carlos Villarroel
- Instituto de Física, Pontificia Universidad Católica de Chile, Casilla 306, Santiago, Chile.
| | - Gustavo Düring
- Instituto de Física, Pontificia Universidad Católica de Chile, Casilla 306, Santiago, Chile.
- ANID - Millenium Nucleus of Soft Smart Mechanical Metamaterials, Santiago, Chile
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7
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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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8
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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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9
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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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10
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Zaccone A. Relaxation and vibrational properties in metal alloys and other disordered systems. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:203001. [PMID: 31962298 DOI: 10.1088/1361-648x/ab6e41] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
The relaxation dynamics and the vibrational spectra of amorphous solids, such as metal alloys, have been intensely investigated as well separated topics in the past. The aim of this review is to summarize recent results in both these areas in an attempt to establish, or unveil, deeper connections between the two phenomena of relaxation and vibration. Theoretical progress in the area of slow relaxation dynamics of liquid and glassy systems and in the area of vibrational spectra of glasses and liquids is reviewed. After laying down a generic modelling framework to connect vibration and relaxation, the physics of metal alloys is considered where the emergence of power-law exponents has been identified both in the vibrational density of states (VDOS) as well as in density correlations. Also, theoretical frameworks which connect the VDOS to the relaxation behaviour and mechanical viscoelastic response in metallic glasses are reviewed. The same generic interpretative framework is then applied to the case of molecular glass formers where the emergence of stretched-exponential relaxation in dielectric relaxation can be put in quantitative relation with the VDOS by means of memory-function approaches. Further connections between relaxation and vibration are provided by the study of phonon linewidths in liquids and glasses, where a natural starting point is given by hydrodynamic theories. Finally, an agenda of outstanding issues including the appearance of compressed exponential relaxation in the intermediate scattering function of experimental and simulated systems (metal alloys, colloidal gels, jammed packings) is presented in light of available (or yet to be developed) mathematical models, and compared to non-exponential behaviour measured with macroscopic means such as mechanical spectroscopy/rheology.
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Affiliation(s)
- Alessio Zaccone
- Department of Physics 'A. Pontremoli', University of Milan, via Celoria 16, 20133 Milano, Italy. Statistical Physics Group, Department of Chemical Engineering and Biotechnology, University of Cambridge, Philippa Fawcett Drive, CB3 0AS Cambridge, United Kingdom. Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, CB30HE Cambridge, United Kingdom
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11
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Kumar P, Korkolis E, Benzi R, Denisov D, Niemeijer A, Schall P, Toschi F, Trampert J. On interevent time distributions of avalanche dynamics. Sci Rep 2020; 10:626. [PMID: 31953412 PMCID: PMC6969144 DOI: 10.1038/s41598-019-56764-6] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2019] [Accepted: 11/29/2019] [Indexed: 11/09/2022] Open
Abstract
Physical systems characterized by stick-slip dynamics often display avalanches. Regardless of the diversity of their microscopic structure, these systems are governed by a power-law distribution of avalanche size and duration. Here we focus on the interevent times between avalanches and show that, unlike their distributions of size and duration, the interevent time distributions are able to distinguish different mechanical states of the system. We use experiments on granular systems and numerical simulations of emulsions to show that systems having the same probability distribution for avalanche size and duration can have different interevent time distributions. Remarkably, these interevent time distributions look similar to those for earthquakes and, if different from an exponential, are indirect evidence of non trivial space-time correlations among avalanches. Our results therefore indicate that interevent time statistics are essential to characterise the dynamics of avalanches.
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Affiliation(s)
- Pinaki Kumar
- Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600, MB, Eindhoven, The Netherlands
| | - Evangelos Korkolis
- Department of Earth Sciences, Utrecht University, P.O. Box 80115, 3508, TC, Utrecht, The Netherlands
| | - Roberto Benzi
- Dip. di Fisica and INFN, Università "Tor Vergata", Via della Ricerca Scientifica 1, I-00133, Roma, Italy
| | - Dmitry Denisov
- Institute of Physics, University of Amsterdam, 1098, XH, Amsterdam, The Netherlands
| | - André Niemeijer
- Department of Earth Sciences, Utrecht University, P.O. Box 80115, 3508, TC, Utrecht, The Netherlands
| | - Peter Schall
- Institute of Physics, University of Amsterdam, 1098, XH, Amsterdam, The Netherlands
| | - Federico Toschi
- Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600, MB, Eindhoven, The Netherlands. .,Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600, MB, Eindhoven, The Netherlands. .,Istituto per le Applicazioni del Calcolo, Consiglio Nazionale delle Ricerche, Via dei Taurini 19, 00185, Rome, Italy.
