1
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Divoux T, Agoritsas E, Aime S, Barentin C, Barrat JL, Benzi R, Berthier L, Bi D, Biroli G, Bonn D, Bourrianne P, Bouzid M, Del Gado E, Delanoë-Ayari H, Farain K, Fielding S, Fuchs M, van der Gucht J, Henkes S, Jalaal M, Joshi YM, Lemaître A, Leheny RL, Manneville S, Martens K, Poon WCK, Popović M, Procaccia I, Ramos L, Richards JA, Rogers S, Rossi S, Sbragaglia M, Tarjus G, Toschi F, Trappe V, Vermant J, Wyart M, Zamponi F, Zare D. Ductile-to-brittle transition and yielding in soft amorphous materials: perspectives and open questions. SOFT MATTER 2024; 20:6868-6888. [PMID: 39028363 DOI: 10.1039/d3sm01740k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/20/2024]
Abstract
Soft amorphous materials are viscoelastic solids ubiquitously found around us, from clays and cementitious pastes to emulsions and physical gels encountered in food or biomedical engineering. Under an external deformation, these materials undergo a noteworthy transition from a solid to a liquid state that reshapes the material microstructure. This yielding transition was the main theme of a workshop held from January 9 to 13, 2023 at the Lorentz Center in Leiden. The manuscript presented here offers a critical perspective on the subject, synthesizing insights from the various brainstorming sessions and informal discussions that unfolded during this week of vibrant exchange of ideas. The result of these exchanges takes the form of a series of open questions that represent outstanding experimental, numerical, and theoretical challenges to be tackled in the near future.
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Affiliation(s)
- Thibaut Divoux
- ENSL, CNRS, Laboratoire de physique, F-69342 Lyon, France.
| | - Elisabeth Agoritsas
- Department of Quantum Matter Physics (DQMP), University of Geneva, Quai Ernest-Ansermet 24, CH-1211 Geneva, Switzerland
| | - Stefano Aime
- Molecular, Macromolecular Chemistry, and Materials, ESPCI Paris, Paris, France
| | - Catherine Barentin
- Univ. de Lyon, Université Claude Bernard Lyon 1, CNRS, Institut Lumière Matière, F-69622 Villeurbanne, France
| | - Jean-Louis Barrat
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | - Roberto Benzi
- Department of Physics & INFN, Tor Vergata University of Rome, Via della Ricerca Scientifica 1, 00133, Rome, Italy
| | - Ludovic Berthier
- Laboratoire Charles Coulomb (L2C), Université Montpellier, CNRS, Montpellier, France
| | - Dapeng Bi
- Department of Physics, Northeastern University, Boston, MA 02115, USA
| | - Giulio Biroli
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | - Daniel Bonn
- Soft Matter Group, van der Waals-Zeeman Institute, University of Amsterdam, Science Park 904, 1098XH Amsterdam, The Netherlands
| | - Philippe Bourrianne
- PMMH, CNRS, ESPCI Paris, Université PSL, Sorbonne Université, Université Paris Cité, Paris, France
| | - Mehdi Bouzid
- Univ. Grenoble Alpes, CNRS, Grenoble INP, 3SR, F-38000 Grenoble, France
| | - Emanuela Del Gado
- Georgetown University, Department of Physics, Institute for Soft Matter Synthesis and Metrology, Washington, DC, USA
| | - Hélène Delanoë-Ayari
- Univ. de Lyon, Université Claude Bernard Lyon 1, CNRS, Institut Lumière Matière, F-69622 Villeurbanne, France
| | - Kasra Farain
- Soft Matter Group, van der Waals-Zeeman Institute, University of Amsterdam, Science Park 904, 1098XH Amsterdam, The Netherlands
| | - Suzanne Fielding
- Department of Physics, Durham University, South Road, Durham DH1 3LE, UK
| | - Matthias Fuchs
- Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany
| | - Jasper van der Gucht
- Physical Chemistry and Soft Matter, Wageningen University & Research, Stippeneng 4, 6708WE Wageningen, The Netherlands
| | - Silke Henkes
