1
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Mondal C, Moshe M, Procaccia I, Roy S. Dipole screening in pure shear strain protocols of amorphous solids. Phys Rev E 2023; 108:L042901. [PMID: 37978588 DOI: 10.1103/physreve.108.l042901] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2023] [Accepted: 09/08/2023] [Indexed: 11/19/2023]
Abstract
When amorphous solids are subjected to simple or pure strain, they exhibit elastic increase in stress, punctuated by plastic events that become denser (in strain) upon increasing the system size. It is customary to assume in theoretical models that the stress released in each plastic event is redistributed according to the linear Eshelby kernel, causing avalanches of additional stress release. Here we demonstrate that, contrary to the uniform affine strain resulting from simple or pure strain, each plastic event is associated with a nonuniform strain that gives rise to a displacement field that contains quadrupolar and dipolar charges that typically screen the linear elastic phenomenology and introduce anomalous length scales and influence the form of the stress redistribution. An important question that opens up is how to take this into account in elastoplastic models of shear induced phenomena like shear banding.
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Affiliation(s)
- Chandana Mondal
- UGC-DAE Consortium for Scientific Research, Indore, Madhya Pradesh 452017, India
| | - Michael Moshe
- Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 9190, Israel
| | - Itamar Procaccia
- Department 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
| | - Saikat Roy
- Department of Chemical Engineering, Indian Institute of Technology Ropar, Punjab 140001, India
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2
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Ishima D, Saitoh K, Otsuki M, Hayakawa H. Theory of rigidity and numerical analysis of density of states of two-dimensional amorphous solids with dispersed frictional grains in the linear response regime. Phys Rev E 2023; 107:054902. [PMID: 37328994 DOI: 10.1103/physreve.107.054902] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2022] [Accepted: 03/23/2023] [Indexed: 06/18/2023]
Abstract
Using the Jacobian matrix, we obtain a theoretical expression of rigidity and the density of states of two-dimensional amorphous solids consisting of frictional grains in the linear response to an infinitesimal strain, in which we ignore the dynamical friction caused by the slip processes of contact points. The theoretical rigidity agrees with that obtained by molecular dynamics simulations. We confirm that the rigidity is smoothly connected to the value in the frictionless limit. We find that there are two modes in the density of states for sufficiently small k_{T}/k_{N}, which is the ratio of the tangential to normal stiffness. Rotational modes exist at low frequencies or small eigenvalues, whereas translational modes exist at high frequencies or large eigenvalues. The location of the rotational band shifts to the high-frequency region with an increase in k_{T}/k_{N} and becomes indistinguishable from the translational band for large k_{T}/k_{N}.
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Affiliation(s)
- Daisuke Ishima
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa-oiwake cho, Sakyo-ku, Kyoto 606-8502, Japan
| | - Kuniyasu Saitoh
- Department of Physics, Faculty of Science, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-ku, Kyoto 603-8555, Japan
| | - Michio Otsuki
- Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Hisao Hayakawa
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa-oiwake cho, Sakyo-ku, Kyoto 606-8502, Japan
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3
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Ishima D, Saitoh K, Otsuki M, Hayakawa H. Eigenvalue analysis of stress-strain curve of two-dimensional amorphous solids of dispersed frictional grains with finite shear strain. Phys Rev E 2023; 107:034904. [PMID: 37073050 DOI: 10.1103/physreve.107.034904] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2022] [Accepted: 03/05/2023] [Indexed: 04/20/2023]
Abstract
The stress-strain curve of two-dimensional frictional dispersed grains interacting with a harmonic potential without considering the dynamical slip under a finite strain is determined by using eigenvalue analysis of the Hessian matrix. After the configuration of grains is obtained, the stress-strain curve based on the eigenvalue analysis is in almost perfect agreement with that obtained by the simulation, even if there are plastic deformations caused by stress avalanches. Unlike the naive expectation, the eigenvalues in our model do not indicate any precursors to the stress-drop events.
