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Maire R, Plati A, Stockinger M, Trizac E, Smallenburg F, Foffi G. Interplay between an Absorbing Phase Transition and Synchronization in a Driven Granular System. PHYSICAL REVIEW LETTERS 2024; 132:238202. [PMID: 38905681 DOI: 10.1103/physrevlett.132.238202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2023] [Accepted: 04/24/2024] [Indexed: 06/23/2024]
Abstract
Absorbing phase transitions (APTs) are widespread in nonequilibrium systems, spanning condensed matter, epidemics, earthquakes, ecology, and chemical reactions. APTs feature an absorbing state in which the system becomes entrapped, along with a transition, either continuous or discontinuous, to an active state. Understanding which physical mechanisms determine the order of these transitions represents a challenging open problem in nonequilibrium statistical mechanics. Here, by numerical simulations and mean-field analysis, we show that a quasi-2D vibrofluidized granular system exhibits a novel form of APT. The absorbing phase is observed in the horizontal dynamics below a critical packing fraction, and can be continuous or discontinuous based on the emergent degree of synchronization in the vertical motion. Our results provide a direct representation of a feasible experimental scenario, showcasing a surprising interplay between dynamic phase transition and synchronization.
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Affiliation(s)
- R Maire
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
| | - A Plati
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
| | - M Stockinger
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
- Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, 14476 Potsdam, Germany
| | - E Trizac
- LPTMS, UMR 8626, CNRS, Université Paris-Saclay, 91405 Orsay, France
- Ecole normale supérieure de Lyon, F-69364 Lyon, France
| | - F Smallenburg
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
| | - G Foffi
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
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2
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Cochran JO, Callaghan GL, Caven MJG, Fielding SM. Slow Fatigue and Highly Delayed Yielding via Shear Banding in Oscillatory Shear. PHYSICAL REVIEW LETTERS 2024; 132:168202. [PMID: 38701472 DOI: 10.1103/physrevlett.132.168202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2022] [Revised: 11/21/2023] [Accepted: 03/15/2024] [Indexed: 05/05/2024]
Abstract
We study theoretically the dynamical process of yielding in cyclically sheared amorphous materials, within a thermal elastoplastic model and the soft glassy rheology model. Within both models we find an initially slow accumulation, over many cycles after the inception of shear, of low levels of damage in the form strain heterogeneity across the sample. This slow fatigue then suddenly gives way to catastrophic yielding and material failure. Strong strain localization in the form of shear banding is key to the failure mechanism. We characterize in detail the dependence of the number of cycles N^{*} before failure on the amplitude of imposed strain, the working temperature, and the degree to which the sample is annealed prior to shear. We discuss our finding with reference to existing experiments and particle simulations, and suggest new ones to test our predictions.
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Affiliation(s)
- James O Cochran
- Department of Physics, Durham University, Science Laboratories, South Road, Durham DH1 3LE, United Kingdom
| | - Grace L Callaghan
- Department of Physics, Durham University, Science Laboratories, South Road, Durham DH1 3LE, United Kingdom
| | - Miles J G Caven
- Department of Physics, Durham University, Science Laboratories, South Road, Durham DH1 3LE, United Kingdom
| | - Suzanne M Fielding
- Department of Physics, Durham University, Science Laboratories, South Road, Durham DH1 3LE, United Kingdom
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3
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Agoritsas E, Barés J. Loss of memory of an elastic line on its way to limit cycles. Phys Rev E 2024; 109:L042901. [PMID: 38755875 DOI: 10.1103/physreve.109.l042901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2023] [Accepted: 03/10/2024] [Indexed: 05/18/2024]
Abstract
Oscillatory-driven amorphous materials forget their initial configuration and converge to limit cycles. Here we investigate this memory loss under a nonquasistatic drive in a minimal model system, with quenched disorder and memory encoded in a spatial pattern, where oscillating protocols are formally replaced by a positive-velocity drive. We consider an elastic line driven athermally in a quenched disorder with biperiodic boundary conditions and tunable system size, thus controlling the area swept by the line per cycle as would the oscillation amplitude. The convergence to disorder-dependent limit cycle is strongly coupled to the nature of its velocity dynamics depending on system size. Based on the corresponding phase diagram, we propose a generic scenario for memory formation in disordered systems under finite driving rate.
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Affiliation(s)
- Elisabeth Agoritsas
- Department of Quantum Matter Physics (DQMP), University of Geneva, Quai Ernest-Ansermet 24, CH-1211 Geneva, Switzerland
| | - Jonathan Barés
- Laboratoire de Mécanique et Génie Civil (LMGC), UMR 5508 CNRS-University Montpellier, 34095 Montpellier, France
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4
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Minogue D, Eskildsen MR, Reichhardt C, Reichhardt CJO. Reversible, irreversible, and mixed regimes for periodically driven disks in random obstacle arrays. Phys Rev E 2024; 109:044905. [PMID: 38755905 DOI: 10.1103/physreve.109.044905] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2024] [Accepted: 03/27/2024] [Indexed: 05/18/2024]
Abstract
We examine an assembly of repulsive disks interacting with a random obstacle array under a periodic drive and find a transition from reversible to irreversible dynamics as a function of drive amplitude or disk density. At low densities and drives, the system rapidly forms a reversible state where the disks return to their exact positions at the end of each cycle. In contrast, at high amplitudes or high densities, the system enters an irreversible state where the disks exhibit normal diffusion. Between these two regimes, there can be an intermediate irreversible state where most of the system is reversible, but localized irreversible regions are present that are prevented from spreading through the system due to a screening effect from the obstacles. We also find states that we term "combinatorial reversible states" in which the disks return to their original positions after multiple driving cycles. In these states, individual disks exchange positions but form the same configurations during the subcycles of the larger reversible cycle.
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Affiliation(s)
- D Minogue
- Department of Physics, University of Notre Dame, Notre Dame, Indiana 46656, USA
| | - M R Eskildsen
- Department of Physics, University of Notre Dame, Notre Dame, Indiana 46656, USA
| | - C Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - C J O Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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5
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Zella L, Moon J, Egami T. Ripples in the bottom of the potential energy landscape of metallic glass. Nat Commun 2024; 15:1358. [PMID: 38355602 PMCID: PMC10866862 DOI: 10.1038/s41467-024-45640-1] [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: 07/26/2023] [Accepted: 01/29/2024] [Indexed: 02/16/2024] Open
Abstract
In the absence of periodicity, the structure of glass is ill-defined, and a large number of structural states are found at similar energy levels. However, little is known about how these states are connected to each other in the potential energy landscape. We simulate mechanical relaxation by molecular dynamics for a prototypical [Formula: see text] metallic glass and follow the mechanical energy loss of each atom to track the change in the state. We find that the energy barriers separating these states are remarkably low, only of the order of 1 meV, implying that even quantum fluctuations can overcome these potential energy barriers. Our observation of numerous small ripples in the bottom of the potential energy landscape puts many assumptions regarding the thermodynamic states of metallic glasses into question and suggests that metallic glasses are not totally frozen at the local atomic level.
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Affiliation(s)
- Leo Zella
- Department of Materials Science and Engineering, The University of Tennessee, Knoxville, TN, 37996, USA
| | - Jaeyun Moon
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN, 37831, USA
- Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY, 14853, USA
| | - Takeshi Egami
- Department of Materials Science and Engineering, The University of Tennessee, Knoxville, TN, 37996, USA.
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN, 37831, USA.
- Department of Physics and Astronomy, The University of Tennessee, Knoxville, TN, 37996, USA.
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6
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Khushika, Laurson L, Jana PK. Reversible-to-irreversible transition of colloidal polycrystals under cyclic athermal quasistatic deformation. Phys Rev E 2023; 108:064612. [PMID: 38243495 DOI: 10.1103/physreve.108.064612] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2023] [Accepted: 11/29/2023] [Indexed: 01/21/2024]
Abstract
Cyclic loading on granular packings and amorphous media exhibits a transition from reversible elastic behavior to irreversible plasticity. The present study compares the irreversibility transition and microscopic details of colloidal polycrystals under oscillatory tensile-compressive and shear strain. Under both modes, the systems exhibit a reversible to irreversible transition. However, the strain amplitude at which the transition is observed is larger in the shear strain than in the tensile-compressive mode. The threshold strain amplitude is confirmed by analyzing the dynamical properties, such as mobility and atomic strain (von Mises shear strain and the volumetric strain). The structural changes are quantified using a hexatic order parameter. Under both modes of deformation, dislocations and grain boundaries in polycrystals disappear, and monocrystals are formed. We also recognize the dislocation motion through grains. The key difference is that strain accumulates diagonally in oscillatory tensile-compressive deformation, whereas in shear deformation, strain accumulation is along the x or y axis.