| | - Jeannot Trampert
- Department of Earth Sciences, Utrecht University, P.O. Box 80115, 3508, TC, Utrecht, The Netherlands
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12
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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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13
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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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14
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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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15
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Pelusi F, Sbragaglia M, Benzi R. Avalanche statistics during coarsening dynamics. SOFT MATTER 2019; 15:4518-4524. [PMID: 31098607 DOI: 10.1039/c9sm00332k] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We study the coarsening dynamics of a two-dimensional system via numerical simulations. The system under consideration is a biphasic system consisting of domains of a dispersed phase closely packed together in a continuous phase and separated by thin interfaces. Such a system is elastic and typically out of equilibrium. The equilibrium state is attained via the coarsening dynamics, wherein the dispersed phase slowly diffuses through the interfaces, causing the domains to change in size and eventually rearrange abruptly. The effect of rearrangements is propagated throughout the system via the intrinsic elastic interactions and may cause rearrangements elsewhere, resulting in intermittent bursts of activity and avalanche behaviour. Here we aim at quantitatively characterizing the corresponding avalanche statistics (i.e. size, duration, and inter-avalanche time). Despite the coarsening dynamics is triggered by an internal driving mechanism, we find quantitative indications that such avalanche statistics displays scaling-laws very similar to those observed in the response of disordered materials to external loads.
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Affiliation(s)
- Francesca Pelusi
- Dipartimento di Fisica, Università di Roma "Tor Vergata" and INFN, Via della Ricerca Scientifica, 1, 00133 Roma RM, Italy.
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16
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Abed Zadeh A, Barés J, Socolar JES, Behringer RP. Seismicity in sheared granular matter. Phys Rev E 2019; 99:052902. [PMID: 31212553 DOI: 10.1103/physreve.99.052902] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/13/2018] [Indexed: 06/09/2023]
Abstract
We report on experiments investigating the dynamics of a slider that is pulled by a spring across a granular medium consisting of a vertical layer of photoelastic disks. The motion proceeds through a sequence of discrete events, analogous to seismic shocks, in which elastic energy stored in the spring is rapidly released. We measure the statistics of several properties of the individual events: the energy loss in the spring, the duration of the movement, and the temporal profile of the slider motion. We also study certain conditional probabilities and the statistics of mainshock-aftershock sequences. At low driving rates, we observe crackling with Omori-Utsu, Båth, and waiting time laws similar to those observed in seismic dynamics. At higher driving rates, where the sequence of events shows strong periodicity, we observe scaling laws and asymmetrical event shapes that are clearly distinguishable from those in the crackling regime.
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Affiliation(s)
- Aghil Abed Zadeh
- Department of Physics & Center for Non-linear and Complex Systems, Duke University, Durham, North Carolina 27708, USA
| | - Jonathan Barés
- Laboratoire de Mécanique et Génie Civil, Université de Montpellier, CNRS, Montpellier, France
| | - Joshua E S Socolar
- Department of Physics & Center for Non-linear and Complex Systems, Duke University, Durham, North Carolina 27708, USA
| | - Robert P Behringer
- Department of Physics & Center for Non-linear and Complex Systems, Duke University, Durham, North Carolina 27708, USA
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17
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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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18
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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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19
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Nicolas A, Rottler J. Orientation of plastic rearrangements in two-dimensional model glasses under shear. Phys Rev E 2018; 97:063002. [PMID: 30011591 DOI: 10.1103/physreve.97.063002] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2018] [Indexed: 06/08/2023]
Abstract
The plastic deformation of amorphous solids is mediated by localized shear transformations involving small groups of particles rearranging irreversibly in an elastic background. We introduce and compare three different computational methods to extract the size and orientation of these shear transformations in simulations of a two-dimensional athermal model glass under simple shear. We find that the shear angles are broadly distributed around the macroscopic shear direction, with a more or less Gaussian distribution with a standard deviation of around 20^{∘}. The distributions of sizes and orientations of shear transformations display no substantial sensitivity to the shear rate. These results can notably be used to refine the description of rearrangements in elastoplastic models.
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Affiliation(s)
- Alexandre Nicolas
- LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| | - Jörg Rottler
- Department of Physics and Astronomy and Quantum Matter Institute, University of British Columbia, Vancouver BC V6T 1Z1, Canada
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20
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Cao X, Nicolas A, Trimcev D, Rosso A. Soft modes and strain redistribution in continuous models of amorphous plasticity: the Eshelby paradigm, and beyond? SOFT MATTER 2018; 14:3640-3651. [PMID: 29611574 DOI: 10.1039/c7sm02510f] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
The deformation of disordered solids relies on swift and localised rearrangements of particles. The inspection of soft vibrational modes can help predict the locations of these rearrangements, while the strain that they actually redistribute mediates collective effects. Here, we study soft modes and strain redistribution in a two-dimensional continuous mesoscopic model based on a Ginzburg-Landau free energy for perfect solids, supplemented with a plastic disorder potential that accounts for shear softening and rearrangements. Regardless of the disorder strength, our numerical simulations show soft modes that are always sharply peaked at the softest point of the material (unlike what happens for the depinning of an elastic interface). Contrary to widespread views, the deformation halo around this peak does not always have a quadrupolar (Eshelby-like) shape. Instead, for finite and narrowly-distributed disorder, it looks like a fracture, with a strain field that concentrates along some easy directions. These findings are rationalised with analytical calculations in the case where the plastic disorder is confined to a point-like 'impurity'. In this case, we unveil a continuous family of elastic propagators, which are identical for the soft modes and for the equilibrium configurations. This family interpolates between the standard quadrupolar propagator and the fracture-like one as the anisotropy of the elastic medium is increased. Therefore, we expect to see a fracture-like propagator when extended regions on the brink of failure have already softened along the shear direction and thus rendered the material anisotropic, but not failed yet. We speculate that this might be the case in carefully aged glasses just before macroscopic failure.