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Affiliation(s)
- Daisuke Ishima
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa-oiwake cho, Sakyo-ku, Kyoto 606-8502, Japan
| | - Kuniyasu Saitoh
- Department of Physics, Faculty of Science, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-ku, Kyoto 603-8555, Japan
| | - Michio Otsuki
- Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Hisao Hayakawa
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa-oiwake cho, Sakyo-ku, Kyoto 606-8502, Japan
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4
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Dattani UA, Karmakar S, Chaudhuri P. Universal mechanical instabilities in the energy landscape of amorphous solids: Evidence from athermal quasistatic expansion. Phys Rev E 2022; 106:055004. [PMID: 36559417 DOI: 10.1103/physreve.106.055004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/24/2021] [Accepted: 11/02/2022] [Indexed: 11/30/2022]
Abstract
Using numerical simulations, we study the failure of an amorphous solid under athermal quasistatic expansion starting from a homogeneous high-density state. During the expansion process, plastic instabilities occur, manifested via sudden jumps in pressure and energy, with the largest event happening via cavitation leading to the material's yielding. We demonstrate that all these plastic events are characterized by saddle-node bifurcation, during which the smallest nonzero eigenvalue of the Hessian matrix vanishes via a square-root singularity. We find that after yielding and prior to complete fracture, the statistics of pressure or energy jumps corresponding to the plastic events show subextensive system-size scaling, similar to the case of simple shear but with different exponents. Thus, overall, our paper reveals universal features in the fundamental characteristics during mechanical failure in amorphous solids under any quasistatic deformation protocol.
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Affiliation(s)
- Umang A Dattani
- The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India.,Homi Bhabha National Institute, Anushaktinagar, Mumbai 400094, India
| | - Smarajit Karmakar
- Tata Institute of Fundamental Research, 36/P, Gopanpally Village, Serilingampally Mandal,Ranga Reddy District, Hyderabad, 500107 Telangana, India
| | - Pinaki Chaudhuri
- The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India.,Homi Bhabha National Institute, Anushaktinagar, Mumbai 400094, India
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5
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Wang C, Tawfick S, Vakakis AF. Time scale disparity yielding acoustic nonreciprocity in a two-dimensional granular-elastic solid interface with asymmetry. Phys Rev E 2021; 104:044906. [PMID: 34781518 DOI: 10.1103/physreve.104.044906] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2021] [Accepted: 09/21/2021] [Indexed: 11/07/2022]
Abstract
We study nonreciprocal wave transmission across the interface of two dissimilar granular media separated by an elastic solid medium. Specifically, a left, larger-scale and a right smaller-scale granular media composed of two-dimensional, initially uncompressed hexagonally packed granules are interfacing with an intermediate linearly elastic solid, modeled either as a thin elastic plate or a linear Euler-Bernoulli beam. The granular media are modeled by discrete elements and the elastic solid by finite elements assuming a plane stress approximation for the thin plate. Accounting for the combined effects of Hertzian, frictional and rotational interactions in the granular media, as well as the highly discontinuous interfacial effects between the (discrete) granular media and the (continuous) intermediate elastic solid, the nonlinear acoustics of the integrated system is computationally studied subject to a half-sine shock excitation applied to a boundary granule of either the left or right granular medium. The highly discontinuous and nonlinear interaction forces coupling the granular media to the elastic solid are accurately computed through an algorithm with interrelated iteration and interpolation at successive adaptive time steps. Numerical convergence is ensured by monitoring the (linearized) eigenvalues of a nonlinear map of interface forces at each (variable) time step. Due to the strong nonlinearity and hierarchical asymmetry of the left and right granular media, time scale disparity occurs in the response of the interface which breaks acoustic reciprocity. Specifically, depending on the location and intensity of the applied shock, propagating wavefronts are excited in the granular media, which, in turn, excite either (slow) low-frequency vibrations or (fast) high-frequency acoustics in the intermediate elastic medium. This scale disparity is due to the size disparity of the left and right granular media, which yields drastically different wave speeds in the resulting propagating wavefronts. As a result, the continuum part of the interface responds with either low-frequency vibrations-when the shock is applied to the larger-scale granular medium, or high-frequency waves-when the shock is applied to the smaller-scale granular medium. This provides the fundamental mechanism for breaking reciprocity in the interface. The nonreciprocal interfacial acoustics studied here apply to a broad class of asymmetric hybrid (discrete-continuum) nonlinear systems and can inform predictive designs of highly effective granular shock protectors or granular acoustic diodes.