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Affiliation(s)
- Khushika
- Department of Chemistry, Birla Institute of Technology and Science, Pilani, Pilani Campus, Rajasthan 333031, India
| | - Lasse Laurson
- Computational Physics Laboratory, Tampere University, P.O. Box 692, FI-33014 Tampere, Finland
| | - Pritam Kumar Jana
- Department of Chemistry, Birla Institute of Technology and Science, Pilani, Pilani Campus, Rajasthan 333031, India
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7
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Movsheva A, Witten TA. Granular convergence as an iterated local map. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2023; 46:84. [PMID: 37721576 DOI: 10.1140/epje/s10189-023-00343-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/07/2023] [Accepted: 08/28/2023] [Indexed: 09/19/2023]
Abstract
Granular convergence is a property of a granular pack as it is repeatedly sheared in a cyclic, quasistatic fashion, as the packing configuration changes via discrete events. Under suitable conditions the set of microscopic configurations encountered converges to a periodic sequence after sufficient shear cycles. Prior work modeled this evolution as the iteration of a pre-determined, random map from a set of discrete configurations into itself. Iterating such a map from a random starting point leads to similar periodic repetition. This work explores the effect of restricting the randomness of such maps in order to account for the local nature of the discrete events. The number of cycles needed for convergence shows similar statistical behavior to that of numerical granular experiments. The number of cycles in a repeating period behaves only qualitatively like these granular studies.
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Affiliation(s)
- Anna Movsheva
- James Franck Institute, University of Chicago, 929 E. 57th Street, Chicago, IL, 60637, USA
| | - Thomas A Witten
- James Franck Institute, University of Chicago, 929 E. 57th Street, Chicago, IL, 60637, USA.
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8
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Kwakernaak LJ, van Hecke M. Counting and Sequential Information Processing in Mechanical Metamaterials. PHYSICAL REVIEW LETTERS 2023; 130:268204. [PMID: 37450791 DOI: 10.1103/physrevlett.130.268204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2023] [Accepted: 05/30/2023] [Indexed: 07/18/2023]
Abstract
Materials with an irreversible response to cyclic driving exhibit an evolving internal state which, in principle, encodes information on the driving history. Here we realize irreversible metamaterials that count mechanical driving cycles and store the result into easily interpretable internal states. We extend these designs to aperiodic metamaterials that are sensitive to the order of different driving magnitudes, and realize "lock and key" metamaterials that only reach a specific state for a given target driving sequence. Our metamaterials are robust, scalable, and extendable, give insight into the transient memories of complex media, and open new routes towards smart sensing, soft robotics, and mechanical information processing.
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Affiliation(s)
- Lennard J Kwakernaak
- Huygens-Kamerlingh Onnes Laboratory, Universiteit Leiden, PO Box 9504, 2300 RA Leiden, Netherlands and AMOLF, Science Park 104, 1098 XG Amsterdam, Netherlands
| | - Martin van Hecke
- Huygens-Kamerlingh Onnes Laboratory, Universiteit Leiden, PO Box 9504, 2300 RA Leiden, Netherlands and AMOLF, Science Park 104, 1098 XG Amsterdam, Netherlands
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9
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Shohat D, Lahini Y. Dissipation Indicates Memory Formation in Driven Disordered Systems. PHYSICAL REVIEW LETTERS 2023; 130:048202. [PMID: 36763418 DOI: 10.1103/physrevlett.130.048202] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2022] [Accepted: 01/04/2023] [Indexed: 06/18/2023]
Abstract
Disordered and amorphous materials often retain memories of perturbations they have experienced since preparation. Studying such memories is a gateway to understanding this challenging class of systems. However, it often requires the ability to measure local structural changes in response to external drives. Here, we show that dissipation is a generic macroscopic indicator of the memory of the largest perturbation. Through experiments in crumpled sheets under cyclic drive, we show that dissipation transiently increases when first surpassing the largest perturbation due to irreversible structural changes with unique statistics. This finding is used to devise novel memory readout protocols based on global observables only. The general applicability of this approach is demonstrated by revealing a similar memory effect in a three-dimensional amorphous solid.
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Affiliation(s)
- Dor Shohat
- Department of Condensed Matter, School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel and Center for Physics and Chemistry of Living Systems, Tel Aviv University, Tel Aviv 69978, Israel
| | - Yoav Lahini
- Department of Condensed Matter, School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel and Center for Physics and Chemistry of Living Systems, Tel Aviv University, Tel Aviv 69978, Israel
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10
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Ghosh A, Radhakrishnan J, Chaikin PM, Levine D, Ghosh S. Coupled Dynamical Phase Transitions in Driven Disk Packings. PHYSICAL REVIEW LETTERS 2022; 129:188002. [PMID: 36374694 DOI: 10.1103/physrevlett.129.188002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2022] [Revised: 07/05/2022] [Accepted: 09/20/2022] [Indexed: 06/16/2023]
Abstract
Under the influence of oscillatory shear, a monolayer of frictional granular disks exhibits two dynamical phase transitions: a transition from an initially disordered state to an ordered crystalline state and a dynamic active-absorbing phase transition. Although there is no reason a priori for these to be at the same critical point, they are. The transitions may also be characterized by the disk trajectories, which are nontrivial loops breaking time-reversal invariance.
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Affiliation(s)
- Akash Ghosh
- Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research, Mumbai 400005, India
| | - Jaikumar Radhakrishnan
- School of Technology and Computer Science, Tata Institute of Fundamental Research, Mumbai 400005, India
| | - Paul M Chaikin
- Center for Soft Matter Research and Department of Physics, New York University, New York, New York 10003, USA
| | - Dov Levine
- Department of Physics, Technion-IIT, 32000 Haifa, Israel
| | - Shankar Ghosh
- Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research, Mumbai 400005, India
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11
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Keim NC, Medina D. Mechanical annealing and memories in a disordered solid. SCIENCE ADVANCES 2022; 8:eabo1614. [PMID: 36197976 PMCID: PMC9534499 DOI: 10.1126/sciadv.abo1614] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/19/2022] [Accepted: 08/18/2022] [Indexed: 06/16/2023]
Abstract
Shearing a disordered or amorphous solid for many cycles with a constant strain amplitude can anneal it, relaxing a sample to a steady state that encodes a memory of that amplitude. This steady state also features a remarkable stability to amplitude variations that allows one to read the memory. Here, we shed light on both annealing and memory by considering how to mechanically anneal a sample to have as little memory content as possible. In experiments, we show that a "ring-down" protocol reaches a comparable steady state but with no discernible memories and minimal structural anisotropy. We introduce a method to characterize the population of rearrangements within a sample and show how it connects with the response to amplitude variation and the size of annealing steps. These techniques can be generalized to other forms of glassy matter and a wide array of disordered solids, especially those that yield by flowing homogeneously.
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Affiliation(s)
- Nathan C. Keim
- Department of Physics, Pennsylvania State University, University Park, PA 16802, USA
- Department of Physics, California Polytechnic State University, San Luis Obispo, CA 93407, USA
| | - Dani Medina
- Department of Physics, California Polytechnic State University, San Luis Obispo, CA 93407, USA
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12
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Cui S, Liu H, Peng H. Anisotropic correlations of plasticity on the yielding of metallic glasses. Phys Rev E 2022; 106:014607. [PMID: 35974506 DOI: 10.1103/physreve.106.014607] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2022] [Accepted: 07/07/2022] [Indexed: 06/15/2023]
Abstract
We report computer simulations on the shear deformation of CuZr metallic glasses at zero and room temperatures. Shear bands emerge in athermal alloys at strain γ_{c}, with a finite-size effect found. The correlation of nonaffine displacement exhibits an exponential decay even after yielding in thermal alloys, but transits to a power law at γ>γ_{c} in athermal ones. The algebraic exponent is around -1 for the decay inside shear bands, consistent with the theoretical prediction in random elastic media. We quantify the anisotropic correlation with harmonic projection, finding the spectrum is weak in the exponential-decay regime, while it displays a strong polar and quadrupolar symmetry in the power-law regime. The nonvanishing quadrupolar symmetry at long distance signifies the nonlocality of plastic correlation in the athermal alloys. In contrast, the plastic correlation was found to be isotropic and localized at the yielding in the thermal alloys without shear bands.
