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Pomyalov A, Barras F, Roch T, Brener EA, Bouchbinder E. The dynamics of unsteady frictional slip pulses. Proc Natl Acad Sci U S A 2023; 120:e2309374120. [PMID: 37590405 PMCID: PMC10450397 DOI: 10.1073/pnas.2309374120] [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: 06/04/2023] [Accepted: 07/19/2023] [Indexed: 08/19/2023] Open
Abstract
Self-healing slip pulses are major spatiotemporal failure modes of frictional systems, featuring a characteristic size [Formula: see text] and a propagation velocity [Formula: see text] ([Formula: see text] is time). Here, we develop a theory of slip pulses in realistic rate- and state-dependent frictional systems. We show that slip pulses are intrinsically unsteady objects-in agreement with previous findings-yet their dynamical evolution is closely related to their unstable steady-state counterparts. In particular, we show that each point along the time-independent [Formula: see text] line, obtained from a family of steady-state pulse solutions parameterized by the driving shear stress [Formula: see text], is unstable. Nevertheless, and remarkably, the [Formula: see text] line is a dynamic attractor such that the unsteady dynamics of slip pulses (when they exist)-whether growing ([Formula: see text]) or decaying ([Formula: see text])-reside on the steady-state line. The unsteady dynamics along the line are controlled by a single slow unstable mode. The slow dynamics of growing pulses, manifested by [Formula: see text], explain the existence of sustained pulses, i.e., pulses that propagate many times their characteristic size without appreciably changing their properties. Our theoretical picture of unsteady frictional slip pulses is quantitatively supported by large-scale, dynamic boundary-integral method simulations.
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Affiliation(s)
- Anna Pomyalov
- Chemical and Biological Physics Department, Weizmann Institute of Science, Rehovot7610001, Israel
| | - Fabian Barras
- The Njord Centre, Department of Physics, University of Oslo, Oslo0316, Norway
- The Njord Centre, Department of Geosciences, University of Oslo, Oslo0316, Norway
| | - Thibault Roch
- Civil Engineering Institute, Materials Science and Engineering Institute, Ecole Polytechnique Fédérale de Lausanne, LausanneCH-1015, Switzerland
| | - Efim A. Brener
- Peter Grünberg Institut, Forschungszentrum Jülich, JülichD-52425, Germany
- Institute for Energy and Climate Research, Forschungszentrum Jülich, JülichD-52425, Germany
| | - Eran Bouchbinder
- Chemical and Biological Physics Department, Weizmann Institute of Science, Rehovot7610001, Israel
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Pomyalov A, Lubomirsky Y, Braverman L, Brener EA, Bouchbinder E. Self-healing solitonic slip pulses in frictional systems. Phys Rev E 2023; 107:L013001. [PMID: 36797875 DOI: 10.1103/physreve.107.l013001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2022] [Accepted: 12/09/2022] [Indexed: 06/18/2023]
Abstract
A prominent spatiotemporal failure mode of frictional systems is self-healing slip pulses, which are propagating solitonic structures that feature a characteristic length. Here, we numerically derive a family of steady state slip pulse solutions along generic and realistic rate-and-state dependent frictional interfaces, separating large deformable bodies in contact. Such nonlinear interfaces feature a nonmonotonic frictional strength as a function of the slip velocity, with a local minimum. The solutions exhibit a diverging length and strongly inertial propagation velocities, when the driving stress approaches the frictional strength characterizing the local minimum from above, and change their character when it is away from it. An approximate scaling theory quantitatively explains these observations. The derived pulse solutions also exhibit significant spatially-extended dissipation in excess of the edge-localized dissipation (the effective fracture energy) and an unconventional edge singularity. The relevance of our findings for available observations is discussed.
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Affiliation(s)
- Anna Pomyalov
- Chemical and Biological Physics Department, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Yuri Lubomirsky
- Chemical and Biological Physics Department, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Lara Braverman
- Chemical and Biological Physics Department, Weizmann Institute of Science, Rehovot 7610001, Israel
- Department of Physics, The University of Chicago, Chicago, Illinois 60637, USA
| | - Efim A Brener
- Peter Grünberg Institut, Forschungszentrum Jülich, D-52425 Jülich, Germany
- Institute for Energy and Climate Research, Forschungszentrum Jülich, D-52425 Jülich, Germany
| | - Eran Bouchbinder
- Chemical and Biological Physics Department, Weizmann Institute of Science, Rehovot 7610001, Israel
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Thøgersen K, Aharonov E, Barras F, Renard F. Minimal model for the onset of slip pulses in frictional rupture. Phys Rev E 2021; 103:052802. [PMID: 34134208 DOI: 10.1103/physreve.103.052802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2020] [Accepted: 04/20/2021] [Indexed: 06/12/2023]
Abstract
We present a minimal one-dimensional continuum model for the transition from cracklike to pulselike propagation of frictional rupture. In its nondimensional form, the model depends on only two free parameters: the nondimensional prestress and an elasticity ratio that accounts for the finite height of the system. The model predicts stable slip pulse solutions for slip boundary conditions, and unstable slip pulse solutions for stress boundary conditions. The results demonstrate that a mechanism based solely on elastic relaxation and redistribution of initial prestress can cause pulselike rupture, without any particular rate or slip dependences of dynamic friction. This means that pulselike propagation along frictional interfaces is likely a generic feature that can occur in systems of finite thickness over a wide range of friction constitutive laws.
