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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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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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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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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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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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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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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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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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