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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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Szuszik C, Main IG, Kun F. Effect of the loading condition on the statistics of crackling noise accompanying the failure of porous rocks. ROYAL SOCIETY OPEN SCIENCE 2023; 10:230528. [PMID: 38026039 PMCID: PMC10663801 DOI: 10.1098/rsos.230528] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/06/2023] [Accepted: 10/25/2023] [Indexed: 12/01/2023]
Abstract
We test the hypothesis that loading conditions affect the statistical features of crackling noise accompanying the failure of porous rocks by performing discrete element simulations of the tensile failure of model rocks and comparing the results to those of compressive simulations of the same samples. Cylindrical samples are constructed by sedimenting randomly sized spherical particles connected by beam elements representing the cementation of granules. Under a slowly increasing external tensile load, the cohesive contacts between particles break in bursts whose size fluctuates over a broad range. Close to failure breaking avalanches are found to localize on a highly stressed region where the catastrophic avalanche is triggered and the specimen breaks apart along a spanning crack. The fracture plane has a random position and orientation falling most likely close to the centre of the specimen perpendicular to the load direction. In spite of the strongly different strengths, degrees of 'brittleness' and spatial structure of damage of tensile and compressive failure of model rocks, our calculations revealed that the size, energy and duration of avalanches, and the waiting time between consecutive events all obey scale-free statistics with power law exponents which agree within their error bars in the two loading cases.
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Affiliation(s)
- Csanád Szuszik
- Department of Theoretical Physics, Doctoral School of Physics, Faculty of Science and Technology, University of Debrecen, PO Box 400, 4002 Debrecen, Hungary
| | - Ian G. Main
- School of Geosciences, University of Edinburgh, Edinburgh EH9 3FE, UK
| | - Ferenc Kun
- Department of Theoretical Physics, Doctoral School of Physics, Faculty of Science and Technology, University of Debrecen, PO Box 400, 4002 Debrecen, Hungary
- Institute for Nuclear Research (Atomki), PO Box 51, 4001 Debrecen, Hungary
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Savolainen J, Laurson L, Alava M. Effect of thresholding on avalanches and their clustering for interfaces with long-range elasticity. Phys Rev E 2022; 105:054152. [PMID: 35706318 DOI: 10.1103/physreve.105.054152] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2021] [Accepted: 05/13/2022] [Indexed: 06/15/2023]
Abstract
Avalanches are often defined as signals higher than some detection level in bursty systems. The choice of the detection threshold affects the number of avalanches, but it can also affect their temporal correlations. We simulated the depinning of a long-range elastic interface and applied different thresholds including a zero one on the data to see how the sizes and durations of events change and how this affects temporal avalanche clustering. Higher thresholds result in steeper size and duration distributions and cause the avalanches to cluster temporally. Using methods from seismology, the frequency of the events in the clusters was found to decrease as a power-law of time, and the size of an event in a cluster was found to help predict how many events it is followed by. The results bring closer theoretical studies of this class of models to real experiments, but also highlight how different phenomena can be obtained from the same set of data.
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Affiliation(s)
- Juha Savolainen
- Department of Applied Physics, Aalto University, PO Box 11000, 00076 Aalto, Finland
| | - Lasse Laurson
- Computational Physics Laboratory, Tampere University, P.O. Box 692, FI-33101 Tampere, Finland
| | - Mikko Alava
- Department of Applied Physics, Aalto University, PO Box 11000, 00076 Aalto, Finland
- NOMATEN Centre of Excellence, National Centre for Nuclear Research, A. Soltana 7, 05-400 Otwock-Swierk, Poland
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Barés J, Bonamy D. Controlling crackling dynamics by triggering low-intensity avalanches. Phys Rev E 2021; 103:053001. [PMID: 34134297 DOI: 10.1103/physreve.103.053001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2020] [Accepted: 04/23/2021] [Indexed: 11/07/2022]
Abstract
We examine the effect of small, spatially localized excitations applied periodically in different manners, on the crackling dynamics of a brittle crack driven slowly in a heterogeneous solid. When properly adjusted, these excitations are observed to radically modify avalanche statistics and considerably limit the magnitude of the largest events. Surprisingly, this does not require information on the front loading state at the time of excitation; applying it either at a random location or at the most loaded point gives the same results. Subsequently, we unravel how the excitation amplitude, spatial extent, and frequency govern the effect. We find that the excitation efficiency is ruled by a single reduced parameter, namely the injected power per unit front length; the suppression of extreme avalanches is maximum at a well-defined optimal value of this control parameter. analysis opens another way to control the largest events in crackling dynamics. Beyond fracture problems, it may be relevant for crackling systems described by models of the same universality class, such as the wetting of heterogeneous substrates or magnetic walls in amorphous magnets.