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Affiliation(s)
- Kjetil Thøgersen
- The Njord Centre, Departments of Physics and Geosciences, University of Oslo, 0316 Oslo, Norway
| | - Einat Aharonov
- Institute of Earth Sciences, The Hebrew University, Jerusalem, 91904, Israel
| | - Fabian Barras
- The Njord Centre, Departments of Physics and Geosciences, University of Oslo, 0316 Oslo, Norway
| | - François Renard
- The Njord Centre, Departments of Physics and Geosciences, University of Oslo, 0316 Oslo, Norway
- Université Grenoble Alpes, Université Savoie Mont Blanc, CNRS, IRD, IFSTTAR, ISTerre, 38000 Grenoble, France
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Spatiotemporal Dynamics of Frictional Systems: The Interplay of Interfacial Friction and Bulk Elasticity. LUBRICANTS 2019. [DOI: 10.3390/lubricants7100091] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Frictional interfaces are abundant in natural and engineering systems, and predicting their behavior still poses challenges of prime scientific and technological importance. At the heart of these challenges lies the inherent coupling between the interfacial constitutive relation—the macroscopic friction law—and the bulk elasticity of the bodies that form the frictional interface. In this feature paper, we discuss the generic properties of a minimal macroscopic friction law and the many ways in which its coupling to bulk elasticity gives rise to rich spatiotemporal frictional dynamics. We first present the widely used rate-and-state friction constitutive framework, discuss its power and limitations, and propose extensions that are supported by experimental data. We then discuss how bulk elasticity couples different parts of the interface, and how the range and nature of this interaction are affected by the system’s geometry. Finally, in light of the coupling between interfacial and bulk physics, we discuss basic phenomena in spatially extended frictional systems, including the stability of homogeneous sliding, the onset of sliding motion and a wide variety of propagating frictional modes (e.g., rupture fronts, healing fronts and slip pulses). Overall, the results presented and discussed in this feature paper highlight the inseparable roles played by interfacial and bulk physics in spatially extended frictional systems.
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Thøgersen K, Sveinsson HA, Amundsen DS, Scheibert J, Renard F, Malthe-Sørenssen A. Minimal model for slow, sub-Rayleigh, supershear, and unsteady rupture propagation along homogeneously loaded frictional interfaces. Phys Rev E 2019; 100:043004. [PMID: 31771025 DOI: 10.1103/physreve.100.043004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2019] [Indexed: 06/10/2023]
Abstract
In nature and experiments, a large variety of rupture speeds and front modes along frictional interfaces are observed. Here, we introduce a minimal model for the rupture of homogeneously loaded interfaces with velocity strengthening dynamic friction, containing only two dimensionless parameters; τ[over ¯], which governs the prestress, and α[over ¯], which is set by the interfacial viscosity. This model contains a large variety of front types, including slow fronts, sub-Rayleigh fronts, supershear fronts, slip pulses, cracks, arresting fronts, and fronts that alternate between arresting and propagating phases. Our results indicate that this wide range of front types is an inherent property of frictional systems with velocity strengthening branches.
