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Spatiotemporal dynamics of frictional systems: The interplay of interfacial friction and bulk elasticity

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Pith's one-line read This paper argues that spatially extended friction cannot be understood from interfacial contact laws alone: bulk elasticity and the interfacial constitutive relation are inseparable, and together they set stability, nucleation, and…

desk verdict A credible feature-paper synthesis of this group's rate-and-state-plus-bulk-elasticity program; the new FEM results are solid, but the propagating-mode taxonomy leans on an N-shaped friction curve that is a constitutive assumption, not a generic consequence of interface-bulk coupling. read the letter →

arxiv 1908.02820 v1 pith:VJXHYDXO submitted 2019-08-07 cond-mat.soft cond-mat.mtrl-sciphysics.geo-ph

Yohai Bar-Sinai , Michael Aldam , Robert Spatschek , Efim A. Brener , Eran Bouchbinder This is my paper · ORCID
classification cond-mat.softcond-mat.mtrl-sciphysics.geo-ph
keywords rate-and-statefrictioninterfacialelasticitybulkfrictionalstabilitycreeppatchesrupturefrontsslippulsesvelocity-strengthening
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that the dynamics of frictional interfaces—steady sliding, creep, rupture, healing, and self-healing pulses—cannot be derived from the interfacial contact law alone. Its central claim is that interfacial friction and the elasticity of the surrounding bulks are inseparable partners: they meet in one master equation, and all spatially extended frictional phenomena emerge from that coupling. The paper extends rate-and-state friction with a reversible elastic interfacial stress and a short-time cutoff, which produces an N-shaped steady-state friction curve. Coupled to bulk elasticity, this single curve controls the stability threshold of homogeneous sliding, the critical size at which creep patches run away, and the width and speed of propagating fronts. If the picture is right, earthquakes, brake squeal, and stick-slip in machines share one quantitative mechanism.

What carries the argument

The central object is the coupled interface–bulk problem in Eq. (3), with the interfacial law on one side and the bulk elastic functionals $\mathcal{F}_\tau$ and $\mathcal{F}_\sigma$ on the other. The load-bearing interfacial ingredient is the extended friction law: a total stress $\tau=\tau^{el}+\tau^{vis}$, an elastic stress that grows as the interface is sheared and relaxes with slip, $\dot{\tau}^{el}=(\mu_0/h)Av-\tau^{el}|v|g(\tau,v)/D$, and a short-time cutoff in the contact area that saturates logarithmic aging and creates the N-shaped steady-state curve. The load-bearing bulk ingredient is the elastodynamic functional $\mathcal{F}_\tau$: in the thin-system limit it reduces to a local scalar wave operator $\mathcal{F}_\tau\simeq\rho H\,\partial_{tt}\delta-\bar\mu H\,\partial_{xx}\delta$, making the analysis tractable, while in infinite systems it is the long-ranged radiation-damping plus singular-integral kernel. Linear stability analysis around homogeneous sliding produces $L_c$, and co-moving-frame analysis of steady fronts ($\xi=x-ct$) produces the width and speed scalings.

What would settle it

Measure a steady-state friction curve $f_{ss}(v)$ on a well-characterized multi-contact interface over slip velocities from well below $D/\varphi_*$ to well above it. If the curve is monotonic (no low-velocity maximum and no high-velocity minimum), then for any load $\tau_0$ there are not three fixed points, and the predicted rupture and healing speed spectra, creep-patch nucleation at $L_c$, and slip-pulse critical nuclei should be absent. Alternatively, in an edge-loaded slab, directly test the nucleation claim by measuring the creep-patch size at runaway as a function of $H$ and checking whether $L_c(H)$ grows like $\sqrt{H}$ for small $H$ and saturates for large $H$.

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Extended reading notes

Core claim

On the paper's own terms, the discovery is that Eq. (3)—the equality between the bulk-mediated interfacial shear and normal stresses and the interfacial constitutive relation—is the organizing equation of frictional dynamics. With an extended rate-and-state law that adds a linear elastic interfacial stress and a short-time cutoff, the steady-state friction curve $f_{ss}(v)$ acquires a generic N-shape: strengthening at very low velocities, weakening in the middle, and strengthening again above a minimum at $v_{\min}\simeq D/\varphi_*$. For loading stresses $\tau_0>\tau_{\min}$ the curve has three homogeneous fixed points, and the unstable middle fixed point, once coupled to bulk elasticity, organizes the dynamics. Homogeneous sliding on the weakening branch is unstable only for wavelengths longer than $L_c\sim\sqrt{\bar\mu H D/[-\sigma_0\,df_{ss}/d\log v]}$, and the same length controls when a growing creep patch loses stability. Steady rupture fronts in thin systems have width $\ell\sim\sqrt{\bar\mu H D/\Delta\tau_{p-r}}$ and speed $c\sim v_p\sqrt{\bar\mu H/(\Delta\tau_{p-r}D)}$; healing fronts have the opposite load dependence of speed, and their crossing with the rupture spectrum at a load $\tau_*$ produces slip pulses that act as critical nuclei for rupture.