- Lorentz Institute, Leiden University, 2300 RA Leiden, The Netherlands
| | - Maziyar Jalaal
- Institute of Physics, University of Amsterdam, Science Park 904, Amsterdam, The Netherlands
| | - Yogesh M Joshi
- Department of Chemical Engineering, Indian Institute of Technology, Kanpur 208016, Uttar Pradesh, India
| | - Anaël Lemaître
- Navier, École des Ponts, Univ Gustave Eiffel, CNRS, Marne-la-Vallée, France
| | - Robert L Leheny
- Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | | | | | - Wilson C K Poon
- SUPA and the School of Physics and Astronomy, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK
| | - Marko Popović
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str.38, 01187 Dresden, Germany
| | - Itamar Procaccia
- Dept. of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
- Sino-Europe Complex Science Center, School of Mathematics, North University of China, Shanxi, Taiyuan 030051, China
| | - Laurence Ramos
- Laboratoire Charles Coulomb (L2C), Université Montpellier, CNRS, Montpellier, France
| | - James A Richards
- SUPA and the School of Physics and Astronomy, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK
| | - Simon Rogers
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Saverio Rossi
- LPTMC, CNRS-UMR 7600, Sorbonne Université, 4 Pl. Jussieu, F-75005 Paris, France
| | - Mauro Sbragaglia
- Department of Physics & INFN, Tor Vergata University of Rome, Via della Ricerca Scientifica 1, 00133, Rome, Italy
| | - Gilles Tarjus
- LPTMC, CNRS-UMR 7600, Sorbonne Université, 4 Pl. Jussieu, F-75005 Paris, France
| | - Federico Toschi
- Department of Applied Physics and Science Education, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
- CNR-IAC, Via dei Taurini 19, 00185 Rome, Italy
| | - Véronique Trappe
- Department of Physics, University of Fribourg, Chemin du Musée 3, Fribourg 1700, Switzerland
| | - Jan Vermant
- Department of Materials, ETH Zürich, Vladimir Prelog Weg 5, 8032 Zürich, Switzerland
| | - Matthieu Wyart
- Department of Quantum Matter Physics (DQMP), University of Geneva, Quai Ernest-Ansermet 24, CH-1211 Geneva, Switzerland
| | - Francesco Zamponi
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, 00185 Rome, Italy
| | - Davoud Zare
- Fonterra Research and Development Centre, Dairy Farm Road, Fitzherbert, Palmerston North 4442, New Zealand
- Nestlé Institute of Food Sciences, Nestlé Research, Vers Chez les Blancs, Lausanne, Switzerland
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2
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Muhaxheri G, Santangelo CD. Bifurcations of inflating balloons and interacting hysterons. Phys Rev E 2024; 110:024209. [PMID: 39295065 DOI: 10.1103/physreve.110.024209] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2024] [Accepted: 07/17/2024] [Indexed: 09/21/2024]
Abstract
While many materials exhibit a complex, hysteretic response to external driving, there has been a surge of interest in how the complex dynamics of internal materials states can be understood and designed to process and store information. We consider a system of connected rubber balloons that can be described by a Preisach model of noninteracting hysterons under pressure control but for which the hysterons become coupled under volume control. We study this system by exploring the possible transition graphs, as well as by introducing a configuration space approach which tracks the volumes of each balloon. Changes in the transition graphs turn out to be related to changes in the topology of the configuration space of the balloons, providing a particularly geometric view of how transition graphs can be designed, as well as additional information on the existence of hidden metastable states. This class of systems is more general than just balloons.