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Affiliation(s)
- Xiangyu Cao
- LPTMS, CNRS, Univ. Paris-Sud, Université Paris Saclay, Orsay, France.
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21
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Barés J, Wang D, Wang D, Bertrand T, O'Hern CS, Behringer RP. Local and global avalanches in a two-dimensional sheared granular medium. Phys Rev E 2017; 96:052902. [PMID: 29347774 DOI: 10.1103/physreve.96.052902] [Citation(s) in RCA: 43] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2017] [Indexed: 06/07/2023]
Abstract
We present the experimental and numerical studies of a two-dimensional sheared amorphous material composed of bidisperse photoelastic disks. We analyze the statistics of avalanches during shear including the local and global fluctuations in energy and changes in particle positions and orientations. We find scale-free distributions for these global and local avalanches denoted by power laws whose cutoffs vary with interparticle friction and packing fraction. Different exponents are found for these power laws depending on the quantity from which variations are extracted. An asymmetry in time of the avalanche shapes is evidenced along with the fact that avalanches are mainly triggered by the shear bands. A simple relation independent of the intensity is found between the number of local avalanches and the global avalanches they form. We also compare these experimental and numerical results for both local and global fluctuations to predictions from mean-field and depinning theories.
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Affiliation(s)
- Jonathan Barés
- Department of Physics and Center for Nonlinear and Complex Systems, Duke University, Durham, North Carolina 27708, USA
| | - Dengming Wang
- Key Laboratory of Mechanics on Western Disaster and Environment, Ministry of Education of China, Lanzhou University, 730000 Lanzhou, China
| | - Dong Wang
- Department of Physics and Center for Nonlinear and Complex Systems, Duke University, Durham, North Carolina 27708, USA
| | - Thibault Bertrand
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06520-8286, USA
| | - Corey S O'Hern
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06520-8286, USA
- Department of Physics, Yale University, New Haven, Connecticut 06520-8286, USA
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520-8286, USA
| | - Robert P Behringer
- Department of Physics and Center for Nonlinear and Complex Systems, Duke University, Durham, North Carolina 27708, USA
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22
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Abstract
Plastic yielding of amorphous solids occurs by power-law distributed deformation avalanches whose universality is still debated. Experiments and molecular dynamics simulations are hampered by limited statistical samples, and although existing stochastic models give precise exponents, they require strong assumptions about fixed deformation directions, at odds with the statistical isotropy of amorphous materials. Here, we introduce a fully tensorial, stochastic mesoscale model for amorphous plasticity that links the statistical physics of plastic yielding to engineering mechanics. It captures the complex shear patterning observed for a wide variety of deformation modes, as well as the avalanche dynamics of plastic flow. Avalanches are described by universal size exponents and scaling functions, avalanche shapes, and local stability distributions, independent of system dimensionality, boundary and loading conditions, and stress state. Our predictions consistently differ from those of mean-field depinning models, providing evidence that plastic yielding is a distinct type of critical phenomenon. The universality class for plastic yield in amorphous materials remains controversial. Here authors present a tensorial mesoscale model that captures both complex shear patterns and avalanche scaling behaviour, which differs from mean-field models and suggests a distinct type of critical phenomenon.