Load-bearing premise

The predictions rest on the assumption that a real interface's steady-state friction curve is N-shaped—weakly strengthening at the lowest slip velocities, weakening in between, and strengthening again above a minimum—so that for $\tau_0>\tau_{\min}$ there are exactly three fixed points; if an interface lacks the low-velocity strengthening branch, or if thermal weakening at high speeds removes the high-velocity minimum, the three-fixed-point structure and the predicted creep-patch, front, and pulse behavior would change.

Editorial extensions

If this is right

  • A velocity-weakening interface is not unstable at arbitrarily long wavelengths: perturbations shorter than $L_c$ decay, so increasing body stiffness or height stabilizes sliding, and the marginal mode sets the nucleation length for runaway slip.
  • Under edge loading, the onset of sliding is a spatially extended creep-patch process: the patch length grows like $\sqrt{H}$ in thin systems and linearly in time in tall systems, and a runaway begins only when the patch reaches $L_c(H)$, which can be computed from homogeneous stability.
  • Rupture-front profiles from thin systems collapse when coordinates are rescaled by $\sqrt{H}$, with width $\ell\sim\sqrt{\bar\mu H D/\Delta\tau_{p-r}}$ and speed $c\sim v_p\sqrt{\bar\mu H/(\Delta\tau_{p-r}D)}$, giving a direct experimental signature.
  • Rupture speed grows from a finite minimum near $\tau_{\min}$ and saturates at the wave speed, while healing speed decreases with load; the two spectra cross at $\tau_*$, where slip pulses appear, and these pulses behave like critical nuclei in a first-order-like transition.
  • Residual stress behind a rupture is not intrinsic to the friction law: steady finite-height fronts leave $\tau_r=\tau_0$, but transient infinite-height ruptures leave a finite stress drop, so interpreting stress drops requires the bulk dynamics.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Because the quantitative predictions hang on the N-shape of $f_{ss}(v)$ rather than on its microscopic origin, the same $L_c$, $\ell$, and $c$ scalings should transfer to any interface with that shape—including lubricated contacts, whose Stribeck curve the paper notes is similar; this transfer is an extrapolation the paper suggests but does not demonstrate.
  • The slip-pulse critical-nucleus picture implies a stochastic nucleation problem not treated here: for a locked interface held above $\tau_*$, the waiting time for a rupture should be controlled by how often local fluctuations exceed the pulse width $L(\tau_0)$, which is testable in controlled loading protocols.
  • The model deliberately excludes high-velocity thermal weakening; at seismic slip rates that weakening would remove the high-velocity strengthening branch, turning the N-shape into a different shape and altering the predicted speed saturation and stress drops.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

1 major / 5 minor

Summary. This feature paper argues that the dynamics of spatially-extended frictional systems are governed by an inseparable coupling between the interfacial constitutive law and bulk elasticity, encapsulated in Eq. (3). The authors first review conventional rate-and-state friction, identify two limitations (absence of a linear reversible interfacial response and divergence at short contact times), and propose an extended rate-and-state model with an interfacial elastic stress (Eqs. (9)-(10)) and a short-time cutoff (Eq. (12)). They then derive an N-shaped steady-state friction curve (Fig. 3) and analyze how this interfacial law, combined with bulk elasticity, controls the linear stability of homogeneous sliding (Eq. (17) for the critical length Lc), the nucleation and propagation of creep patches (Sec. IV B), and steady-state propagating rupture fronts, healing fronts, and slip pulses (Sec. IV C, Eqs. (18)-(20)). The paper supports its analytical scaling predictions with quasi-1D and 2D treadmill FEM calculations, and it demonstrates the extended friction model on load-hold-unload experiments (Fig. 2).