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3
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Liu J, Teunisse M, Korovin G, Vermaire IR, Jin L, Bense H, van Hecke M. Controlled pathways and sequential information processing in serially coupled mechanical hysterons. Proc Natl Acad Sci U S A 2024; 121:e2308414121. [PMID: 38768343 PMCID: PMC11145188 DOI: 10.1073/pnas.2308414121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2023] [Accepted: 03/21/2024] [Indexed: 05/22/2024] Open
Abstract
The complex sequential response of frustrated materials results from the interactions between material bits called hysterons. Hence, a central challenge is to understand and control these interactions, so that materials with targeted pathways and functionalities can be realized. Here, we show that hysterons in serial configurations experience geometrically controllable antiferromagnetic-like interactions. We create hysteron-based metamaterials that leverage these interactions to realize targeted pathways, including those that break the return point memory property, characteristic of independent or weakly interacting hysterons. We uncover that the complex response to sequential driving of such strongly interacting hysteron-based materials can be described by finite state machines. We realize information processing operations such as string parsing in materia, and outline a general framework to uncover and characterize the FSMs for a given physical system. Our work provides a general strategy to understand and control hysteron interactions, and opens a broad avenue toward material-based information processing.
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Affiliation(s)
- Jingran Liu
- Huygens-Kamerlingh Onnes Lab, Leiden Institute of Physics, Universiteit Leiden, NL-2300 RALeiden, The Netherlands
- Laboratory for Multiscale Mechanics and Medical Science, State Key Lab for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi’an Jiaotong University, Xi’an710049, China
| | - Margot Teunisse
- Huygens-Kamerlingh Onnes Lab, Leiden Institute of Physics, Universiteit Leiden, NL-2300 RALeiden, The Netherlands
- AMOLF, 1098 XGAmsterdam, The Netherlands
| | - George Korovin
- Huygens-Kamerlingh Onnes Lab, Leiden Institute of Physics, Universiteit Leiden, NL-2300 RALeiden, The Netherlands
| | - Ivo R. Vermaire
- Huygens-Kamerlingh Onnes Lab, Leiden Institute of Physics, Universiteit Leiden, NL-2300 RALeiden, The Netherlands
| | - Lishuai Jin
- Huygens-Kamerlingh Onnes Lab, Leiden Institute of Physics, Universiteit Leiden, NL-2300 RALeiden, The Netherlands
- AMOLF, 1098 XGAmsterdam, The Netherlands
| | - Hadrien Bense
- AMOLF, 1098 XGAmsterdam, The Netherlands
- Nonlinear Physical Chemistry Unit, Université Libre de Bruxelles, 1050Bruxelles, Belgium
| | - Martin van Hecke
- Huygens-Kamerlingh Onnes Lab, Leiden Institute of Physics, Universiteit Leiden, NL-2300 RALeiden, The Netherlands
- AMOLF, 1098 XGAmsterdam, The Netherlands
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4
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Sirote-Katz C, Shohat D, Merrigan C, Lahini Y, Nisoli C, Shokef Y. Emergent disorder and mechanical memory in periodic metamaterials. Nat Commun 2024; 15:4008. [PMID: 38773062 PMCID: PMC11109184 DOI: 10.1038/s41467-024-47780-w] [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: 09/27/2023] [Accepted: 04/12/2024] [Indexed: 05/23/2024] Open
Abstract
Ordered mechanical systems typically have one or only a few stable rest configurations, and hence are not considered useful for encoding memory. Multistable and history-dependent responses usually emerge from quenched disorder, for example in amorphous solids or crumpled sheets. In contrast, due to geometric frustration, periodic magnetic systems can create their own disorder and espouse an extensive manifold of quasi-degenerate configurations. Inspired by the topological structure of frustrated artificial spin ices, we introduce an approach to design ordered, periodic mechanical metamaterials that exhibit an extensive set of spatially disordered states. While our design exploits the correspondence between frustration in magnetism and incompatibility in meta-mechanics, our mechanical systems encompass continuous degrees of freedom, and thus generalize their magnetic counterparts. We show how such systems exhibit non-Abelian and history-dependent responses, as their state can depend on the order in which external manipulations were applied. We demonstrate how this richness of the dynamics enables to recognize, from a static measurement of the final state, the sequence of operations that an extended system underwent. Thus, multistability and potential to perform computation emerge from geometric frustration in ordered mechanical lattices that create their own disorder.