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Affiliation(s)
- Chongan Wang
- Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Sameh Tawfick
- Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Alexander F Vakakis
- Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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6
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Chattoraj J, Huy NH, Aggarwal S, Habibullah MS, Farbiz F. Shear-induced mixing of granular materials featuring broad granule size distributions. Phys Rev E 2021; 104:044910. [PMID: 34781494 DOI: 10.1103/physreve.104.044910] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2021] [Accepted: 10/13/2021] [Indexed: 11/07/2022]
Abstract
Granular flows during a shear-induced mixing process are studied using discrete element methods. The aim is to understand the underlying elementary mechanisms of transition from unmixed to mixed phases for a granular material featuring a broad distribution of particles, which we investigate systematically by varying the strain rate and system size. Here the strain rate varies over four orders of magnitude and the system size varies from ten thousand to more than a million granules. A strain rate-dependent transition from quasistatic to purely inertial flow is observed. At the macroscopic scale, the contact stresses drop due to the formation of shear-induced instabilities that serves as an onset of granular flows and initiates mixing between the granules. The stress-drop displays a profound system size dependence. At the granular scale, mixing dynamics are correlated with the formation of shear bands, which result in significantly different timescales of mixing, especially for those regions that are close to the system walls and the bulk. Overall, our results reveal that although the transient dynamics display a generic behavior, these have a significant finite-size effect. In contrast, macroscopic behaviors at steady states have negligible system size dependence.
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Affiliation(s)
- Joyjit Chattoraj
- Institute of High Performance Computing, Agency for Science Technology and Research, 138632 Singapore
| | - Nguyen Hoang Huy
- Institute of High Performance Computing, Agency for Science Technology and Research, 138632 Singapore
| | - Saurabh Aggarwal
- Institute of High Performance Computing, Agency for Science Technology and Research, 138632 Singapore
| | | | - Farzam Farbiz
- Institute of High Performance Computing, Agency for Science Technology and Research, 138632 Singapore
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7
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Zhu L, Lu H, Guo X, Liu H. Triggering flow of jammed cohesive granular materials using modulated pulsed airflow. AIChE J 2021. [DOI: 10.1002/aic.17411] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
Affiliation(s)
- Lizhuo Zhu
- Shanghai Engineering Research Center of Coal Gasification East China University of Science and Technology Shanghai China
| | - Haifeng Lu
- Shanghai Engineering Research Center of Coal Gasification East China University of Science and Technology Shanghai China
| | - Xiaolei Guo
- Shanghai Engineering Research Center of Coal Gasification East China University of Science and Technology Shanghai China
| | - Haifeng Liu
- Shanghai Engineering Research Center of Coal Gasification East China University of Science and Technology Shanghai China
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8
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Chen S, Peterson CW, Parker JA, Rice SA, Ferguson AL, Scherer NF. Data-driven reaction coordinate discovery in overdamped and non-conservative systems: application to optical matter structural isomerization. Nat Commun 2021; 12:2548. [PMID: 33953159 PMCID: PMC8099877 DOI: 10.1038/s41467-021-22794-w] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2020] [Accepted: 03/22/2021] [Indexed: 11/09/2022] Open
Abstract
Optical matter (OM) systems consist of (nano-)particle constituents in solution that can self-organize into ordered arrays that are bound by electrodynamic interactions. They also manifest non-conservative forces, and the motions of the nano-particles are overdamped; i.e., they exhibit diffusive trajectories. We propose a data-driven approach based on principal components analysis (PCA) to determine the collective modes of non-conservative overdamped systems, such as OM structures, and harmonic linear discriminant analysis (HLDA) of time trajectories to estimate the reaction coordinate for structural transitions. We demonstrate the approach via electrodynamics-Langevin dynamics simulations of six electrodynamically-bound nanoparticles in an incident laser beam. The reaction coordinate we discover is in excellent accord with a rigorous committor analysis, and the identified mechanism for structural isomerization is in very good agreement with the experimental observations. The PCA-HLDA approach to data-driven discovery of reaction coordinates can aid in understanding and eventually controlling non-conservative and overdamped systems including optical and active matter systems.