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23
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Zhang D, Dahmen KA, Ostoja-Starzewski M. Scaling of slip avalanches in sheared amorphous materials based on large-scale atomistic simulations. Phys Rev E 2017; 95:032902. [PMID: 28415186 DOI: 10.1103/physreve.95.032902] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2016] [Indexed: 11/07/2022]
Abstract
Atomistic simulations of binary amorphous systems with over 4 million atoms are performed. Systems of two interatomic potentials of the Lennard-Jones type, LJ12-6 and LJ9-6, are simulated. The athermal quasistatic shearing protocol is adopted, where the shear strain is applied in a stepwise fashion with each step followed by energy minimization. For each avalanche event, the shear stress drop (Δσ), the hydrostatic pressure drop (Δσ_{h}), and the potential energy drop (ΔE) are computed. It is found that, with the avalanche size increasing, the three become proportional to each other asymptotically. The probability distributions of avalanche sizes are obtained and values of scaling exponents fitted. In particular, the distributions follow a power law, P(ΔU)∼ΔU^{-τ}, where ΔU is a measure of avalanche sizes defined based on shear stress drops. The exponent τ is 1.25±0.1 for the LJ12-6 systems, and 1.15±0.1 for the LJ9-6 systems. The value of τ for the LJ12-6 systems is consistent with that from an earlier atomistic simulation study by Robbins et al. [Phys. Rev. Lett. 109, 105703 (2012)]PRLTAO0031-900710.1103/PhysRevLett.109.105703, but the fitted values of other scaling exponents differ, which may be because the shearing protocol used here differs from that in their study.
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Affiliation(s)
- Dansong Zhang
- Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Karin A Dahmen
- Department of Physics, Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Martin Ostoja-Starzewski
- Department of Mechanical Science and Engineering, Institute for Condensed Matter Theory and Beckman Institute, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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24
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Ghosh A, Budrikis Z, Chikkadi V, Sellerio AL, Zapperi S, Schall P. Direct Observation of Percolation in the Yielding Transition of Colloidal Glasses. PHYSICAL REVIEW LETTERS 2017; 118:148001. [PMID: 28430459 DOI: 10.1103/physrevlett.118.148001] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/19/2016] [Indexed: 06/07/2023]
Abstract
When strained beyond the linear regime, soft colloidal glasses yield to steady-state plastic flow in a way that is similar to the deformation of conventional amorphous solids. Because of the much larger size of the colloidal particles with respect to the atoms comprising an amorphous solid, colloidal glasses allow us to obtain microscopic insight into the nature of the yielding transition, as we illustrate here combining experiments, atomistic simulations, and mesoscopic modeling. Our results unanimously show growing clusters of nonaffine deformation percolating at yielding. In agreement with percolation theory, the spanning cluster is fractal with a fractal dimension d_{f}≃2, and the correlation length diverges upon approaching the critical yield strain. These results indicate that percolation of highly nonaffine particles is the hallmark of the yielding transition in disordered glassy systems.
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Affiliation(s)
- Antina Ghosh
- Institute of Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
- Max Planck Institute for Intelligent Systems, 70569 Stuttgart, Germany
| | - Zoe Budrikis
- ISI Foundation, Via Alassio 11C, Torino 10126, Italy
| | - Vijayakumar Chikkadi
- Institute of Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
- Max Planck Institute for Intelligent Systems, 70569 Stuttgart, Germany
| | - Alessandro L Sellerio
- Center for Complexity and Biosystems, Department of Physics, University of Milano, via Celoria 16, 20133 Milano, Italy
| | - Stefano Zapperi
- ISI Foundation, Via Alassio 11C, Torino 10126, Italy
- Center for Complexity and Biosystems, Department of Physics, University of Milano, via Celoria 16, 20133 Milano, Italy
- Istituto di Chimica della Materia Condensata e di Tecnologie per l'Energia, CNR-Consiglio Nazionale delle Ricerche, Via R. Cozzi 53, 20125 Milano, Italy
- Department of Applied Physics, Aalto University, P.O. Box 11100, FIN-00076 Aalto, Espoo, Finland
| | - Peter Schall
- Institute of Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
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Herrero-Gómez C, Samwer K. Stress and temperature dependence of the avalanche dynamics during creep deformation of metallic glasses. Sci Rep 2016; 6:33503. [PMID: 27654069 PMCID: PMC5031975 DOI: 10.1038/srep33503] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/10/2016] [Accepted: 08/25/2016] [Indexed: 11/09/2022] Open
Abstract
The understanding of the mesoscopic origin of plasticity in metallic glasses remains still an open issue. At the microscopic level, Shear Transformation Zones (STZ), composed by dozens of atoms, have been identified as the basic unit of the deformation process. Macroscopically, metallic glasses perform either homogeneous or inhomogeneous flow depending on the experimental conditions. However, the emergence of macroscopic behavior resulting from STZ interactions is still an open issue and is of great interest. In the current work we present an approach to analyze the different interaction mechanisms of STZ's by studying the statistics of the avalanches produced by a metallic glass during tensile creep deformation. We identified a crossover between different regimes of avalanches, and we analyzed the dependence of such crossover on the experimental conditions, namely stress and temperature. We interpret such crossover as a transition from 3D random STZ activity to localized 2D nano-shear bands. The experimental time at which the crossover takes place seems to depend on the overall strain and strain rate in the sample.