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Affiliation(s)
- Chaviva Sirote-Katz
- Department of Biomedical Engineering, Tel Aviv University, Tel Aviv, 69978, Israel
| | - Dor Shohat
- School of Physics and Astronomy, Tel Aviv University, Tel Aviv, 69978, Israel
| | - Carl Merrigan
- School of Mechanical Engineering, Tel Aviv University, Tel Aviv, 69978, Israel
| | - Yoav Lahini
- School of Physics and Astronomy, Tel Aviv University, Tel Aviv, 69978, Israel
- Center for Physics and Chemistry of Living Systems, Tel Aviv University, Tel Aviv, 69978, Israel
| | - Cristiano Nisoli
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
| | - Yair Shokef
- School of Mechanical Engineering, Tel Aviv University, Tel Aviv, 69978, Israel.
- Center for Physics and Chemistry of Living Systems, Tel Aviv University, Tel Aviv, 69978, Israel.
- Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv, 69978, Israel.
- International Institute for Sustainability with Knotted Chiral Meta Matter, Hiroshima University, Higashi-Hiroshima, Hiroshima, 739-8526, Japan.
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5
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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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6
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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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7
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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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8
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Lindeman CW, Hagh VF, Ip CI, Nagel SR. Competition between Energy and Dynamics in Memory Formation. PHYSICAL REVIEW LETTERS 2023; 130:197201. [PMID: 37243648 DOI: 10.1103/physrevlett.130.197201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/31/2022] [Revised: 03/10/2023] [Accepted: 04/19/2023] [Indexed: 05/29/2023]
Abstract
Bistable objects that are pushed between states by an external field are often used as a simple model to study memory formation in disordered materials. Such systems, called hysterons, are typically treated quasistatically. Here, we generalize hysterons to explore the effect of dynamics in a simple spring system with tunable bistability and study how the system chooses a minimum. Changing the timescale of the forcing allows the system to transition between a situation where its fate is determined by following the local energy minimum to one where it is trapped in a shallow well determined by the path taken through configuration space. Oscillatory forcing can lead to transients lasting many cycles, a behavior not possible for a single quasistatic hysteron.
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Affiliation(s)
- Chloe W Lindeman
- Department of Physics and The James Franck and Enrico Fermi Institutes The University of Chicago, Chicago, Illinois 60637, USA
| | - Varda F Hagh
- Department of Physics and The James Franck and Enrico Fermi Institutes The University of Chicago, Chicago, Illinois 60637, USA
| | - Chi Ian Ip
- Department of Physics and The James Franck and Enrico Fermi Institutes The University of Chicago, Chicago, Illinois 60637, USA
| | - Sidney R Nagel
- Department of Physics and The James Franck and Enrico Fermi Institutes The University of Chicago, Chicago, Illinois 60637, USA
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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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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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11
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Affiliation(s)
- Muhittin Mungan
- Institut für Angewandte Mathematik, Universität Bonn, 53115 Bonn, Germany
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12
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Shohat D, Hexner D, Lahini Y. Memory from coupled instabilities in unfolded crumpled sheets. Proc Natl Acad Sci U S A 2022; 119:e2200028119. [PMID: 35867743 PMCID: PMC9282240 DOI: 10.1073/pnas.2200028119] [Citation(s) in RCA: 14] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2022] [Accepted: 04/30/2022] [Indexed: 11/18/2022] Open
Abstract
Crumpling an ordinary thin sheet transforms it into a structure with unusual mechanical behaviors, such as enhanced rigidity, emission of crackling noise, slow relaxations, and memory retention. A central challenge in explaining these behaviors lies in understanding the contribution of the complex geometry of the sheet. Here we combine cyclic driving protocols and three-dimensional (3D) imaging to correlate the global mechanical response and the underlying geometric transformations in unfolded crumpled sheets. We find that their response to cyclic strain is intermittent, hysteretic, and encodes a memory of the largest applied compression. Using 3D imaging we show that these behaviors emerge due to an interplay between localized and interacting geometric instabilities in the sheet. A simple model confirms that these minimal ingredients are sufficient to explain the observed behaviors. Finally, we show that after training, multiple memories can be encoded, a phenomenon known as return point memory. Our study lays the foundation for understanding the complex mechanics of crumpled sheets and presents an experimental and theoretical framework for the study of memory formation in systems of interacting instabilities.