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Affiliation(s)
- Shiheng Cui
- School of Materials Science and Engineering, Central South University, 932 South Lushan Road, Changsha 410083, China
| | - Huashan Liu
- School of Materials Science and Engineering, Central South University, 932 South Lushan Road, Changsha 410083, China
| | - Hailong Peng
- School of Materials Science and Engineering, Central South University, 932 South Lushan Road, Changsha 410083, China
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13
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Chattopadhyay S, Majumdar S. Inter-particle adhesion induced strong mechanical memory in a dense granular suspension. J Chem Phys 2022; 156:241102. [DOI: 10.1063/5.0089721] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Repeated/cyclic shearing can drive amorphous solids to a steady state encoding a memory of the applied strain amplitude. However, recent experiments find that the effect of such memory formation on the mechanical properties of the bulk material is rather weak. Here, we study the memory effect in a yield stress solid formed by a dense suspension of cornstarch particles in paraffin oil. Under cyclic shear, the system evolves toward a steady state showing training-induced strain stiffening and plasticity. A readout reveals that the system encodes a strong memory of the training amplitude ( γ T) as indicated by a large change in the differential shear modulus. We observe that memory can be encoded for a wide range of γ T values both above and below the yielding albeit the strength of the memory decreases with increasing γ T. In situ boundary imaging shows strain localization close to the shearing boundaries, while the bulk of the sample moves like a solid plug. In the steady state, the average particle velocity [Formula: see text] inside the solid-like region slows down with respect to the moving plate as γ approaches γ T; however, as the readout strain crosses γ T, [Formula: see text] suddenly increases. We demonstrate that inter-particle adhesive interaction is crucial for such a strong memory effect. Interestingly, our system can also remember more than one input only if the training strain with smaller amplitude is applied last.
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14
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Otsuki M, Hayakawa H. Softening and Residual Loss Modulus of Jammed Grains under Oscillatory Shear in an Absorbing State. PHYSICAL REVIEW LETTERS 2022; 128:208002. [PMID: 35657892 DOI: 10.1103/physrevlett.128.208002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/21/2021] [Revised: 12/26/2021] [Accepted: 04/22/2022] [Indexed: 06/15/2023]
Abstract
From a theoretical study of the mechanical response of jammed materials comprising frictionless and overdamped particles under oscillatory shear, we find that the material becomes soft, and the loss modulus remains nonzero even in an absorbing state where any irreversible plastic deformation does not exist. The trajectories of the particles in this region exhibit hysteresis loops. We succeed in clarifying the origin of the softening of the material and the residual loss modulus with the aid of Fourier analysis. We also clarify the roles of the yielding point in the softening to distinguish the plastic deformation from reversible deformation in the absorbing state.
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Affiliation(s)
- Michio Otsuki
- Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Hisao Hayakawa
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawaoiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan
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15
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Parley JT, Sastry S, Sollich P. Mean-Field Theory of Yielding under Oscillatory Shear. PHYSICAL REVIEW LETTERS 2022; 128:198001. [PMID: 35622036 DOI: 10.1103/physrevlett.128.198001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/25/2022] [Accepted: 04/13/2022] [Indexed: 06/15/2023]
Abstract
We study a mean field elastoplastic model, embedded within a disordered landscape of local yield barriers, to shed light on the behavior of athermal amorphous solids subject to oscillatory shear. We show that the model presents a genuine dynamical transition between an elastic and a yielded state, and qualitatively reproduces the dependence on the initial degree of annealing found in particle simulations. For initial conditions prepared below the analytically derived threshold energy, we observe a nontrivial, nonmonotonic approach to the yielded state. The timescale diverges as one approaches the yielding point from above, which we identify with the fatigue limit. We finally discuss the connections to brittle yielding under uniform shear.
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Affiliation(s)
- Jack T Parley
- Institut für Theoretische Physik, University of Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
| | - Srikanth Sastry
- Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkar Campus, 560064 Bengaluru, India
| | - Peter Sollich
- Institut für Theoretische Physik, University of Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany and Department of Mathematics, King's College London, London WC2R 2LS, United Kingdom
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16
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szulc A, Mungan M, Regev I. Cooperative effects driving the multi-periodic dynamics of cyclically sheared amorphous solids. J Chem Phys 2022; 156:164506. [DOI: 10.1063/5.0087164] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
When subject to cyclic forcing, amorphous solids can reach periodic, repetitive states, where the system behaves plastically, but the particles return to their initial positions after one or more forcing cycles, where the latter response is called multi-periodic. It is known that plasticity in amorphous materials is mediated by local rearrangements called ``soft spots' or ``shear transformation zones'.Experiments and simulations indicate that soft spots can be modeled as hysteretic two-state entities interacting via quadrupolar displacement fields generated when they switch states and that these interactions can give rise to multi-periodic behavior. However, how interactions facilitate multi-periodicity is unknown. Here we show, using a model of random interacting two-state systems and molecular dynamics simulations, that multi-periodicity arises from oscillations in the magnitudes of the switching field of soft spots which cause soft spots to be active during some forcing cycles and idle during others. We demonstrate that these oscillations result from cooperative effects facilitated by the frustrated interactions between the soft spots. The presence of such mechanisms has implications for manipulating memory in frustrated hysteretic systems.
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Affiliation(s)
- asaf szulc
- Department of Physics, Ben-Gurion University of the Negev, Israel
| | - Muhittin Mungan
- Rheinische Friedrich Wilhelms Universität Bonn Institute of Applied Mathematics, Germany
| | - Ido Regev
- Solar energy and environmental physics, Ben-Gurion University of the Negev - Sede Boqer Campus, Israel
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17
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Reichhardt C, Reichhardt C. Reversible to Irreversible Transitions for Cyclically Driven Particles on Periodic Obstacle Arrays. J Chem Phys 2022; 156:124901. [DOI: 10.1063/5.0087916] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We examine the collective dynamics of disks moving through a square array of obstacles under cyclic square wave driving. Below a critical density we find that system organizes into a reversible state in which the disks return to the same positions at the end of every drive cycle. Above this density, the dynamics are irreversible and the disks do not return to the same positions after each cycle. The critical density depends strongly on the angle θ between the driving direction and a symmetry axis of the obstacle array, with the highest critical densities appearing at commensurate angles such as θ=0{degree sign} and θ=45{degree sign} and the lowest critical densities falling at θ=arctan(0.618), the inverse of the golden ratio, where the flow is the most frustrated. As the density increases, the number of cycles required to reach a reversible state grows as a power law with an exponent near ν=1.36, similar to what is found in periodically driven colloidal and superconducting vortex systems.
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Affiliation(s)
| | - Cynthia Reichhardt
- Theoretical Division, Los Alamos National Laboratory, United States of America
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18
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Liu C, Ferrero EE, Jagla EA, Martens K, Rosso A, Talon L. The Fate of Shear-Oscillated Amorphous Solids. J Chem Phys 2022; 156:104902. [DOI: 10.1063/5.0079460] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Chen Liu
- Columbia University Department of Chemistry, United States of America
| | | | - Eduardo A. Jagla
- Teoria de solidos, Centro Atomico Bariloche, Comision Nacional de Energia Atomica, Argentina
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19
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Sun A, Wang Y, Chen Y, Shang J, Zheng J, Yu S, Su S, Sun X, Zhang J. Turbulent-like velocity fluctuations in two-dimensional granular materials subject to cyclic shear. SOFT MATTER 2022; 18:983-989. [PMID: 35014635 DOI: 10.1039/d1sm01516h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
We perform a systematic experimental study to investigate the velocity fluctuations in the two-dimensional granular matter of low and high friction coefficients subjected to cyclic shear of a range of shear amplitudes, whose velocity fields are strikingly turbulent-like with vortices of different scales. The scaling behaviors of both the transverse velocity power spectra ET(k) ∝ k-αT and, more severely, the longitudinal velocity power spectra EL(k) ∝ k-αL are affected by the prominent peak centered around k ≈ 2π of the inter-particle distance due to the static structure factor of the hard-particle nature in contrast to the real turbulence. To reduce the strong peak effect to the actual values of αν (the subscript 'ν' refers to either T or L), we subsequently analyze the second-order velocity structure functions of S(2)ν(r) in real space, which show the power-law scalings of S(2)ν(r) ∝ rβν for both modes. From the values of βν, we deduce the corresponding αν from the scaling relations of αν = βν + 2. The deduced values of αν increase continuously with the shear amplitude γm, showing no signature of yielding transition, and are slightly larger than αν = 2.0 at the limit of γm → 0, which corresponds to the elastic limit of the system, for all γm. The inter-particle friction coefficients show no significant effect on the turbulent-like velocity fluctuations. Our findings suggest that the turbulent-like collective particle motions are governed by both the elasticity and plasticity in cyclically sheared granular materials.
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Affiliation(s)
- Aile Sun
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China.
| | - Yinqiao Wang
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China.
| | - Yangrui Chen
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China.
| | - Jin Shang
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China.
| | - Jie Zheng
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China.
| | - Shuchang Yu
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China.
| | - Siyuan Su
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China.
| | - Xulai Sun
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China.
| | - Jie Zhang
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China.
- Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
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20
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Mitra S, Marín-Aguilar S, Sastry S, Smallenburg F, Foffi G. Correlation between plastic rearrangements and local structure in a cyclically driven glass. J Chem Phys 2022; 156:074503. [DOI: 10.1063/5.0077851] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
| | | | - Srikanth Sastry
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, India
| | | | - Giuseppe Foffi
- Laboratoire de Physique des Solides, Laboratoire de Physique des Solides, France
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21
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Bhowmik BP, Hentschel HGE, Procaccia I. Scaling theory for Wöhler plots in amorphous solids under cyclic forcing. Phys Rev E 2022; 105:015001. [PMID: 35193186 DOI: 10.1103/physreve.105.015001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2021] [Accepted: 12/17/2021] [Indexed: 11/07/2022]
Abstract
In mechanical engineering Wöhler plots serve to measure the average number of load cycles before materials break, as a function of the maximal stress in each cycle. Although such plots have been prevalent in engineering for more than 150 years, their theoretical understanding is lacking. Recently a scaling theory of Wöhler plots in the context of cyclic bending was offered [Bhowmik, arXiv:2103.03040 (2021)]. Here we elaborate further on cyclic bending and extend the considerations to cyclic tensile loads on an amorphous strip of material; the scaling theory applies to both types of cyclic loading equally well. On the basis of atomistic simulations we conclude that the crucial quantities to focus on are the accumulated damage and the average damage per cycle. The dependence of these quantities on the loading determines the statistics of the number of cycles to failure. Finally, we consider the probability distribution functions of the number of cycles to failure and demonstrate that the scaling theory allows prediction of these distributions at one value of the forcing amplitude from measurements and another value.
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Affiliation(s)
- Bhanu Prasad Bhowmik
- Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
| | - H G E Hentschel
- Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel.,Department of Physics, Emory University, Atlanta, Georgia 30322, USA
| | - Itamar Procaccia
- Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel.,Center for OPTical IMagery Analysis and Learning, Northwestern Polytechnical University, Xi'an, 710072 China
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22
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Zhai C, Albayrak N, Engqvist J, Hall SA, Wright J, Majkut M, Herbold EB, Hurley RC. Quantifying local rearrangements in three-dimensional granular materials: Rearrangement measures, correlations, and relationship to stresses. Phys Rev E 2022; 105:014904. [PMID: 35193203 DOI: 10.1103/physreve.105.014904] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2021] [Accepted: 01/04/2022] [Indexed: 06/14/2023]
Abstract
Quantifying the ways in which local particle rearrangements contribute to macroscopic plasticity is one of the fundamental pursuits of granular mechanics and soft matter physics. Here we examine local rearrangements that occur naturally during the deformation of three samples of 3D granular materials subjected to distinct boundary conditions by employing in situ x-ray measurements of particle-resolved structure and stress. We focus on five distinct rearrangement measures, their statistics, interrelationships, contributions to macroscopic deformation, repeatability, and dependence on local structure and stress. Our most significant findings are that local rearrangements (1) are correlated on a scale of three to four particle diameters, (2) exhibit volumetric strain-shear strain and nonaffine displacement-rotation coupling, (3) exhibit correlations that suggest either rearrangement repeatability or that rearrangements span multiple steps of incremental sample strain, and (4) show little dependence on local stress but correlate with quantities describing local structure, such as porosity. Our results are presented in the context of relevant plasticity theories and are consistent with recent findings suggesting that local structure may play at least as important of a role as local stress in determining the nature of local rearrangements.
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Affiliation(s)
- Chongpu Zhai
- State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi'an Jiaotong University, Xi'an, China and Department of Mechanical Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Nahuel Albayrak
- Hopkins Extreme Materials Institute, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Jonas Engqvist
- Division for Solid Mechanics, Lund University, Lund 22100, Sweden
| | | | | | | | - Eric B Herbold
- Atmospheric, Earth, & Energy Division, Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Ryan C Hurley
- Department of Mechanical Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA and Hopkins Extreme Materials Institute, Johns Hopkins University, Baltimore, Maryland 21218, USA
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23
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Mungan M, Sastry S. Metastability as a Mechanism for Yielding in Amorphous Solids under Cyclic Shear. PHYSICAL REVIEW LETTERS 2021; 127:248002. [PMID: 34951789 DOI: 10.1103/physrevlett.127.248002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2021] [Revised: 09/12/2021] [Accepted: 11/16/2021] [Indexed: 06/14/2023]
Abstract
We consider the yielding behavior of amorphous solids under cyclic shear deformation and show that it can be mapped into a random walk in a confining potential with an absorbing boundary. The resulting dynamics is governed by the first passage time into the absorbing state and suffices to capture the essential qualitative features recently observed in atomistic simulations of amorphous solids. Our results provide insight into the mechanism underlying yielding and its robustness. When the possibility of activated escape from absorbing states is added, it leads to a unique determination of a threshold energy and yield strain, suggesting thereby an appealing approach to understanding fatigue failure.
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Affiliation(s)
- Muhittin Mungan
- Institut für angewandte Mathematik, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany
| | - Srikanth Sastry
- Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkar Campus, 560064 Bengaluru, India
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24
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Lindeman CW, Nagel SR. Multiple memory formation in glassy landscapes. SCIENCE ADVANCES 2021; 7:eabg7133. [PMID: 34380622 PMCID: PMC8357226 DOI: 10.1126/sciadv.abg7133] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2021] [Accepted: 06/28/2021] [Indexed: 05/06/2023]
Abstract
Cyclically sheared jammed packings form memories of the shear amplitude at which they were trained by falling into periodic orbits where each particle returns to the identical position in subsequent cycles. While simple models that treat clusters of rearranging particles as isolated two-state systems offer insight into this memory formation, they fail to account for the long training times and multiperiod orbits observed in simulated sheared packings. We show that adding interactions between rearranging clusters overcomes these deficiencies. In addition, interactions allow simultaneous encoding of multiple memories, which would not have been possible otherwise. These memories are different in an essential way from those found in other systems, such as multiple transient memories observed in sheared suspensions, and contain information about the strength of the interactions.
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Affiliation(s)
- Chloe W Lindeman
- Department of Physics and The James Franck and Enrico Fermi Institutes, University of Chicago, Chicago, IL 60637, USA.
| | - Sidney R Nagel
- Department of Physics and The James Franck and Enrico Fermi Institutes, University of Chicago, Chicago, IL 60637, USA
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25
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Keim NC, Paulsen JD. Multiperiodic orbits from interacting soft spots in cyclically sheared amorphous solids. SCIENCE ADVANCES 2021; 7:7/33/eabg7685. [PMID: 34380623 PMCID: PMC8357233 DOI: 10.1126/sciadv.abg7685] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2021] [Accepted: 06/03/2021] [Indexed: 05/06/2023]
Abstract
When an amorphous solid is deformed cyclically, it may reach a steady state in which the paths of constituent particles trace out closed loops that repeat in each driving cycle. A remarkable variant has been noticed in simulations where the period of particle motions is a multiple of the period of driving, but the reasons for this behavior have remained unclear. Motivated by mesoscopic features of displacement fields in experiments on jammed solids, we propose and analyze a simple model of interacting soft spots-locations where particles rearrange under stress and that resemble two-level systems with hysteresis. We show that multiperiodic behavior can arise among just three or more soft spots that interact with each other, but in all cases it requires frustrated interactions, illuminating this otherwise elusive type of interaction. We suggest directions for seeking this signature of frustration in experiments and for achieving it in designed systems.
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Affiliation(s)
- Nathan C Keim
- Department of Physics, Pennsylvania State University, University Park, PA 16802, USA.
- Department of Physics, California Polytechnic State University, San Luis Obispo, CA 93407, USA
| | - Joseph D Paulsen
- Department of Physics, Syracuse University, Syracuse, NY 13244, USA.
- BioInspired Syracuse: Institute for Material and Living Systems, Syracuse University, Syracuse, NY 13244, USA
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26
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Xu H, Andresen JC, Regev I. Yielding in an amorphous solid subject to constant stress at finite temperatures. Phys Rev E 2021; 103:052604. [PMID: 34134346 DOI: 10.1103/physreve.103.052604] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2020] [Accepted: 04/22/2021] [Indexed: 11/07/2022]
Abstract
Understanding the nature of the yield transition is a long-standing problem in the physics of amorphous solids. Here we use molecular dynamics simulations to study the response of amorphous solids to constant stresses at finite temperatures. We compare amorphous solids that are prepared using fast and slow quenches and show that for thermal systems, the steady-state velocity exhibits a continuous transition from very slow creep to a finite strain rate as a function of the stress. This behavior is observed for both well-annealed and poorly annealed systems. However, the transient dynamics is different in the latter and involves overcoming an energy barrier. Due to the different simulation protocol, the strain rate as a function of stress and temperature follows a scaling relation that is different from the ones that are shown for systems where the strain is controlled. Collapsing the data using this scaling relation allows us to calculate critical exponents for the dynamics close to yield, including an exponent for thermal rounding. We also demonstrate that strain slips due to avalanche events above yield follow standard scaling relations and we extract critical exponents that are comparable to the ones obtained in previous studies that performed simulations of both molecular dynamics and elastoplastic models using strain-rate control.