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Affiliation(s)
- Carlos Herrero-Gómez
- Physikalisches Institut, Georg-August Universität Göttingen, Friederich-Hund-Platz 1, 37077 Göttingen, Germany
| | - Konrad Samwer
- Physikalisches Institut, Georg-August Universität Göttingen, Friederich-Hund-Platz 1, 37077 Göttingen, Germany
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26
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Tyukodi B, Patinet S, Roux S, Vandembroucq D. From depinning transition to plastic yielding of amorphous media: A soft-modes perspective. Phys Rev E 2016; 93:063005. [PMID: 27415352 DOI: 10.1103/physreve.93.063005] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2015] [Indexed: 06/06/2023]
Abstract
A mesoscopic model of amorphous plasticity is discussed in the context of depinning models. After embedding in a d+1-dimensional space, where the accumulated plastic strain lives along the additional dimension, the gradual plastic deformation of amorphous media can be regarded as the motion of an elastic manifold in a disordered landscape. While the associated depinning transition leads to scaling properties, the quadrupolar Eshelby interactions at play in amorphous plasticity induce specific additional features like shear-banding and weak ergodicity breakdown. The latters are shown to be controlled by the existence of soft modes of the elastic interaction, the consequence of which is discussed in the context of depinning.
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Affiliation(s)
- Botond Tyukodi
- PMMH, ESPCI/CNRS-UMR 7636/Université Paris 6 UPMC/Université Paris 7 Diderot, 10 rue Vauquelin, 75231 Paris Cedex 05, France
- Physics Department, University Babeş-Bolyai, Cluj, Romania
| | - Sylvain Patinet
- PMMH, ESPCI/CNRS-UMR 7636/Université Paris 6 UPMC/Université Paris 7 Diderot, 10 rue Vauquelin, 75231 Paris Cedex 05, France
| | - Stéphane Roux
- LMT, ENS-Cachan/CNRS-UMR 8535/Université Paris-Saclay, 61 Avenue du Président Wilson, 94235 Cachan Cedex, France
| | - Damien Vandembroucq
- PMMH, ESPCI/CNRS-UMR 7636/Université Paris 6 UPMC/Université Paris 7 Diderot, 10 rue Vauquelin, 75231 Paris Cedex 05, France
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27
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Papanikolaou S. Shearing a glass and the role of pinning delay in models of interface depinning. Phys Rev E 2016; 93:032610. [PMID: 27078417 DOI: 10.1103/physreve.93.032610] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2015] [Indexed: 11/07/2022]
Abstract
When a disordered solid is sheared, yielding is followed by the onset of intermittent response that is characterized by slip in local regions usually labeled shear-transformation zones. Such intermittent response resembles the behavior of earthquakes or contact depinning, where a well-defined landscape of pinning disorder prohibits the deformation of an elastic medium. Nevertheless, a disordered solid is evidently different in that pinning barriers of particles are due to neighbors that are also subject to motion. Microscopic yielding leads to destruction of the local microstructure and local heating. It is natural to assume that locally a liquid emerges for a finite timescale before cooling down to a transformed configuration. For including this characteristic transient in glass depinning models, we propose a general mechanism that involves a "pinning delay" time T(pd), during which each region that slipped evolves as a fluid. The new timescale can be as small as a single avalanche time step. This is a local, effective, and dynamical in nature mechanism that may be thought as dynamical softening. We demonstrate that the inclusion of this mechanism causes a drift of the critical exponents toward higher values for the slip sizes τ, until a transition to permanent shear-banding behavior happens causing almost oscillatory, stick-slip response. Moreover, it leads to a proliferation of large events that are highly inhomogeneous and resemble sharp slip band formation.
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Affiliation(s)
- Stefanos Papanikolaou
- Department of Mechanical Engineering, The Johns Hopkins University, 3400 North Charles Street, Baltimore, Maryland 21218, USA and Hopkins Extreme Materials Institute, The Johns Hopkins University, 3400 North Charles Street, Baltimore, Maryland 21218, USA
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28
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Liu C, Ferrero EE, Puosi F, Barrat JL, Martens K. Driving Rate Dependence of Avalanche Statistics and Shapes at the Yielding Transition. PHYSICAL REVIEW LETTERS 2016; 116:065501. [PMID: 26918998 DOI: 10.1103/physrevlett.116.065501] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2015] [Indexed: 06/05/2023]
Abstract
We study stress time series caused by plastic avalanches in athermally sheared disordered materials. Using particle-based simulations and a mesoscopic elastoplastic model, we analyze system size and shear-rate dependence of the stress-drop duration and size distributions together with their average temporal shape. We find critical exponents different from mean-field predictions, and a clear asymmetry for individual avalanches. We probe scaling relations for the rate dependency of the dynamics and we report a crossover towards mean-field results for strong driving.