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Affiliation(s)
- Dor Shohat
- Department of Condensed Matter, School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel
- Center for Physics and Chemistry of Living Systems, Tel-Aviv University, Tel Aviv 69978, Israel
| | - Daniel Hexner
- Faculty of Mechanical Engineering, Technion, Haifa 32000, Israel
| | - Yoav Lahini
- Department of Condensed Matter, School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel
- Center for Physics and Chemistry of Living Systems, Tel-Aviv University, Tel Aviv 69978, Israel
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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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Ding J, van Hecke M. Sequential snapping and pathways in a mechanical metamaterial. J Chem Phys 2022; 156:204902. [DOI: 10.1063/5.0087863] [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
Materials that feature bistable elements, hysterons, exhibit memory effects. Often, these hysterons are difficult to observe or control directly. Here, we introduce a mechanical metamaterial in which slender elements, interacting with pushers, act as mechanical hysterons. We show how we can tune the hysteron properties and pathways under cyclic compression by the geometric design of these elements and how we can tune the pathways of a given sample by tilting one of the boundaries. Furthermore, we investigate the effect of the coupling of a global shear mode to the hysterons as an example of the interactions between hysteron and non-hysteron degrees of freedom. We hope our work will inspire further studies on designer matter with targeted pathways.
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Affiliation(s)
- Jiangnan Ding
- Huygens-Kamerlingh Onnes Lab, Leiden University, P.O. Box 9504, 2300 RA Leiden, The Netherlands and AMOLF, Science Park 104, 1098 XG Amsterdam, The Netherlands
| | - Martin van Hecke
- Huygens-Kamerlingh Onnes Lab, Leiden University, P.O. Box 9504, 2300 RA Leiden, The Netherlands and AMOLF, Science Park 104, 1098 XG Amsterdam, The Netherlands
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15
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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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16
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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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17
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Mari R, Bertin E, Nardini C. Absorbing phase transitions in systems with mediated interactions. Phys Rev E 2022; 105:L032602. [PMID: 35428140 DOI: 10.1103/physreve.105.l032602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2021] [Accepted: 02/11/2022] [Indexed: 06/14/2023]
Abstract
Experiments of periodically sheared colloidal suspensions or soft amorphous solids display a transition from reversible to irreversible particle motion that, when analyzed stroboscopically in time, is interpreted as an absorbing phase transition with infinitely many absorbing states. In these systems, interactions mediated by hydrodynamics or elasticity are present, causing passive regions to be affected by nearby active ones. We show that mediated interactions induce a universality class of absorbing phase transitions distinct from conserved directed percolation, and we obtain the corresponding critical exponents. We do so with large-scale numerical simulations of a minimal model for the stroboscopic dynamics of sheared soft materials and we derive the minimal field theoretical description.