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Affiliation(s)
- Shiqi Chen
- Department of Chemistry, University of Chicago, Chicago, IL, USA
- James Franck Institute, University of Chicago, Chicago, IL, USA
| | - Curtis W Peterson
- Department of Chemistry, University of Chicago, Chicago, IL, USA
- James Franck Institute, University of Chicago, Chicago, IL, USA
| | - John A Parker
- James Franck Institute, University of Chicago, Chicago, IL, USA
- Department of Physics, University of Chicago, Chicago, IL, USA
| | - Stuart A Rice
- Department of Chemistry, University of Chicago, Chicago, IL, USA
- James Franck Institute, University of Chicago, Chicago, IL, USA
| | - Andrew L Ferguson
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL, USA.
| | - Norbert F Scherer
- Department of Chemistry, University of Chicago, Chicago, IL, USA.
- James Franck Institute, University of Chicago, Chicago, IL, USA.
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9
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Lemaître A, Mondal C, Procaccia I, Roy S, Wang Y, Zhang J. Frictional Granular Matter: Protocol Dependence of Mechanical Properties. PHYSICAL REVIEW LETTERS 2021; 126:075501. [PMID: 33666446 DOI: 10.1103/physrevlett.126.075501] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/02/2020] [Accepted: 01/12/2021] [Indexed: 06/12/2023]
Abstract
Theoretical treatments of frictional granular matter often assume that it is legitimate to invoke classical elastic theory to describe its coarse-grained mechanical properties. Here, we show, based on experiments and numerical simulations, that this is generically not the case since stress autocorrelation functions decay more slowly than what is expected from elasticity theory. It was theoretically shown that standard elastic decay demands pressure and torque density fluctuations to be normal, with possibly one of them being hyperuniform. However, generic compressed frictional assemblies exhibit abnormal pressure fluctuations, failing to conform with the central limit theorem. The physics of this failure is linked to correlations built in the material during compression from a dilute configuration prior to jamming. By changing the protocol of compression, one can observe different pressure fluctuations, and stress autocorrelations decay at large scales.