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Affiliation(s)
- Chen Liu
- Université Grenoble Alpes, LIPHY, F-38000 Grenoble, France
- CNRS, LIPHY, F-38000 Grenoble, France
| | - Ezequiel E Ferrero
- Université Grenoble Alpes, LIPHY, F-38000 Grenoble, France
- CNRS, LIPHY, F-38000 Grenoble, France
| | - Francesco Puosi
- Université Grenoble Alpes, LIPHY, F-38000 Grenoble, France
- CNRS, LIPHY, F-38000 Grenoble, France
- Ecole Normale Supérieure de Lyon, Laboratoire de Physique CNRS, 46 allée d'Italie, 69364 Lyon Cedex 7, France
| | - Jean-Louis Barrat
- Université Grenoble Alpes, LIPHY, F-38000 Grenoble, France
- CNRS, LIPHY, F-38000 Grenoble, France
| | - Kirsten Martens
- Université Grenoble Alpes, LIPHY, F-38000 Grenoble, France
- CNRS, LIPHY, F-38000 Grenoble, France
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29
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Tyukodi B, Lemarchand CA, Hansen JS, Vandembroucq D. Finite-size effects in a model for plasticity of amorphous composites. Phys Rev E 2016; 93:023004. [PMID: 26986402 DOI: 10.1103/physreve.93.023004] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2015] [Indexed: 06/05/2023]
Abstract
We discuss the plastic behavior of an amorphous matrix reinforced by hard particles. A mesoscopic depinning-like model accounting for Eshelby elastic interactions is implemented. Only the effect of a plastic disorder is considered. Numerical results show a complex size dependence of the effective flow stress of the amorphous composite. In particular, the departure from the mixing law shows opposite trends associated to the competing effects of the matrix and the reinforcing particles, respectively. The reinforcing mechanisms and their effects on localization are discussed. Plastic strain is shown to gradually concentrate on the weakest band of the system. This correlation of the plastic behavior with the material structure is used to design a simple analytical model. The latter nicely captures reinforcement size effects in (logN/N)(1/2), where N is the linear size of the system, observed numerically. Predictions of the effective flow stress accounting for further logarithmic corrections show a very good agreement with numerical results.
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Affiliation(s)
- Botond Tyukodi
- Laboratoire PMMH, CNRS-UMR 7636/ESPCI/UPMC/Univ. Paris 7 Diderot, 10, rue Vauquelin, 75231 Paris cedex 05, France
- Babeş-Bolyai University, Department of Physics, 1 str. Mihail Kogălniceanu, 400084 Cluj Napoca, Romania
| | - Claire A Lemarchand
- DNRF Centre "Glass and Time," IMFUFA, Department of Sciences, Roskilde University, Postbox 260, DK-4000 Roskilde, Denmark
| | - Jesper S Hansen
- DNRF Centre "Glass and Time," IMFUFA, Department of Sciences, Roskilde University, Postbox 260, DK-4000 Roskilde, Denmark
| | - Damien Vandembroucq
- Laboratoire PMMH, CNRS-UMR 7636/ESPCI/UPMC/Univ. Paris 7 Diderot, 10, rue Vauquelin, 75231 Paris cedex 05, France
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Benzi R, Sbragaglia M, Bernaschi M, Succi S, Toschi F. Cooperativity flows and shear-bandings: a statistical field theory approach. SOFT MATTER 2016; 12:514-530. [PMID: 26486875 DOI: 10.1039/c5sm01862e] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Cooperativity effects have been proposed to explain the non-local rheology in the dynamics of soft jammed systems. Based on the analysis of the free-energy model proposed by L. Bocquet, A. Colin and A. Ajdari, Phys. Rev. Lett., 2009, 103, 036001, we show that cooperativity effects resulting from the non-local nature of the fluidity (inverse viscosity) are intimately related to the emergence of shear-banding configurations. This connection materializes through the onset of inhomogeneous compact solutions (compactons), wherein the fluidity is confined to finite-support subregions of the flow and strictly zero elsewhere. The compacton coexistence with regions of zero fluidity ("non-flowing vacuum") is shown to be stabilized by the presence of mechanical noise, which ultimately shapes up the equilibrium distribution of the fluidity field, the latter acting as an order parameter for the flow-noflow transitions occurring in the material.
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Affiliation(s)
- R Benzi
- Department of Physics and INFN, University of "Tor Vergata", Via della Ricerca Scientifica 1, 00133 Rome, Italy.
| | - M Sbragaglia
- Department of Physics and INFN, University of "Tor Vergata", Via della Ricerca Scientifica 1, 00133 Rome, Italy.