Significance. If the results hold, this paper provides a useful synthesis of a substantial body of work on the interface-bulk coupling in frictional systems. Its strengths include clean analytical scaling derivations for Lc, the transition length l, and the propagation speed c; direct comparison of these scalings against FEM calculations over a 16-fold range of H (Fig. 6-7); and several falsifiable predictions, such as the c(τ0) spectrum with a finite minimal speed near τmin and the H-dependent collapse of rupture-front profiles. The paper is also transparent about its constitutive assumptions and about the regimes it does not cover, which is commendable. The central caveat is that the propagating-mode taxonomy in Sec. IV C depends on the N-shaped steady-state friction curve, a constitutive assumption that is not itself a consequence of the interface-bulk coupling in Eq. (3).

major comments (1)
  1. [Sec. IV C and Sec. II B 2] The propagating-mode analysis in Sec. IV C (the three-fixed-point structure, the rupture/healing/slip-pulse classification, the speed spectra in Fig. 7, and the slip-pulse nucleation scenario in Fig. 8) presupposes the N-shaped steady-state friction curve of Fig. 3, with a low-velocity strengthening branch, an intermediate velocity-weakening branch, and a high-velocity strengthening branch below the onset of thermal weakening. This shape is not implied by the interface-bulk coupling in Eq. (3); it follows from the specific constitutive choices in Eqs. (A1)-(A3), and the paper itself notes in Sec. II B 2 that for α>β the curve is purely velocity-strengthening and that thermal softening at very high slip rates is excluded. For a real interface that lacks the low-velocity strengthening branch, or for which flash heating or thermal weakening sets in before the minimum at vmin, the three-fixed-point structure disappears, and the predicted rupture and healing speed spectra and the slip-pulse nucleation scenario would change qualitatively. Because the abstract and conclusions present these propagating modes as generic outcomes of the interface-bulk interplay, this constitutive assumption is load-bearing for the paper's central claim and should be explicitly flagged as a condition on those claims, not merely noted as a caveat deep in Sec. II B 2; I recommend adding a qualifier to the abstract and conclusions.
minor comments (5)
  1. [Sec. II B 1 and Appendix B] The demonstration in Fig. 2b, presented as a semi-quantitative reproduction of the load-hold-unload experiments, is partly constructed: the interfacial elastic stiffness ratio µ0/h is extracted from the initial linear slope of the very same experimental data, so the agreement is a fit rather than an independent prediction. The authors disclose this in Appendix B, but the main text should make clearer that Fig. 2b is a consistency check, not a parameter-free validation.
  2. [Figure 2] In the reproduction of Fig. 2a, neither the shear force axis nor the slip displacement axis is explicitly labeled with units in the figure or its caption; since the figure is compared with experimental data from [50], the axes should be identified (e.g., FS in N and δ in µm) to allow the reader to assess the claimed semi-quantitative agreement.
  3. [Throughout] There are several typographical errors that should be corrected in a revision: 'viscoealstic' (Sec. II B 1), 'Bolzmann' (Sec. II A), 'lenthscale' (Sec. IV C), 'here with' instead of 'here' (Sec. IV C), and 'Sciense & Buisness' in reference [2].
  4. [Sec. IV C, Eq. (18)] The scaling relation c/l ∼ vp/D is introduced with a brief heuristic argument about accumulated slip; the sentence that this relation 'can be somewhat more formally rationalized using Eq. (8)' would benefit from a short derivation or a specific reference, since Eq. (18) is used as the basis for the subsequent scaling predictions in Eqs. (19)-(20).
  5. [Sec. III, Eq. (14)] The transition from Eq. (13) to Eq. (14) states that in the quasi-static limit the radiation-damping term is negligible, but the text does not explain why the time-integral structure in s(x,t) also drops out; a sentence clarifying that Eq. (14) corresponds to a quasi-static, non-inertial limit would prevent confusion.

Circularity Check

1 steps flagged · score 2.0 of 10

The Fig. 2b 'reproduction' of the PMMA experiments fits mu0/h and tau_c to the same FS(delta) data it reproduces; the central stability and rupture-front scalings are otherwise self-contained.

  1. fitted input called prediction [Sec. II B 1 and Appendix B (Eq. (11), Fig. 2b; determination of mu0/h and tau_c).]
    ""The only missing parameter is the interfacial elasticity ratio mu0/h, which is directly extracted from the initial linear slope in the FS(delta) experimental data (dashed line in Fig. 2a) according to dFS/ddelta= mu0 FN / (h sigma_H) [1 + b log(1 + phi(t=0)/phi*)], resulting in f~0 = D mu0/(h sigma_H) = 0.209" ... "we set tau_c = 70 MPa" ... "The solutions of these equations for the two experimental protocols ... are presented in Fig. 2b, reproducing all of the experimental observations semi-quantitatively.""