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Affiliation(s)
- Haiyan Xu
- Alexandre Yersin Department of Solar Energy and Environmental Physics, Jacob Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus 84990, Israel
| | - Juan Carlos Andresen
- Department of Physics, Ben Gurion University of the Negev, Beer Sheva 84105, Israel
| | - Ido Regev
- Alexandre Yersin Department of Solar Energy and Environmental Physics, Jacob Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus 84990, Israel
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27
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Regev I, Attia I, Dahmen K, Sastry S, Mungan M. Topology of the energy landscape of sheared amorphous solids and the irreversibility transition. Phys Rev E 2021; 103:062614. [PMID: 34271642 DOI: 10.1103/physreve.103.062614] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2021] [Accepted: 06/03/2021] [Indexed: 06/13/2023]
Abstract
Recent experiments and simulations of amorphous solids plastically deformed by an oscillatory drive have found a surprising behavior-for small strain amplitudes the dynamics can be reversible, which is contrary to the usual notion of plasticity as an irreversible form of deformation. This reversibility allows the system to reach limit cycles in which plastic events repeat indefinitely under the oscillatory drive. It was also found that reaching reversible limit cycles can take a large number of driving cycles and it was surmised that the plastic events encountered during the transient period are not encountered again and are thus irreversible. Using a graph representation of the stable configurations of the system and the plastic events connecting them, we show that the notion of reversibility in these systems is more subtle. We find that reversible plastic events are abundant and that a large portion of the plastic events encountered during the transient period are actually reversible in the sense that they can be part of a reversible deformation path. More specifically, we observe that the transition graph can be decomposed into clusters of configurations that are connected by reversible transitions. These clusters are the strongly connected components of the transition graph and their sizes turn out to be power-law distributed. The largest of these are grouped in regions of reversibility, which in turn are confined by regions of irreversibility whose number proliferates at larger strains. Our results provide an explanation for the irreversibility transition-the divergence of the transient period at a critical forcing amplitude. The long transients result from transition between clusters of reversibility in a search for a cluster large enough to contain a limit cycle of a specific amplitude. For large enough amplitudes, the search time becomes very large, since the sizes of the limit cycles become incompatible with the sizes of the regions of reversibility.
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Affiliation(s)
- Ido Regev
- Department of Solar Energy and Environmental Physics, Jacob Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus 84990, Israel
| | - Ido Attia
- Jacob Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus 84990, Israel
| | - Karin Dahmen
- Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801, USA
| | - Srikanth Sastry
- Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkar Campus, 560064 Bengaluru, India
| | - Muhittin Mungan
- Institut für angewandte Mathematik, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany
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28
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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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29
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Otsuki M, Hayakawa H. Shear modulus and reversible particle trajectories of frictional granular materials under oscillatory shear. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:70. [PMID: 34014409 DOI: 10.1140/epje/s10189-021-00075-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2021] [Accepted: 05/05/2021] [Indexed: 06/12/2023]
Abstract
In this study, we numerically investigated the mechanical responses and trajectories of frictional granular particles under oscillatory shear in the reversible phase where particle trajectories form closed loops below the yielding point. When the friction coefficient is small, the storage modulus exhibits softening, and the loss modulus remains finite in the quasi-static limit. As the friction coefficient increases, the softening and residual loss modulus are suppressed. The storage and loss moduli satisfy scaling laws if they are plotted as functions of the areas of the loop trajectories divided by the strain amplitude and diameter of grains, at least for small values of the areas.
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Affiliation(s)
- Michio Otsuki
- Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka, 560-8531, Japan.
| | - Hisao Hayakawa
- Yukawa Institute for Theoretical Physics, Kyoto University, Sakyo-ku, Kyoto, 606-8502, Japan
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30
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Teich EG, Galloway KL, Arratia PE, Bassett DS. Crystalline shielding mitigates structural rearrangement and localizes memory in jammed systems under oscillatory shear. SCIENCE ADVANCES 2021; 7:7/20/eabe3392. [PMID: 33980482 PMCID: PMC8115929 DOI: 10.1126/sciadv.abe3392] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2020] [Accepted: 03/23/2021] [Indexed: 05/06/2023]
Abstract
The nature of yield in amorphous materials under stress has yet to be fully elucidated. In particular, understanding how microscopic rearrangement gives rise to macroscopic structural and rheological signatures in disordered systems is vital for the prediction and characterization of yield and the study of how memory is stored in disordered materials. Here, we investigate the evolution of local structural homogeneity on an individual particle level in amorphous jammed two-dimensional (athermal) systems under oscillatory shear and relate this evolution to rearrangement, memory, and macroscale rheological measurements. We define the structural metric crystalline shielding, and show that it is predictive of rearrangement propensity and structural volatility of individual particles under shear. We use this metric to identify localized regions of the system in which the material's memory of its preparation is preserved. Our results contribute to a growing understanding of how local structure relates to dynamic response and memory in disordered systems.
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Affiliation(s)
- Erin G Teich
- Department of Bioengineering, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - K Lawrence Galloway
- Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Paulo E Arratia
- Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104, USA
- Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Danielle S Bassett
- Department of Bioengineering, University of Pennsylvania, Philadelphia, PA 19104, USA.
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104, USA
- Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA
- Santa Fe Institute, Santa Fe, NM 87501, USA
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31
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Reichhardt C, Reichhardt CJO. Directional clogging and phase separation for disk flow through periodic and diluted obstacle arrays. SOFT MATTER 2021; 17:1548-1557. [PMID: 33331385 DOI: 10.1039/d0sm01714k] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
We model collective disk flow though a square array of obstacles as the flow direction is changed relative to the symmetry directions of the array. At lower disk densities there is no clogging for any driving direction, but as the disk density increases, the average disk velocity decreases and develops a drive angle dependence. For certain driving angles, the flow is reduced or drops to zero when the system forms a heterogeneous clogged state consisting of high density clogged regions coexisting with empty regions. The clogged states are fragile and can be unclogged by changing the driving angle. For large obstacle sizes, we find a uniform clogged state that is distinct from the collective clogging regime. Within the clogged phases, depinning transitions can occur as a function of increasing driving force, with intermittent motion appearing just above the depinning threshold. The clogging is robust against the random removal or dilution of the obstacle sites, and the disks are able to form system-spanning clogged clusters even under increasing dilution. If the dilution becomes too large, however, the clogging behavior is lost.
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Affiliation(s)
- C Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
| | - C J O Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
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32
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Basak S, Dahmen KA, Carlson EW. Period multiplication cascade at the order-by-disorder transition in uniaxial random field XY magnets. Nat Commun 2020; 11:4665. [PMID: 32938909 PMCID: PMC7495492 DOI: 10.1038/s41467-020-18270-6] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2019] [Accepted: 08/07/2020] [Indexed: 11/09/2022] Open
Abstract
Uniaxial random field disorder induces a spontaneous transverse magnetization in the XY model. Adding a rotating driving field, we find a critical point attached to the number of driving cycles needed to complete a limit cycle, the first discovery of this phenomenon in a magnetic system. Near the critical drive, time crystal behavior emerges, in which the period of the limit cycles becomes an integer n > 1 multiple of the driving period. The period n can be engineered via specific disorder patterns. Because n generically increases with system size, the resulting period multiplication cascade is reminiscent of that occurring in amorphous solids subject to oscillatory shear near the onset of plastic deformation, and of the period bifurcation cascade near the onset of chaos in nonlinear systems, suggesting it is part of a larger class of phenomena in transitions of dynamical systems. Applications include magnets, electron nematics, and quantum gases.
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Affiliation(s)
- S Basak
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, 47907, USA.,Purdue Quantum Science and Engineering Institute, West Lafayette, IN, 47907, USA
| | - K A Dahmen
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA
| | - E W Carlson
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, 47907, USA. .,Purdue Quantum Science and Engineering Institute, West Lafayette, IN, 47907, USA. .,LPEM, ESPCI Paris, PSL Research University; CNRS; Sorbonne Université, 75005, Paris, France.