| | - M Bernaschi
- Istituto per le Applicazioni del Calcolo CNR, Via dei Taurini 19, 00185 Rome, Italy
| | - S Succi
- Istituto per le Applicazioni del Calcolo CNR, Via dei Taurini 19, 00185 Rome, Italy
| | - F Toschi
- Istituto per le Applicazioni del Calcolo CNR, Via dei Taurini 19, 00185 Rome, Italy and Department of Physics and Department of Mathematics and Computer Science and J. M. Burgerscentrum, Eindhoven University of Technology, 5600 MB, Eindhoven, Netherlands
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Puosi F, Olivier J, Martens K. Probing relevant ingredients in mean-field approaches for the athermal rheology of yield stress materials. SOFT MATTER 2015; 11:7639-7647. [PMID: 26294288 DOI: 10.1039/c5sm01694k] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Although the notion of mechanical noise is expected to play a key role in the non-linear rheology of athermally sheared amorphous systems, its characterization has so far remained elusive. Here, we show using molecular dynamic simulations that in spite of the presence of strong spatio-temporal correlations in the system, the local stress exhibits normal diffusion under the effect of the mechanical noise in the finite driving regime. The diffusion constant appears to be proportional to the mean plastic activity. Our data suggests that the corresponding proportionality constant is density independent, and can be directly related to the specific form of the rheological flow curve, pointing the way to a generic way of modeling mechanical noise in mean-field equations.
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Affiliation(s)
- Francesco Puosi
- Laboratoire de Physique de l'École Normale Supérieure de Lyon, Université de Lyon, CNRS, 46 Allée d'Italie, 69364 Lyon cédex 07, France.
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Chevalier T, Talon L. Moving line model and avalanche statistics of Bingham fluid flow in porous media. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2015; 38:76. [PMID: 26187726 DOI: 10.1140/epje/i2015-15076-5] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/26/2015] [Revised: 05/27/2015] [Accepted: 06/09/2015] [Indexed: 06/04/2023]
Abstract
In this article, we propose a simple model to understand the critical behavior of path opening during flow of a yield stress fluid in porous media as numerically observed by Chevalier and Talon (2015). This model can be mapped to the problem of a contact line moving in an heterogeneous field. Close to the critical point, this line presents an avalanche dynamic where the front advances by a succession of waiting time and large burst events. These burst events are then related to the non-flowing (i.e. unyielded) areas. Remarkably, the statistics of these areas reproduce the same properties as in the direct numerical simulations. Furthermore, even if our exponents seem to be close to the mean field universal exponents, we report an unusual bump in the distribution which depends on the disorder. Finally, we identify a scaling invariance of the cluster spatial shape that is well fit, to first order, by a self-affine parabola.
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Affiliation(s)
- Thibaud Chevalier
- CNRS, Laboratoire FAST, UMR 7608, Université Paris-Sud, F-91405, Orsay, France,
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Quenched pinning and collective dislocation dynamics. Sci Rep 2015; 5:10580. [PMID: 26024505 PMCID: PMC4650641 DOI: 10.1038/srep10580] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2014] [Accepted: 04/20/2015] [Indexed: 11/09/2022] Open
Abstract
Several experiments show that crystalline solids deform in a bursty and intermittent fashion. Power-law distributed strain bursts in compression experiments of micron-sized samples, and acoustic emission energies from larger-scale specimens, are the key signatures of the underlying critical-like collective dislocation dynamics - a phenomenon that has also been seen in discrete dislocation dynamics (DDD) simulations. Here we show, by performing large-scale two-dimensional DDD simulations, that the character of the dislocation avalanche dynamics changes upon addition of sufficiently strong randomly distributed quenched pinning centres, present e.g. in many alloys as immobile solute atoms. For intermediate pinning strength, our results adhere to the scaling picture of depinning transitions, in contrast to pure systems where dislocation jamming dominates the avalanche dynamics. Still stronger disorder quenches the critical behaviour entirely.
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Niiyama T, Shimokawa T. Atomistic mechanisms of intermittent plasticity in metals: dislocation avalanches and defect cluster pinning. Phys Rev E 2015; 91:022401. [PMID: 25768512 DOI: 10.1103/physreve.91.022401] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2014] [Indexed: 11/07/2022]
Abstract
Intermittent plastic deformation in crystals with power-law behaviors has been reported in previous experimental studies. The power-law behavior is reminiscent of self-organized criticality, and mesoscopic models have been proposed that describe this behavior in crystals. In this paper, we show that intermittent plasticity in metals under tensile deformation can be observed in molecular dynamics models, using embedded atom method potentials for Ni, Cu, and Al. Power-law behaviors of stress drop and waiting time of plastic deformation events are observed. It is shown that power-law behavior is due to dislocation avalanche motions in Cu and Ni. A different mechanism of dislocation pinning is found in Al. These different stress relaxation mechanisms give different power-law exponents. We propose a probabilistic model to describe the novel dislocation motion in Al and analytically deduce the power-law behavior.