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Affiliation(s)
- Kjetil Thøgersen
- Physics of Geological Processes, The NJORD Centre, University of Oslo, 0316 Oslo, Norway
- Department of Geosciences, University of Oslo, 0316 Oslo, Norway
| | - Henrik Andersen Sveinsson
- Physics of Geological Processes, The NJORD Centre, University of Oslo, 0316 Oslo, Norway
- Department of Physics, University of Oslo, 0316 Oslo, Norway
| | | | - Julien Scheibert
- Univ Lyon, Ecole Centrale de Lyon, ENISE, ENTPE, CNRS, Laboratoire de Tribologie et Dynamique des Systèmes LTDS, UMR 5513, F-69134, Ecully, France
| | - François Renard
- Physics of Geological Processes, The NJORD Centre, University of Oslo, 0316 Oslo, Norway
- Department of Geosciences, University of Oslo, 0316 Oslo, Norway
- University Grenoble Alpes, University Savoie Mont Blanc, CNRS, IRD, IFSTTAR, ISTerre, 38000 Grenoble, France
| | - Anders Malthe-Sørenssen
- Physics of Geological Processes, The NJORD Centre, University of Oslo, 0316 Oslo, Norway
- Department of Physics, University of Oslo, 0316 Oslo, Norway
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Brener EA, Aldam M, Barras F, Molinari JF, Bouchbinder E. Unstable Slip Pulses and Earthquake Nucleation as a Nonequilibrium First-Order Phase Transition. PHYSICAL REVIEW LETTERS 2018; 121:234302. [PMID: 30576171 DOI: 10.1103/physrevlett.121.234302] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2018] [Revised: 09/20/2018] [Indexed: 06/09/2023]
Abstract
The onset of rapid slip along initially quiescent frictional interfaces, the process of "earthquake nucleation," and dissipative spatiotemporal slippage dynamics play important roles in a broad range of physical systems. Here we first show that interfaces described by generic friction laws feature stress-dependent steady-state slip pulse solutions, which are unstable in the quasi-1D approximation of thin elastic bodies. We propose that such unstable slip pulses of linear size L^{*} and characteristic amplitude are "critical nuclei" for rapid slip in a nonequilibrium analogy to equilibrium first-order phase transitions and quantitatively support this idea by dynamical calculations. We then perform 2D numerical calculations that indicate that the nucleation length L^{*} exists also in 2D and that the existence of a fracture mechanics Griffith-like length L_{G}<L^{*} gives rise to a richer phase diagram that features also sustained slip pulses.
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Affiliation(s)
- Efim A Brener
- Peter Grünberg Institut, Forschungszentrum Jülich, D-52425 Jülich, Germany
| | - Michael Aldam
- Chemical and Biological Physics Department, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Fabian Barras
- Civil Engineering Institute, Materials Science and Engineering Institute, Ecole Polytechnique Fédérale de Lausanne, Station 18, CH-1015 Lausanne, Switzerland
| | - Jean-François Molinari
- Civil Engineering Institute, Materials Science and Engineering Institute, Ecole Polytechnique Fédérale de Lausanne, Station 18, CH-1015 Lausanne, Switzerland
| | - Eran Bouchbinder
- Chemical and Biological Physics Department, Weizmann Institute of Science, Rehovot 7610001, Israel
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Vanossi A, Dietzel D, Schirmeisen A, Meyer E, Pawlak R, Glatzel T, Kisiel M, Kawai S, Manini N. Recent highlights in nanoscale and mesoscale friction. BEILSTEIN JOURNAL OF NANOTECHNOLOGY 2018; 9:1995-2014. [PMID: 30116691 PMCID: PMC6071713 DOI: 10.3762/bjnano.9.190] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/16/2018] [Accepted: 06/27/2018] [Indexed: 05/31/2023]
Abstract
Friction is the oldest branch of non-equilibrium condensed matter physics and, at the same time, the least established at the fundamental level. A full understanding and control of friction is increasingly recognized to involve all relevant size and time scales. We review here some recent advances on the research focusing of nano- and mesoscale tribology phenomena. These advances are currently pursued in a multifaceted approach starting from the fundamental atomic-scale friction and mechanical control of specific single-asperity combinations, e.g., nanoclusters on layered materials, then scaling up to the meso/microscale of extended, occasionally lubricated, interfaces and driven trapped optical systems, and eventually up to the macroscale. Currently, this "hot" research field is leading to new technological advances in the area of engineering and materials science.
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Affiliation(s)
- Andrea Vanossi
- CNR-IOM Democritos National Simulation Center, Via Bonomea 265, 34136 Trieste, Italy
- International School for Advanced Studies (SISSA), Via Bonomea 265, 34136 Trieste, Italy
| | - Dirk Dietzel
- Institute of Applied Physics, University of Giessen, 33492 Giessen, Germany
| | - Andre Schirmeisen
- Institute of Applied Physics, University of Giessen, 33492 Giessen, Germany
| | - Ernst Meyer
- Department of Physics, University of Basel, Klingelbergstr. 82, CH-4056 Basel, Switzerland
| | - Rémy Pawlak
- Department of Physics, University of Basel, Klingelbergstr. 82, CH-4056 Basel, Switzerland
| | - Thilo Glatzel
- Department of Physics, University of Basel, Klingelbergstr. 82, CH-4056 Basel, Switzerland
| | - Marcin Kisiel
- Department of Physics, University of Basel, Klingelbergstr. 82, CH-4056 Basel, Switzerland
| | - Shigeki Kawai
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1, Namiki, Tsukuba, Ibaraki 305-0044, Japan
| | - Nicola Manini
- Dipartimento di Fisica, Università degli Studi di Milano, via Celoria 16, 20133 Milano, Italy
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