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33
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Reichhardt C, Reichhardt CJO. Jamming, fragility and pinning phenomena in superconducting vortex systems. Sci Rep 2020; 10:11625. [PMID: 32669592 PMCID: PMC7363902 DOI: 10.1038/s41598-020-68417-0] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2020] [Accepted: 06/03/2020] [Indexed: 11/09/2022] Open
Abstract
We examine driven superconducting vortices interacting with quenched disorder under a sequence of perpendicular drive pulses. As a function of disorder strength, we find four types of behavior distinguished by the presence or absence of memory effects. The fragile and jammed states exhibit memory, while the elastic and pinning dominated regimes do not. In the fragile regime, the system organizes into a pinned state during the first pulse, flows during the second perpendicular pulse, and then returns to a pinned state during the third pulse which is parallel to the first pulse. This behavior is the hallmark of the fragility proposed for jamming in particulate matter. For stronger disorder, we observe a robust jamming state with memory where the system reaches a pinned or reduced flow state during the perpendicular drive pulse, similar to the shear jamming of granular systems. We show signatures of the different states in the spatial vortex configurations, and find that memory effects arise from coexisting elastic and pinned components of the vortex assembly. The sequential perpendicular driving protocol we propose for distinguishing fragile, jammed, and pinned phases should be general to the broader class of driven interacting particles in the presence of quenched disorder.
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Affiliation(s)
- Charles Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
| | - Cynthia J O Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA.
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34
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Terzi MM, Mungan M. State transition graph of the Preisach model and the role of return-point memory. Phys Rev E 2020; 102:012122. [PMID: 32795063 DOI: 10.1103/physreve.102.012122] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2020] [Accepted: 06/22/2020] [Indexed: 06/11/2023]
Abstract
The Preisach model has been useful as a null model for understanding memory formation in periodically driven disordered systems. In amorphous solids, for example, the athermal response to shear is due to localized plastic events (soft spots). As shown recently by Mungan et al. [Phys. Rev. Lett. 123, 178002 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.178002], the plastic response to applied shear can be rigorously described in terms of a directed network whose transitions correspond to one or more soft spots changing states. The topology of this graph depends on the interactions between soft spots and when such interactions are negligible, the resulting description becomes that of the Preisach model. A first step in linking transition graph topology with the underlying soft-spot interactions is therefore to determine the structure of such graphs in the absence of interactions. Here we perform a detailed analysis of the transition graph of the Preisach model. We highlight the important role played by return-point memory in organizing the graph into a hierarchy of loops and subloops. Our analysis reveals that the topology of a large portion of this graph is actually not governed by the values of the switching fields that describe the hysteretic behavior of the individual elements but by a coarser parameter, a permutation ρ which prescribes the sequence in which the individual hysteretic elements change their states as the main hysteresis loop is traversed. This in turn allows us to derive combinatorial properties, such as the number of major loops in the transition graph as well as the number of states |R| constituting the main hysteresis loop and its nested subloops. We find that |R| is equal to the number of increasing subsequences contained in the permutation ρ.
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Affiliation(s)
- M Mert Terzi
- Université Paris-Saclay, CNRS, LPTMS, 91405 Orsay, France
| | - Muhittin Mungan
- Institut für Angewandte Mathematik, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany
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35
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Yeh WT, Ozawa M, Miyazaki K, Kawasaki T, Berthier L. Glass Stability Changes the Nature of Yielding under Oscillatory Shear. PHYSICAL REVIEW LETTERS 2020; 124:225502. [PMID: 32567904 DOI: 10.1103/physrevlett.124.225502] [Citation(s) in RCA: 39] [Impact Index Per Article: 9.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/28/2019] [Accepted: 05/18/2020] [Indexed: 06/11/2023]
Abstract
We perform molecular dynamics simulations to investigate the effect of a glass preparation on its yielding transition under oscillatory shear. We use swap Monte Carlo to investigate a broad range of glass stabilities from poorly annealed to highly stable systems. We observe a qualitative change in the nature of yielding, which evolves from ductile to brittle as glass stability increases. Our results disentangle the relative role of mechanical and thermal annealing on the mechanical properties of amorphous solids, which is relevant for various experimental situations from the rheology of soft materials to fatigue failure in metallic glasses.
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Affiliation(s)
- Wei-Ting Yeh
- Department of Physics, Nagoya University, 464-8602 Nagoya, Japan
| | - Misaki Ozawa
- Laboratoire Charles Coulomb (L2C), Université de Montpellier, CNRS, 34095 Montpellier, France
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université Paris Sciences et Lettres, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | | | - Takeshi Kawasaki
- Department of Physics, Nagoya University, 464-8602 Nagoya, Japan
| | - Ludovic Berthier
- Laboratoire Charles Coulomb (L2C), Université de Montpellier, CNRS, 34095 Montpellier, France
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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36
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Galloway KL, Jerolmack DJ, Arratia PE. Quantification of plasticity via particle dynamics above and below yield in a 2D jammed suspension. SOFT MATTER 2020; 16:4373-4382. [PMID: 32253419 DOI: 10.1039/c9sm02482d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
The yield transition of amorphous materials is characterized by a swift increase of energy dissipation. The connection between particle dynamics, dissipation, and overall material rheology, however, has still not been elucidated. Here, we take a new approach relating trajectories to yielding, using a custom built interfacial stress rheometer, which allows for measurement of shear moduli (G',G'') of a dense athermal suspension's microstructure while simultaneously tracking particle trajectories undergoing cyclic shear. We find an increase in total area traced by particle trajectories as the system is stressed well below to well above yield. Trajectories may be placed into three categories: reversibly elastic paths; reversibly plastic paths, associated with smooth limit cycles; and irreversibly plastic paths, in which particles do not return to their original position. We find that above yield, reversibly plastic trajectories are predominantly found near to the shearing surface, whereas reversibly elastic paths are more prominent near the stationary wall. This spatial transition between particles acting as liquids to those acting as solids is characteristic of a 'melting front', which is observed to shift closer to the wall with increasing strain. We introduce a non-dimensional measure of plastic dissipation based on particle trajectories that scales linearly with strain amplitude both above and below yield, and that is unity at the rheological yield point. Surprisingly, this relation collapses for three systems of varying degrees of disorder.
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Affiliation(s)
- K Lawrence Galloway
- Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104, USA. @seas.upenn.edu
| | - Douglas J Jerolmack
- Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104, USA. @seas.upenn.edu and Department of Earth and Environmental Science, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Paulo E Arratia
- Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104, USA. @seas.upenn.edu
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37
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Das P, Vinutha HA, Sastry S. Unified phase diagram of reversible-irreversible, jamming, and yielding transitions in cyclically sheared soft-sphere packings. Proc Natl Acad Sci U S A 2020; 117:10203-10209. [PMID: 32341154 PMCID: PMC7229761 DOI: 10.1073/pnas.1912482117] [Citation(s) in RCA: 26] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Self-organization, and transitions from reversible to irreversible behavior, of interacting particle assemblies driven by externally imposed stresses or deformation is of interest in comprehending diverse phenomena in soft matter. They have been investigated in a wide range of systems, such as colloidal suspensions, glasses, and granular matter. In different density and driving regimes, such behavior is related to yielding of amorphous solids, jamming, memory formation, etc. How these phenomena are related to each other has not, however, been much studied. In order to obtain a unified view of the different regimes of behavior, and transitions between them, we investigate computationally the response of soft-sphere assemblies to athermal cyclic-shear deformation over a wide range of densities and amplitudes of shear deformation. Cyclic-shear deformation induces transitions from reversible to irreversible behavior in both unjammed and jammed soft-sphere packings. Well above the minimum isotropic jamming density ([Formula: see text]), this transition corresponds to yielding. In the vicinity of the jamming point, up to a higher-density limit, we designate [Formula: see text], an unjammed phase emerges between a localized, absorbing phase and a diffusive, irreversible, phase. The emergence of the unjammed phase signals the shifting of the jamming point to higher densities as a result of annealing and opens a window where shear jamming becomes possible for frictionless packings. Below [Formula: see text], two distinct localized states, termed point- and loop-reversible, are observed. We characterize in detail the different regimes and transitions between them and obtain a unified density-shear amplitude phase diagram.
