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  Dynamic instabilities of frictional sliding at a bimaterial interface

Brener, E. A., Weikamp, M., Spatschek, R. P., Bar-Sinai, Y., & Bouchbinder, E. (2016). Dynamic instabilities of frictional sliding at a bimaterial interface. Journal of the Mechanics and Physics of Solids, 89, 149-173. doi:10.1016/j.jmps.2016.01.009.

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Item Permalink: http://hdl.handle.net/21.11116/0000-0001-B90B-3 Version Permalink: http://hdl.handle.net/21.11116/0000-0001-B90C-2
Genre: Journal Article

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Brener, Efim A.1, Author              
Weikamp, Marc2, Author              
Spatschek, Robert Philipp2, 3, Author              
Bar-Sinai, Yohai4, Author              
Bouchbinder, Eran4, Author              
Affiliations:
1Peter-Grünberg-Institut 2, Forschungszentrum Jülich, D-52425 Jülich, Germany, ou_persistent22              
2Mescoscale Simulations, Computational Materials Design, Max-Planck-Institut für Eisenforschung GmbH, Max Planck Society, ou_1863343              
3Institute for Energy and Climate Research, Forschungszentrum Jülich GmbH, Jülich, Germany, ou_persistent22              
4Chemical Physics Department, Weizmann Institute of Science, Rehovot 76100, Israel, ou_persistent22              

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Free keywords: Dynamics; Interfaces (materials); Linear stability analysis; Shear flow; Shear waves; Stability; Stabilization; Tribology, Bi-material interfaces; Dynamics instabilities; Elasto-dynamics; Frictional constitutive laws; Frictional resistance; Rate and state friction; Rupture; Steady-state condition, Friction
 Abstract: Understanding the dynamic stability of bodies in frictional contact steadily sliding one over the other is of basic interest in various disciplines such as physics, solid mechanics, materials science and geophysics. Here we report on a two-dimensional linear stability analysis of a deformable solid of a finite height H, steadily sliding on top of a rigid solid within a generic rate-and-state friction type constitutive framework, fully accounting for elastodynamic effects. We derive the linear stability spectrum, quantifying the interplay between stabilization related to the frictional constitutive law and destabilization related both to the elastodynamic bi-material coupling between normal stress variations and interfacial slip, and to finite size effects. The stabilizing effects related to the frictional constitutive law include velocity-strengthening friction (i.e. an increase in frictional resistance with increasing slip velocity, both instantaneous and under steady-state conditions) and a regularized response to normal stress variations. We first consider the small wave-number k limit and demonstrate that homogeneous sliding in this case is universally unstable, independent of the details of the friction law. This universal instability is mediated by propagating waveguide-like modes, whose fastest growing mode is characterized by a wave-number satisfying kH∼O(1) and by a growth rate that scales with H-1. We then consider the limit kH→∞ and derive the stability phase diagram in this case. We show that the dominant instability mode travels at nearly the dilatational wave-speed in the opposite direction to the sliding direction. In a certain parameter range this instability is manifested through unstable modes at all wave-numbers, yet the frictional response is shown to be mathematically well-posed. Instability modes which travel at nearly the shear wave-speed in the sliding direction also exist in some range of physical parameters. Previous results obtained in the quasi-static regime appear relevant only within a narrow region of the parameter space. Finally, we show that a finite-time regularized response to normal stress variations, within the framework of generalized rate-and-state friction models, tends to promote stability. The relevance of our results to the rupture of bi-material interfaces is briefly discussed. © 2016 Elsevier Ltd. All rights reserved.

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Language(s): eng - English
 Dates: 2016-04
 Publication Status: Published in print
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Method: Peer
 Identifiers: DOI: 10.1016/j.jmps.2016.01.009
BibTex Citekey: Brener2016149
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Title: Journal of the Mechanics and Physics of Solids
Source Genre: Journal
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Publ. Info: London : Pergamon
Pages: - Volume / Issue: 89 Sequence Number: - Start / End Page: 149 - 173 Identifier: ISSN: 0022-5096
CoNE: /journals/resource/954925419037