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Affiliation(s)
- Anaël Lemaître
- NAVIER, UMR 8205, École des Ponts ParisTech, IFSTTAR, CNRS, UPE, Champs-sur-Marne 77420, France
| | - Chandana Mondal
- Department of Chemical Physics, the Weizmann Institute of Science, Rehovot 76100, Israel
| | - Itamar Procaccia
- Department of Chemical Physics, the Weizmann Institute of Science, Rehovot 76100, Israel
- Center for OPTical IMagery Analysis and Learning, Northwestern Polytechnical University, Xi'an 710072, China
| | - Saikat Roy
- Department of Chemical Physics, the Weizmann Institute of Science, Rehovot 76100, Israel
- Department of Chemical Engineering, Indian Institute of Technology Ropar, Punjab, 140001, India
| | - Yinqiao Wang
- School of Physics and Astronomy, Shanghai Jiao Tong University, 800 Dong Chuan Road, 200240 Shanghai, China
| | - Jie Zhang
- School of Physics and Astronomy, Shanghai Jiao Tong University, 800 Dong Chuan Road, 200240 Shanghai, China
- Institute of Natural Sciences, Shanghai Jiao Tong University, 200240 Shanghai, China
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10
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Charan H, Gendelman O, Procaccia I, Sheffer Y. Giant amplification of small perturbations in frictional amorphous solids. Phys Rev E 2020; 101:062902. [PMID: 32688538 DOI: 10.1103/physreve.101.062902] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2020] [Accepted: 06/02/2020] [Indexed: 11/07/2022]
Abstract
Catastrophic events in nature can be often triggered by small perturbations, with "remote triggering" of earthquakes being an important example. Here we present a mechanism for the giant amplification of small perturbations that is expected to be generic in systems whose dynamics is not derivable from a Hamiltonian. We offer a general discussion of the typical instabilities involved (being oscillatory with an exponential increase of noise) and examine in detail the normal forms that determine the relevant dynamics. The high sensitivity to external perturbations is explained for systems with and without dissipation. Numerical examples are provided using the dynamics of frictional granular matter. Finally, we point out the relationship of the presently discussed phenomenon to the highly topical issue of "exceptional points" in quantum models with non-Hermitian Hamiltonians.
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Affiliation(s)
- Harish Charan
- Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
| | - Oleg Gendelman
- Faculty of Mechanical Engineering, Technion, Haifa 32000, Israel
| | - Itamar Procaccia
- Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel.,Center for OPTical IMagery Analysis and Learning, Northwestern Polytechnical University, Xi'an, 710072 China
| | - Yarden Sheffer
- Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
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11
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Ikeda H, Brito C, Wyart M, Zamponi F. Jamming with Tunable Roughness. PHYSICAL REVIEW LETTERS 2020; 124:208001. [PMID: 32501092 DOI: 10.1103/physrevlett.124.208001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/09/2020] [Accepted: 05/04/2020] [Indexed: 06/11/2023]
Abstract
We introduce a new model to study the effect of surface roughness on the jamming transition. By performing numerical simulations, we show that for a smooth surface, the jamming transition density and the contact number at the transition point both increase upon increasing asphericity, as for ellipsoids and spherocylinders. Conversely, for a rough surface, both quantities decrease, in quantitative agreement with the behavior of frictional particles. Furthermore, in the limit corresponding to the Coulomb friction law, the model satisfies a generalized isostaticity criterion proposed in previous studies. We introduce a counting argument that justifies this criterion and interprets it geometrically. Finally, we propose a simple theory to predict the contact number at finite friction from the knowledge of the force distribution in the infinite friction limit.
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Affiliation(s)
- Harukuni Ikeda
- Graduate School of Arts and Sciences, The University of Tokyo Tokyo 153-8902, Japan
| | - Carolina Brito
- Instituto de Física, UFRGS, 91501-970, Porto Alegre, Brazil
| | - Matthieu Wyart
- Institute of Physics, EPFL, CH-1015 Lausanne, Switzerland
| | - Francesco Zamponi
- Laboratoire de Physique de l'École Normale Supérieure, Université PSL, CNRS, Sorbonne Université, Université de Paris, 75005 Paris, France
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12
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Bonfanti S, Chattoraj J, Guerra R, Procaccia I, Zapperi S. Oscillatory instabilities in three-dimensional frictional granular matter. Phys Rev E 2020; 101:052902. [PMID: 32575318 DOI: 10.1103/physreve.101.052902] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2019] [Accepted: 03/29/2020] [Indexed: 06/11/2023]
Abstract
The dynamics of amorphous granular matter with frictional interactions cannot be derived in general from a Hamiltonian and therefore displays oscillatory instabilities stemming from the onset of complex eigenvalues in the stability matrix. These instabilities were discovered in the context of one- and two-dimensional systems, while the three-dimensional case was never studied in detail. Here we fill this gap by deriving and demonstrating the presence of oscillatory instabilities in a three-dimensional granular packing. We study binary assemblies of spheres of two sizes interacting via classical Hertz and Mindlin force laws for the longitudinal and tangent interactions, respectively. We formulate analytically the stability matrix in three dimensions and observe that a couple of complex eigenvalues emerge at the onset of the instability as in the case of frictional disks in two dimensions. The dynamics then shows oscillatory exponential growth in the mean-square displacement, followed by a catastrophic event in which macroscopic portions of mechanical stress and energy are lost. The generality of these results for any choice of forces that break the symplectic Hamiltonian symmetry is discussed.