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Affiliation(s)
- Pallabi Das
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Bengaluru 560064, India
| | - H A Vinutha
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Bengaluru 560064, India
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- Department of Chemistry, University of Cambridge, Cambridge CB21EW, United Kingdom
| | - Srikanth Sastry
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Bengaluru 560064, India;
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38
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Szulc A, Gat O, Regev I. Forced deterministic dynamics on a random energy landscape: Implications for the physics of amorphous solids. Phys Rev E 2020; 101:052616. [PMID: 32575307 DOI: 10.1103/physreve.101.052616] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/06/2020] [Accepted: 04/21/2020] [Indexed: 06/11/2023]
Abstract
The dynamics of supercooled liquids and plastically deformed amorphous solids is known to be dominated by the structure of their rough energy landscapes. Recent experiments and simulations on amorphous solids subjected to oscillatory shear at athermal conditions have shown that for small strain amplitudes these systems reach limit cycles of different periodicities after a transient. However, for larger strain amplitudes the transients become longer and for strain amplitudes exceeding a critical value the system reaches a diffusive steady state. This behavior cannot be explained using the current mean-field models of amorphous plasticity. Here we show that this phenomenology can be described and explained using a simple model of forced dynamics on a multidimensional random energy landscape. In this model, the existence of limit cycles can be ascribed to confinement of the dynamics to a small part of the energy landscape which leads to self-intersection of state-space trajectories and the transition to the diffusive regime for larger forcing amplitudes occurs when the forcing overcomes this confinement.
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Affiliation(s)
- Asaf Szulc
- Department of Physics, Ben Gurion University of the Negev, Beer Sheva 84105, Israel
| | - Omri Gat
- Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Ido Regev
- The Jacob Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus 84990, Israel
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39
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Mo R, Liao Q, Xu N. Rheological similarities between dense self-propelled and sheared particulate systems. SOFT MATTER 2020; 16:3642-3648. [PMID: 32219271 DOI: 10.1039/d0sm00101e] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Different from previous modeling of self-propelled particles, we develop a method to propel particles with a constant average velocity instead of a constant force. This constant propulsion velocity (CPV) approach is validated by its agreement with the conventional constant propulsion force (CPF) approach in the flowing regime. However, the CPV approach shows its advantage of accessing quasistatic flows of yield stress fluids with a vanishing propulsion velocity, while the CPF approach is usually unable to because of finite system size. Taking this advantage, we realize cyclic self-propulsion and study the evolution of the propulsion force with the propelled particle displacement, both in the quasistatic flow regime. By mapping the shear stress and shear rate to the propulsion force and propulsion velocity, we find similar rheological behaviors of self-propelled systems to sheared systems, including the yield force gap between the CPF and CPV approaches, propulsion force overshoot, reversible-irreversible transition under cyclic propulsion, and propulsion bands in plastic flows. These similarities suggest underlying connections between self-propulsion and shear, although they act on systems in different ways.
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Affiliation(s)
- Ruoyang Mo
- Hefei National Laboratory for Physical Sciences at the Microscale, CAS Key Laboratory of Microscale Magnetic Resonance and Department of Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China.
| | - Qinyi Liao
- Hefei National Laboratory for Physical Sciences at the Microscale, CAS Key Laboratory of Microscale Magnetic Resonance and Department of Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China.
| | - Ning Xu
- Hefei National Laboratory for Physical Sciences at the Microscale, CAS Key Laboratory of Microscale Magnetic Resonance and Department of Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China.
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40
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Ness C, Cates ME. Absorbing-State Transitions in Granular Materials Close to Jamming. PHYSICAL REVIEW LETTERS 2020; 124:088004. [PMID: 32167320 DOI: 10.1103/physrevlett.124.088004] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/27/2019] [Accepted: 01/27/2020] [Indexed: 06/10/2023]
Abstract
We consider a model for driven particulate matter in which absorbing states can be reached both by particle isolation and by particle caging. The model predicts a nonequilibrium phase diagram in which analogs of hydrodynamic and elastic reversibility emerge at low and high volume fractions respectively, partially separated by a diffusive, nonabsorbing region. We thus find a single phase boundary that spans the onset of chaos in sheared suspensions to the onset of yielding in jammed packings. This boundary has the properties of a nonequilibrium second order phase transition, leading us to write a Manna-like mean field description that captures the model predictions. Dependent on contact details, jamming marks either a direct transition between the two absorbing states, or occurs within the diffusive region.
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Affiliation(s)
- Christopher Ness
- Department of Chemical Engineering and Biotechnology, University of Cambridge, Cambridge CB3 0AS, United Kingdom
- School of Engineering, University of Edinburgh, Edinburgh EH9 3FB, United Kingdom
| | - Michael E Cates
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, United Kingdom
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41
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Abstract
The effect of periodic shear on strain localization in disordered solids is investigated using molecular dynamics simulations. We consider a binary mixture of one million atoms annealed to a low temperature with different cooling rates and then subjected to oscillatory shear deformation with a strain amplitude slightly above the critical value. It is found that the yielding transition occurs during one cycle but the accumulation of irreversible displacements and initiation of the shear band proceed over larger number of cycles for more slowly annealed glasses. The spatial distribution and correlation function of nonaffine displacements reveal that their collective dynamics changes from homogeneously distributed small clusters to a system-spanning shear band. The analysis of spatially averaged profiles of nonaffine displacements indicates that the location of a shear band in periodically loaded glasses can be identified at least several cycles before yielding. These insights are important for the development of novel processing methods and prediction of the fatigue lifetime of metallic glasses.
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42
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Schinasi-Lemberg E, Regev I. Annealing and rejuvenation in a two-dimensional model amorphous solid under oscillatory shear. Phys Rev E 2020; 101:012603. [PMID: 32069668 DOI: 10.1103/physreve.101.012603] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2019] [Indexed: 06/10/2023]
Abstract
We study the annealing and rejuvenation behavior of a two-dimensional amorphous solid model under oscillatory shear. We show that, depending on the cooling protocol used to create the initial configuration, the mean potential energy can either decrease or increase under subyield oscillatory shear. For post-yield oscillatory shear, the mean potential energy increases and is independent on the initial conditions. We explain this behavior by modeling the dynamics using a simple model of forced dynamics on a random energy landscape and show that the model reproduces the qualitative behavior of the mean potential energy and mean-square displacement observed in the particle based simulations. This suggests that some important aspects of the dynamics of amorphous solids can be understood by studying the properties of random energy landscapes and without explicitly taking into account the complex real-space interactions which are involved in plastic deformation.
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Affiliation(s)
- Eden Schinasi-Lemberg
- The Jacob Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus 84990, Israel
| | - Ido Regev
- The Jacob Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus 84990, Israel
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43
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Bera PK, Kandar AK, Krishnaswamy R, Sood AK. Experimental signatures of a nonequilibrium phase transition near the crossover point of a Langmuir monolayer. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:504004. [PMID: 31491774 DOI: 10.1088/1361-648x/ab4235] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We investigate the response of the two-dimensional (2D) continuous non-particulate film of surfactant sorbitan tristearate confined at the air-water interface under oscillatory shear deformation. The time dependence of various rheological parameters show critical-like behavior at a value of strain amplitude close to the crossover point of elastic ([Formula: see text]) and viscous ([Formula: see text]) shear moduli. Imposing oscillatory shear of different strain amplitudes ([Formula: see text]) above and below the crossover strain amplitude ([Formula: see text]) over a large number of cycles, we quantify the temporal dependence of interfacial viscous modulus, phase angle ([Formula: see text]) as well as higher harmonic components of stress. The number of shear cycles ([Formula: see text]) required for these quantities to reach the steady state value diverges near [Formula: see text]. The steady state values of the third harmonic ([Formula: see text]) show order parameter like behavior indicating the importance of higher order harmonics near the nonequilibrium transition. We further show that the energy dissipation per cycle per unit volume has a marked change near [Formula: see text], consistent with continuum level nonequilibrium shear-transformation-zone model of amorphous viscoplasticity.