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Affiliation(s)
- Jonathan Barés
- Laboratoire de Mécanique et Génie Civil, UMR 5508 CNRS-University Montpellier, 34095 Montpellier, France
| | - Daniel Bonamy
- Service de Physique de l'État Condensée, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette Cedex, France
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Le Priol C, Chopin J, Le Doussal P, Ponson L, Rosso A. Universal Scaling of the Velocity Field in Crack Front Propagation. PHYSICAL REVIEW LETTERS 2020; 124:065501. [PMID: 32109111 DOI: 10.1103/physrevlett.124.065501] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/20/2019] [Revised: 12/11/2019] [Accepted: 01/15/2020] [Indexed: 06/10/2023]
Abstract
The propagation of a crack front in disordered materials is jerky and characterized by bursts of activity, called avalanches. These phenomena are the manifestation of an out-of-equilibrium phase transition originated by the disorder. As a result avalanches display universal scalings which are, however, difficult to characterize in experiments at a finite drive. Here, we show that the correlation functions of the velocity field along the front allow us to extract the critical exponents of the transition and to identify the universality class of the system. We employ these correlations to characterize the universal behavior of the transition in simulations and in an experiment of crack propagation. This analysis is robust, efficient, and can be extended to all systems displaying avalanche dynamics.
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Affiliation(s)
- Clément Le Priol
- CNRS-Laboratoire de Physique de l'Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex, France
| | - Julien Chopin
- Instituto de Física, Universidade Federal da Bahia, Salvador-BA, 40170-115, Brazil
| | - Pierre Le Doussal
- CNRS-Laboratoire de Physique de l'Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex, France
| | - Laurent Ponson
- Institut Jean le Rond d'Alembert, Sorbonne Université, 75252 Paris Cedex 05, France
| | - Alberto Rosso
- LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
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Barés J, Bonamy D, Rosso A. Seismiclike organization of avalanches in a driven long-range elastic string as a paradigm of brittle cracks. Phys Rev E 2019; 100:023001. [PMID: 31574622 DOI: 10.1103/physreve.100.023001] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2019] [Indexed: 11/07/2022]
Abstract
Crack growth in heterogeneous materials sometimes exhibits crackling dynamics, made of successive impulselike events with specific scale-invariant time and size organization reminiscent of earthquakes. Here, we examine this dynamics in a model which identifies the crack front with a long-range elastic line driven in a random potential. We demonstrate that, under some circumstances, fracture grows intermittently, via scale-free impulse organized into aftershock sequences obeying the fundamental laws of statistical seismology. We examine the effects of the driving rate and system overall stiffness (unloading factor) onto the scaling exponents and cutoffs associated with the time and size organization. We unravel the specific conditions required to observe a seismiclike organization in the crack propagation problem. Beyond failure problems, implications of these results to other crackling systems are finally discussed.
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Affiliation(s)
- Jonathan Barés
- Laboratoire de Mécanique et Génie Civil, Université de Montpellier, CNRS, Montpellier, France
| | - Daniel Bonamy
- SPEC/SPHYNX, DSM/IRAMIS CEA Saclay, Bat. 772, F-91191 Gif-sur-Yvette, France
| | - Alberto Rosso
- LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
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Biswas S, Goehring L, Chakrabarti BK. Statistical physics of fracture and earthquakes. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2018; 377:rsta.2018.0202. [PMID: 30478212 PMCID: PMC6282412 DOI: 10.1098/rsta.2018.0202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 07/23/2018] [Indexed: 06/09/2023]
Abstract
Manifestations of emergent properties in stressed disordered materials are often the result of an interplay between strong perturbations in the stress field around defects. The collective response of a long-ranged correlated multi-component system is an ideal playing field for statistical physics. Hence, many aspects of such collective responses in widely spread length and energy scales can be addressed by the tools of statistical physics. In this theme issue, some of these aspects are treated from various angles of experiments, simulations and analytical methods, and connected together by their common base of complex-system dynamics.This article is part of the theme issue 'Statistical physics of fracture and earthquakes' .
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Affiliation(s)
- Soumyajyoti Biswas
- Max Planck Institute of Dynamics and Self-Organization, Am Fassberg 17, 37073 Göttingen, Germany
| | - Lucas Goehring
- School of Science and Technology, Nottingham Trent University, Clifton Lane, Nottingham NG11 8NS, UK
| | - Bikas K Chakrabarti
- Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700064, India
- S. N. Bose National Centre for Basic Sciences, JD Block, Bidhannagar, Kolkata 700108, India
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