    The extended model is said to reproduce the experimental FS(delta) response of Fig. 2a, but the elastic stiffness ratio mu0/h is extracted from the initial linear slope of that same dataset, and the yield stress tau_c is chosen so that irreversible response begins near 7 N in that same dataset. The linear branch of the model therefore matches the experiment by construction, and the agreement in Fig. 2b is a consistency check of the fitted parameters rather than an independent prediction of the constitutive extension. This fit is localized to the small-stress illustration and does not feed the Lc, l, or c scalings of Secs. IV A-C, whose parameters are fixed in Table I rather than fitted to rupture properties.

full rationale

The central derivations of the paper are not circular. Eq. (17) and Eqs. (19)-(20) follow from linearization of Eq. (3) plus the stated constitutive equations and are compared with FEM calculations and quasi-1D calculations whose material parameters are listed in Table I; neither the critical nucleation length nor the rupture-front width and speed are used to fit those parameters, so the reported agreement is a nontrivial check of the analytical scalings. The N-shaped steady-state curve of Fig. 3 is an explicit constitutive assumption built from the cutoff in Eq. (12), the aging law, and g(v), with the paper itself noting that for alpha > beta the curve is purely velocity-strengthening and that high-velocity thermal softening is excluded; this is a model limitation rather than a circular derivation, since the shape is not claimed to be a consequence of the interface-bulk coupling. The heavy self-citation (e.g., refs. 43, 60, 61, 87, 102) is visible, but the load-bearing formulas are restated and derived in the present text, and no self-citation is invoked as a uniqueness theorem to forbid alternatives. The one genuine circular element is the small-stress example: Appendix B fits mu0/h to the initial slope of the same FS(delta) data shown in Fig. 2a and chooses tau_c to match the onset of nonlinearity in that data, then presents the resulting curves as reproducing the observations. Because this fitted demonstration is secondary, and the paper explicitly disclaims quantitative fitting ('no attempt has been made to quantitatively reproduce the experimental data'), the appropriate score is low rather than a finding of pervasive circularity.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central theoretical results (Lc, l, c scalings) are derived analytically from the extended RSF law and linear elastodynamics without fitting to the displayed FEM data; that part of the ledger is clean. The two parameters that carry circular risk are tau_c and mu0/h used in the Fig. 2b demonstration, both set using the experimental data of [50] that the model is then said to reproduce. The remaining entries are standard domain assumptions (linear elasticity, locality of the interface law, quasi-static approximation) and the specific N-shape of the steady-state friction curve, which is load-bearing for the mode analysis.

free parameters (4)
  • Interfacial yield stress tau_c = 70 MPa for Fig. 2b
    Chosen so that irreversible slip onset in the model occurs near 7 N in the load-hold-unload protocol of Berthoud and Baumberger 1998 [50]; a fit to the same experimental data the model is said to reproduce.
  • Interfacial elastic stiffness ratio mu0/h (through f~0) = f~0 = D mu0/(h sigma_H) = 0.209 for Fig. 2b
    Extracted directly from the initial linear slope of the FS(delta) experimental data (Appendix B), making the Fig. 2b demonstration a parameter-based reproduction rather than a parameter-free prediction.
  • Velocity cutoff v* in g(v) = 10^-7 m/s
    A regularization parameter in g(v) = sqrt(1 + (v*/v)^2); the authors state predictions are insensitive to its precise value as long as it is much smaller than other velocity scales.
  • Mass density rho in treadmill FEM = 60 kg/m^3
    Set unrealistically small so that wave speeds are unrealistically large, deliberately suppressing inertial saturation; a computational convenience rather than a physical material property.
assumptions (5)
  • domain assumption Linear elastodynamics describes the bulk (Hooke's law with momentum balance rho u_ddot = div sigma).
    Stated in Sec. III and used throughout; the authors list viscoelasticity, poroelasticity, plasticity, and off-fault damage as possible additional bulk physics in Sec. V.
  • domain assumption The interfacial constitutive relation is local, depending on delta, v, phi, tau_el but not on spatial derivatives.
    Assumed in the RSF framework (Eq. (1)); nonlocality enters only through the bulk functionals F_tau and F_sigma (Eqs. (2)-(3)).
  • domain assumption The quasi-static approximation holds for creep patches and for small-H rupture fronts (neglect of radiation damping and inertial terms).
    Used in deriving Lc (Eq. (17)) and the small-H scaling (Eq. (19)); the paper notes that strongly inertial effects set in only as c approaches the wave speed.
  • domain assumption For creep patches, the average slip velocity scales with the driving velocity vd, so homogeneous linear stability applies locally.
    Invoked in Sec. IV B to predict creep-patch instability at Lc(H); validated a posteriori against FEM (Fig. 5).
  • domain assumption The steady-state friction curve fss(v) is N-shaped with three fixed points for tau0 > tau_min.
    Underlies the rupture, healing, and slip-pulse analysis in Sec. IV C; depends on the short-time cutoff (Eq. (12)) and aging law (Eq. (8)), and is asserted to be supported by experimental data [43].