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Affiliation(s)
- Romain Mari
- Université Grenoble Alpes & CNRS, LIPhy, 38000 Grenoble, France
| | - Eric Bertin
- Université Grenoble Alpes & CNRS, LIPhy, 38000 Grenoble, France
| | - Cesare Nardini
- Service de Physique de l'État Condensé, CNRS UMR 3680, CEA-Saclay, 91191 Gif-sur-Yvette, France
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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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van Hecke M. Profusion of transition pathways for interacting hysterons. Phys Rev E 2021; 104:054608. [PMID: 34942848 DOI: 10.1103/physreve.104.054608] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2021] [Accepted: 10/14/2021] [Indexed: 11/07/2022]
Abstract
The response, pathways, and memory effects of cyclically driven complex media can be captured by hysteretic elements called hysterons. Here we demonstrate the profound impact of hysteron interactions on pathways and memory. Specifically, while the Preisach model of independent hysterons features a restricted class of pathways which always satisfy return point memory, we show that three interacting hysterons generate more than 15 000 transition graphs, with most violating return point memory and having features completely distinct from the Preisach model. Exploring these opens a route to designer pathways and information processing in complex matter.
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Affiliation(s)
- Martin van Hecke
- AMOLF, Science Park 104, 1098 XG Amsterdam, Netherlands and Huygens-Kamerlingh Onnes Lab, Universiteit Leiden, P.O. Box 9504, NL-2300 RA Leiden, Netherlands
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20
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Bense H, van Hecke M. Complex pathways and memory in compressed corrugated sheets. Proc Natl Acad Sci U S A 2021; 118:e2111436118. [PMID: 34876523 PMCID: PMC8685682 DOI: 10.1073/pnas.2111436118] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 11/08/2021] [Indexed: 01/19/2023] Open
Abstract
The nonlinear response of driven complex materials-disordered magnets, amorphous media, and crumpled sheets-features intricate transition pathways where the system repeatedly hops between metastable states. Such pathways encode memory effects and may allow information processing, yet tools are lacking to experimentally observe and control these pathways, and their full breadth has not been explored. Here we introduce compression of corrugated elastic sheets to precisely observe and manipulate their full, multistep pathways, which are reproducible, robust, and controlled by geometry. We show how manipulation of the boundaries allows us to elicit multiple targeted pathways from a single sample. In all cases, each state in the pathway can be encoded by the binary state of material bits called hysterons, and the strength of their interactions plays a crucial role. In particular, as function of increasing interaction strength, we observe Preisach pathways, expected in systems of independently switching hysterons; scrambled pathways that evidence hitherto unexplored interactions between these material bits; and accumulator pathways which leverage these interactions to perform an elementary computation. Our work opens a route to probe, manipulate, and understand complex pathways, impacting future applications in soft robotics and information processing in materials.
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Affiliation(s)
| | - Martin van Hecke
- AMOLF, 1098 XG Amsterdam, The Netherlands
- Huygens-Kamerlingh Onnes Laboratory, Leiden University, 2300 RA Leiden, The Netherlands
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21
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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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22
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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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23
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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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24
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Sastry S. Models for the Yielding Behavior of Amorphous Solids. PHYSICAL REVIEW LETTERS 2021; 126:255501. [PMID: 34241520 DOI: 10.1103/physrevlett.126.255501] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2020] [Accepted: 05/18/2021] [Indexed: 06/13/2023]
Abstract
Investigations of plastic deformation and yielding of amorphous solids reveal a strong dependence of their yielding behavior on the degree of annealing. Above a threshold degree of annealing, the nature of yielding changes qualitatively, becoming progressively more discontinuous. Theoretical investigations of yielding in amorphous solids have almost exclusively focused on uniform deformation, but cyclic deformation reveals intriguing features that remain uninvestigated. Focusing on athermal cyclic deformation, I investigate a family of models, which reproduce key features observed in simulations, and provide an interpretation for the intriguing presence of a threshold energy.
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Affiliation(s)
- Srikanth Sastry
- Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur Campus, Bengaluru 560064, India
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25
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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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26
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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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27
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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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28
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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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29
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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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