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Affiliation(s)
- Silvia Bonfanti
- Center for Complexity and Biosystems, Department of Physics, University of Milan, via Celoria 16, 20133 Milan, Italy
| | - Joyjit Chattoraj
- School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore
- Institute of High Performance Computing, Agency for Science, Technology and Research, Singapore
| | - Roberto Guerra
- Center for Complexity and Biosystems, Department of Physics, University of Milan, via Celoria 16, 20133 Milan, Italy
| | - Itamar Procaccia
- Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Stefano Zapperi
- Center for Complexity and Biosystems, Department of Physics, University of Milan, via Celoria 16, 20133 Milan, Italy
- CNR-Consiglio Nazionale delle Ricerche, Istituto di Chimica della Materia Condensata e di Tecnologie per l'Energia, Via R. Cozzi 53, 20125 Milan, Italy
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13
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Charan H, Chattoraj J, Ciamarra MP, Procaccia I. Transition from Static to Dynamic Friction in an Array of Frictional Disks. PHYSICAL REVIEW LETTERS 2020; 124:030602. [PMID: 32031841 DOI: 10.1103/physrevlett.124.030602] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/28/2019] [Indexed: 06/10/2023]
Abstract
The nature of an instability that controls the transition from static to dynamical friction is studied in the context of an array of frictional disks that are pressed from above on a substrate. In this case the forces are all explicit and Newtonian dynamics can be employed without any phenomenological assumptions. We show that an oscillatory instability that had been discovered recently is responsible for the transition, allowing individual disks to spontaneously reach the Coulomb limit and slide with dynamic friction. The transparency of the model allows a full understanding of the phenomenon, including the speeds of the waves that travel from the trailing to the leading edge and vice versa.
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Affiliation(s)
- Harish Charan
- Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Joyjit Chattoraj
- School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Massimo Pica Ciamarra
- School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Itamar Procaccia
- Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100, Israel
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14
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Chattoraj J, Gendelman O, Ciamarra MP, Procaccia I. Noise amplification in frictional systems: Oscillatory instabilities. Phys Rev E 2019; 100:042901. [PMID: 31770870 DOI: 10.1103/physreve.100.042901] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2019] [Indexed: 06/10/2023]
Abstract
It was discovered recently that frictional granular materials can exhibit an important mechanism for instabilities, i.e., the appearance of pairs of complex eigenvalues in their stability matrix. The consequence is an oscillatory exponential growth of small perturbations which are tamed by dynamical nonlinearities. The amplification can be giant, many orders of magnitude, and it ends with a catastrophic system-spanning plastic event. Here we follow up on this discovery, explore the scaling laws characterizing the onset of the instability, the scenarios of the development of the instability with and without damping, and the nature of the eventual system-spanning events. The possible relevance to earthquake physics and to the transition from static to dynamic friction is discussed.
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Affiliation(s)
- Joyjit Chattoraj
- School of Physical and Mathematical Sciences, Nanyang Technological University, 637371 Singapore
| | - Oleg Gendelman
- Faculty of Mechanical Engineering, Technion, Haifa 32000, Israel
| | - Massimo Pica Ciamarra
- School of Physical and Mathematical Sciences, Nanyang Technological University, 637371 Singapore
- CNR-SPIN, Dipartimento di Scienze Fisiche, Università di Napoli Federico II, I-80126, Napoli, Italy
| | - Itamar Procaccia
- Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
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