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Pith. "Pith review of Spatiotemporal dynamics of frictional systems: The interplay of interfacial friction and bulk elasticity." pith.science (2026). https://pith.science/paper/VJXHYDXO

@misc{pith2026190802820,
  author       = {Pith},
  title        = {Pith review of: Spatiotemporal dynamics of frictional systems: The interplay of interfacial friction and bulk elasticity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VJXHYDXO}},
  note         = {Machine review of arXiv:1908.02820}
}
read the original 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 the 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.

Figures

Figures reproduced from arXiv: 1908.02820 by the authors.

Figure 1
Figure 1. FIG. 1: A schematic of a frictional system. Two macroscopic bodies are in contact, the interface between them is [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Frictional dynamics under small stresses and the existence of a linear reversible frictional response. (a) [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: The generic form of steady-state frictional resistance [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: FIG. 4: Linear stability spectrum of homogeneous steady sliding. Plotted is the growth rate of perturbations [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: Loss of stability in transient, spatially inhomogeneous frictional dynamics under sideways loading (adapted [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: Spatial profiles of steady-state rupture fronts for varying [PITH_FULL_IMAGE:figures/full_fig_p014_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: Steady-state rupture front speeds. (a) The propagation speed [PITH_FULL_IMAGE:figures/full_fig_p016_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8: (a) A steady-state slip pulse of characteristic size [PITH_FULL_IMAGE:figures/full_fig_p017_8.png]

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Reference graph

Works this paper leans on

118 extracted references · 71 canonical work pages

  1. [1]

    The Friction and Lubrication of Solids ; Clarendon Press, 1950

    Bowden, F.P.; Tabor, D. The Friction and Lubrication of Solids ; Clarendon Press, 1950

    1950

  2. [2]

    Sliding friction: physical principles and applications ; Springer Sciense & Buisness Media, 1998

    Persson, B.N.J. Sliding friction: physical principles and applications ; Springer Sciense & Buisness Media, 1998

    1998

  3. [3]

    Brittle Fracture Theory Describes the Onset of Frictional Motion

    Svetlizky, I.; Bayart, E.; Fineberg, J. Brittle Fracture Theory Describes the Onset of Frictional Motion. Annu. Rev. Condens. Matter Phys. 2019, 10, 031218–013327. doi:10.1146/annurev-conmatphys-031218-013327. 21

    doi:10.1146/annurev-conmatphys-031218-013327 2019

  4. [4]

    Simulations of atomic-scale sliding friction

    Sørensen, M.; Jacobsen, K.; Stoltze, P. Simulations of atomic-scale sliding friction. Phys. Rev. B 1996, 53, 2101–2113. doi:10.1103/PhysRevB.53.2101

    work page doi:10.1103/physrevb.53.2101 1996

  5. [5]

    Frictional ageing from interfacial bonding and the origins of rate and state friction

    Li, Q.; Tullis, T.E.; Goldsby, D.L.; Carpick, R.W. Frictional ageing from interfacial bonding and the origins of rate and state friction. Nature 2011, 480, 233–236. doi:10.1038/nature10589

    work page doi:10.1038/nature10589 2011

  6. [6]

    Colloquium: Modeling friction: From nanoscale to mesoscale

    Vanossi, A.; Manini, N.; Urbakh, M.; Zapperi, S.; Tosatti, E. Colloquium: Modeling friction: From nanoscale to mesoscale. Rev. Mod. Phys. 2013, 85, 529–552. doi:10.1103/RevModPhys.85.529

    doi:10.1103/revmodphys.85.529 2013

  7. [7]

    A Survey of Models, Analysis Tools and Compensations Methods for the Control of Machines with Friction.Automatica 1994, 30, 1083–1138