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Affiliation(s)
- Tomoaki Niiyama
- College of Science and Engineering, Kanazawa University, Kakuma-machi, Kanazawa, Ishikawa 920-1192, Japan
| | - Tomotsugu Shimokawa
- College of Science and Engineering, Kanazawa University, Kakuma-machi, Kanazawa, Ishikawa 920-1192, Japan
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Kale S, Ostoja-Starzewski M. Morphological study of elastic-plastic-brittle transitions in disordered media. Phys Rev E 2014; 90:042405. [PMID: 25375508 DOI: 10.1103/physreve.90.042405] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/02/2014] [Indexed: 11/07/2022]
Abstract
We use a spring lattice model with springs following a bilinear elastoplastic-brittle constitutive behavior with spatial disorder in the yield and failure thresholds to study patterns of plasticity and damage evolution. The elastic-perfectly plastic transition is observed to follow percolation scaling with the correlation length critical exponent ν≈1.59, implying the universality class corresponding to the long-range correlated percolation. A quantitative analysis of the plastic strain accumulation reveals a dipolar anisotropy (for antiplane loading) which vanishes with increasing hardening modulus. A parametric study with hardening modulus and ductility controlled through the spring level constitutive response demonstrates a wide spectrum of behaviors with varying degree of coupling between plasticity and damage evolution.
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Affiliation(s)
- Sohan Kale
- Department of Mechanical Science and Engineering, Institute for Condensed Matter Theory and Beckman Institute, University of Illinois at Urbana-Champaign, Urbana 61801, USA
| | - Martin Ostoja-Starzewski
- Department of Mechanical Science and Engineering, Institute for Condensed Matter Theory and Beckman Institute, University of Illinois at Urbana-Champaign, Urbana 61801, USA
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Lin J, Lerner E, Rosso A, Wyart M. Scaling description of the yielding transition in soft amorphous solids at zero temperature. Proc Natl Acad Sci U S A 2014; 111:14382-7. [PMID: 25246567 PMCID: PMC4210034 DOI: 10.1073/pnas.1406391111] [Citation(s) in RCA: 126] [Impact Index Per Article: 12.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Yield stress materials flow if a sufficiently large shear stress is applied. Although such materials are ubiquitous and relevant for industry, there is no accepted microscopic description of how they yield, even in the simplest situations in which temperature is negligible and in which flow inhomogeneities such as shear bands or fractures are absent. Here we propose a scaling description of the yielding transition in amorphous solids made of soft particles at zero temperature. Our description makes a connection between the Herschel-Bulkley exponent characterizing the singularity of the flow curve near the yield stress Σc, the extension and duration of the avalanches of plasticity observed at threshold, and the density P(x) of soft spots, or shear transformation zones, as a function of the stress increment x beyond which they yield. We argue that the critical exponents of the yielding transition may be expressed in terms of three independent exponents, θ, df, and z, characterizing, respectively, the density of soft spots, the fractal dimension of the avalanches, and their duration. Our description shares some similarity with the depinning transition that occurs when an elastic manifold is driven through a random potential, but also presents some striking differences. We test our arguments in an elasto-plastic model, an automaton model similar to those used in depinning, but with a different interaction kernel, and find satisfying agreement with our predictions in both two and three dimensions.
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Affiliation(s)
- Jie Lin
- Center for Soft Matter Research, Department of Physics, New York University, New York, NY 10003; and
| | - Edan Lerner
- Center for Soft Matter Research, Department of Physics, New York University, New York, NY 10003; and
| | - Alberto Rosso
- Laboratoire de Physique Théorique et Modèles Statistiques (Centre National de la Recherche Scientifique, Unité Mixte de Recherche 8626), Université de Paris-Sud, 91405 Orsay Cedex, France
| | - Matthieu Wyart
- Center for Soft Matter Research, Department of Physics, New York University, New York, NY 10003; and
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Nicolas A, Martens K, Bocquet L, Barrat JL. Universal and non-universal features in coarse-grained models of flow in disordered solids. SOFT MATTER 2014; 10:4648-4661. [PMID: 24839104 DOI: 10.1039/c4sm00395k] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We study the two-dimensional (2D) shear flow of amorphous solids within variants of an elastoplastic model, paying particular attention to spatial correlations and time fluctuations of, e.g., local stresses. The model is based on the local alternation between an elastic regime and plastic events during which the local stress is redistributed. The importance of a fully tensorial description of the stress and of the inclusion of (coarse-grained) convection in the model is investigated; scalar and tensorial models yield similar results, while convection enhances fluctuations and breaks the spurious symmetry between the flow and velocity gradient directions, for instance when shear localisation is observed. Besides, correlation lengths measured with diverse protocols are discussed. One class of such correlation lengths simply scale with the spacing between homogeneously distributed, simultaneous plastic events. This leads to a scaling of the correlation length with the shear rate as γ̇(-1/2) in 2D in the athermal regime, regardless of the details of the model. The radius of the cooperative disk, defined as the near-field region in which plastic events induce a stress redistribution that is not amenable to a mean-field treatment, notably follows this scaling. On the other hand, the cooperative volume measured from the four-point stress susceptibility and its dependence on the system size and the shear rate are model-dependent.
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