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Affiliation(s)
- P K Bera
- Department of Physics, Indian Institute of Science, Bangalore, 560012, India
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44
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Critical behavior near the reversible-irreversible transition in periodically driven vortices under random local shear. Sci Rep 2019; 9:16447. [PMID: 31712623 PMCID: PMC6848189 DOI: 10.1038/s41598-019-51060-9] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2019] [Accepted: 09/24/2019] [Indexed: 11/11/2022] Open
Abstract
When many-particle (vortex) assemblies with disordered distribution are subjected to a periodic shear with a small amplitude \documentclass[12pt]{minimal}
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\begin{document}$${\boldsymbol{d}}$$\end{document}d, the particles gradually self-organize to avoid next collisions and transform into an organized configuration. We can detect it from the time-dependent voltage \documentclass[12pt]{minimal}
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\begin{document}$${\boldsymbol{V}}{\boldsymbol{(}}{\boldsymbol{t}}{\boldsymbol{)}}$$\end{document}V(t) (average velocity) that increases towards a steady-state value. For small \documentclass[12pt]{minimal}
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\begin{document}$${\boldsymbol{d}}$$\end{document}d, the particles settle into a reversible state where all the particles return to their initial position after each shear cycle, while they reach an irreversible state for \documentclass[12pt]{minimal}
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\begin{document}$${\boldsymbol{d}}$$\end{document}d above a threshold \documentclass[12pt]{minimal}
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\begin{document}$${{\boldsymbol{d}}}_{{\boldsymbol{c}}}$$\end{document}dc. Here, we investigate the general phenomenon of a reversible-irreversible transition (RIT) using periodically driven vortices in a strip-shaped amorphous film with random pinning that causes local shear, as a function of \documentclass[12pt]{minimal}
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\begin{document}$${\boldsymbol{V}}{\boldsymbol{(}}{\boldsymbol{t}}{\boldsymbol{)}}$$\end{document}V(t), we observe a critical behavior of RIT, not only on the irreversible side, but also on the reversible side of the transition, which is the first under random local shear. The relaxation time \documentclass[12pt]{minimal}
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\begin{document}$${\boldsymbol{\tau }}{\boldsymbol{(}}{\boldsymbol{d}}{\boldsymbol{)}}$$\end{document}τ(d) to reach either the reversible or irreversible state shows a power-law divergence at \documentclass[12pt]{minimal}
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\begin{document}$${{\boldsymbol{d}}}_{{\boldsymbol{c}}}$$\end{document}dc. The critical exponent is determined with higher accuracy and is, within errors, in agreement with the value expected for an absorbing phase transition in the two-dimensional directed-percolation universality class. As \documentclass[12pt]{minimal}
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\begin{document}$${\boldsymbol{d}}$$\end{document}d is decreased down to the intervortex spacing in the reversible regime, \documentclass[12pt]{minimal}
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\begin{document}$${\boldsymbol{\tau }}{\boldsymbol{(}}{\boldsymbol{d}}{\boldsymbol{)}}$$\end{document}τ(d) deviates downward from the power-law relation, reflecting the suppression of intervortex collisions. We also suggest the possibility of a narrow smectic-flow regime, which is predicted to intervene between fully reversible and irreversible flow.
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45
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Mungan M, Sastry S, Dahmen K, Regev I. Networks and Hierarchies: How Amorphous Materials Learn to Remember. PHYSICAL REVIEW LETTERS 2019; 123:178002. [PMID: 31702267 DOI: 10.1103/physrevlett.123.178002] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/22/2019] [Indexed: 06/10/2023]
Abstract
We consider the slow and athermal deformations of amorphous solids and show how the ensuing sequence of discrete plastic rearrangements can be mapped onto a directed network. The network topology reveals a set of highly connected regions joined by occasional one-way transitions. The highly connected regions include hierarchically organized hysteresis cycles and subcycles. At small to moderate strains this organization leads to near-perfect return point memory. The transitions in the network can be traced back to localized particle rearrangements (soft spots) that interact via Eshelby-type deformation fields. By linking topology to dynamics, the network representations provide new insight into the mechanisms that lead to reversible and irreversible behavior in amorphous solids.
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Affiliation(s)
- Muhittin Mungan
- Institut für angewandte Mathematik, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany
| | - Srikanth Sastry
- Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkar Campus, 560064 Bengaluru, India
| | - Karin Dahmen
- Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801, USA
| | - Ido Regev
- Jacob Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus 84990, Israel
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46
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Nagasawa K, Miyazaki K, Kawasaki T. Classification of the reversible-irreversible transitions in particle trajectories across the jamming transition point. SOFT MATTER 2019; 15:7557-7566. [PMID: 31528879 DOI: 10.1039/c9sm01488h] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
The reversible-irreversible (RI) transition of particle trajectories in athermal colloidal suspensions under cyclic shear deformation is an archetypal nonequilibrium phase transition which has attracted much attention recently. Most studies of the RI transitions have focused on either dilute limit or very high densities well above the jamming transition point. The transition between the two limiting cases is largely unexplored. In this paper, we study the RI transition of athermal frictionless colloidal particles over a wide range of densities, with emphasis on the region below φJ, by using oscillatory sheared molecular dynamics simulation. We reveal that the nature of the RI transitions in the intermediate densities is very rich. As demonstrated by the previous work by Schreck et al. [Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2013, 88, 052205], there exist the point-reversible and the loop-reversible phases depending on the density and the shear strain amplitude. We find that, between the two reversible phases, a quasi-irreversible phase where the particles' trajectories are highly non-affine and diffusive. The averaged number of contacts of particles is found to characterize the phase boundaries. We also find that the system undergoes the yielding transition below but in the vicinity of φJ when the strain with a small but finite strain rate is applied. This yielding transition line matches with the RI transition line separating the loop-reversible from the irreversible phases. Surprisingly, the nonlinear rheological response called "softening" has been observed even below φJ. These findings imply that geometrical properties encoded in the sheared configurations control the dynamical transitions.
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Affiliation(s)
- Kentaro Nagasawa
- Department of Physics, Nagoya University, Nagoya 464-8602, Japan. and Department of Physics, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan
| | | | - Takeshi Kawasaki
- Department of Physics, Nagoya University, Nagoya 464-8602, Japan.
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47
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Abstract
Disordered magnets, martensitic mixed crystals, and glassy solids can be irreversibly deformed by subjecting them to external deformation. The deformation produces a smooth, reversible response punctuated by abrupt relaxation "glitches." Under appropriate repeated forward and reverse deformation producing multiple glitches, a strict repetition of a single sequence of microscopic configurations often emerges. We exhibit these features by describing the evolution of the system configuration from glitch to glitch as a mapping of N states into one another. A map U controls forward deformation; a second map D controls reverse deformation. Iteration of a given sequence of forward and reverse maps, e.g., DDDDUUUU necessarily produces a convergence to a fixed cyclic repetition of states covering multiple glitches. The repetition may have a period of more than one strain cycle, as recently observed in simulations. Using numerical sampling, we characterize the convergence properties of four types of random maps implementing successive physical restrictions. The most restrictive is the much-studied Preisach model. These maps show only the most qualitative resemblance to annealing simulations. However, they suggest further properties needed for a realistic mapping scheme.
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Affiliation(s)
- Muhittin Mungan
- Institut für angewandte Mathematik, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany
| | - Thomas A Witten
- Department of Physics and James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
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48
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Mukherji S, Kandula N, Sood AK, Ganapathy R. Strength of Mechanical Memories is Maximal at the Yield Point of a Soft Glass. PHYSICAL REVIEW LETTERS 2019; 122:158001. [PMID: 31050530 DOI: 10.1103/physrevlett.122.158001] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/26/2018] [Indexed: 06/09/2023]
Abstract
We show experimentally that both single and multiple mechanical memories can be encoded in an amorphous bubble raft, a prototypical soft glass, subject to an oscillatory strain. In line with recent numerical results, we find that multiple memories can be formed sans external noise. By systematically investigating memory formation for a range of training strain amplitudes spanning yield, we find clear signatures of memory even beyond yielding. Most strikingly, the extent to which the system recollects memory is largest for training amplitudes near the yield strain and is a direct consequence of the spatial extent over which the system reorganizes during the encoding process. Our study further suggests that the evolution of force networks on training plays a decisive role in memory formation in jammed packings.
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Affiliation(s)
- Srimayee Mukherji
- Chemistry and Physics of Materials Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore 560064, India
| | - Neelima Kandula
- Chemistry and Physics of Materials Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore 560064, India
| | - A K Sood
- Department of Physics, Indian Institute of Science, Bangalore 560012, India
- International Centre for Materials Science, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore 560064, India
| | - Rajesh Ganapathy
- International Centre for Materials Science, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore 560064, India
- School of Advanced Materials, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore 560064, India
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49
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Reichhardt C, Reichhardt CJO. Reversibility, pattern formation, and edge transport in active chiral and passive disk mixtures. J Chem Phys 2019; 150:064905. [DOI: 10.1063/1.5085209] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Affiliation(s)
- C. Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - C. J. O. Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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50
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Regev I, Lookman T. Critical diffusivity in the reversibility-irreversibility transition of amorphous solids under oscillatory shear. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:045101. [PMID: 30523892 DOI: 10.1088/1361-648x/aaf1ea] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Recently it was shown that under oscillatory shear at zero temperature an amorphous solid transitions from asymptotically periodic to asymptotically diffusive steady-state at a critical maximal strain amplitude. Current understanding of the physics behind this transition is lacking. Here we show, using computer simulations, evidence that the diffusivity of the vector of coordinates of the particles comprising an amorphous solid, when subject to oscillatory shear, undergoes a second order phase transition at the reversibility-irreversibility transition point. We explain how such a transition is consistent with dissipative forced dynamics on a complex energy landscape, such as is known to exist in amorphous solids. We demonstrate that as the forcing increases, more and more state-space volume becomes accessible to the system, making it less probable for the state-space trajectory of the system to self-intersect and form a limit-cycle, which explains the slowing-down observed at the transition.
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Affiliation(s)
- Ido Regev
- Jacob Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus 84990, Israel
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