    Armstrong-H´ elouvry, B.; Dupont, P.; Canudas de Wit, C. A Survey of Models, Analysis Tools and Compensations Methods for the Control of Machines with Friction.Automatica 1994, 30, 1083–1138. doi:http://dx.doi.org/10.1016/0005- 1098(94)90209-7

    doi:10.1016/0005- 1994

  8. [8]

    Hysteretic effects of dry friction: modelling and experi- mental studies

    Wojewoda, J.; Stefa´ nski, A.; Wiercigroch, M.; Kapitaniak, T. Hysteretic effects of dry friction: modelling and experi- mental studies. Philos. Trans. A. Math. Phys. Eng. Sci. 2008, 366, 747–765. doi:10.1098/rsta.2007.2125

    arXiv 2008

Show all 118 references
  1. [9]

    Laboratoty-derived friction laws and their application to seismic faulting

    Marone, C. Laboratoty-derived friction laws and their application to seismic faulting. Annu. Rev. Earth Planet. Sci. 1998, 26, 643–696. doi:10.1146/annurev.earth.26.1.643

    1998 doi

  2. [10]

    Dynamic ruptures in recent models of earthquake faults

    Ben-Zion, Y. Dynamic ruptures in recent models of earthquake faults. J. Mech. Phys. Solids 2001, 49, 2209–2244. doi:10.1016/S0022-5096(01)00036-9

    2001 doi

  3. [11]

    The mechanics of earthquakes and faulting ; Cambridge university press, 2002

    Scholz, C.H. The mechanics of earthquakes and faulting ; Cambridge university press, 2002

    2002

  4. [12]

    The physics of rock failure and earthquakes ; Cambridge University Press, 2013

    Ohnaka, M. The physics of rock failure and earthquakes ; Cambridge University Press, 2013

    2013

  5. [13]

    Friction experiments on the nanometre scale

    Gnecco, E.; Bennewitz, R.; Gyalog, T.; Meyer, E. Friction experiments on the nanometre scale. J. Phys. Condens. Matter 2001, 13, 202. doi:10.1088/0953-8984/13/31/202

    2001 doi

  6. [14]

    Solid friction from stickslip down to pinning and aging

    Baumberger, T.; Caroli, C. Solid friction from stickslip down to pinning and aging. Adv. Phys. 2006, 55, 279–348. doi:10.1080/00018730600732186

    2006 doi

  7. [15]

    Collective behavior of earthquakes and faults: Continuum-discrete transitions, progressive evolutionary changes, and different dynamic regimes

    Ben-Zion, Y. Collective behavior of earthquakes and faults: Continuum-discrete transitions, progressive evolutionary changes, and different dynamic regimes. Rev. Geophys. 2008, 46, RG4006. doi:10.1029/2008RG000260

    2008 doi

  8. [16]

    Modeling and simulation in tribology across scales: An overview

    Vakis, A.; Yastrebov, V.; Scheibert, J.; Nicola, L.; Dini, D.; Minfray, C.; Almqvist, A.; Paggi, M.; Lee, S.; Limbert, G.; Molinari, J.; Anciaux, G.; Aghababaei, R.; Echeverri Restrepo, S.; Papangelo, A.; Cammarata, A.; Nicolini, P.; Putignano, C.; Carbone, G.; Stupkiewicz, S....

    2018 doi

  9. [17]

    Time-dependent friction and the mechanics of stick-slip

    Dieterich, J.H. Time-dependent friction and the mechanics of stick-slip. Pure Appl. Geophys. 1978, 116, 790–806. doi:10.1007/BF00876539

    1978 doi

  10. [18]

    Modeling of rock friction: 1

    Dieterich, J.H. Modeling of rock friction: 1. Experimental results and constitutive equations. J. Geophys. Res. Solid Earth 1979, 84, 2161. doi:10.1029/JB084iB05p02161

    1979 doi

  11. [19]

    Stability of Steady Frictional Slipping

    Rice, J.R.; Ruina, A.L. Stability of Steady Frictional Slipping. J. Appl. Mech. 1983, 50, 343–349. doi:10.1115/1.3167042

    1983 doi

  12. [20]

    Slip instability and state variable friction laws

    Ruina, A.L. Slip instability and state variable friction laws. J. Geophys. Res. 1983, 88, 10359–10370. doi:10.1029/JB088iB12p10359

    1983 doi

  13. [21]

    Creep, stick-slip, and dry-friction dynamics: Experiments and a heuristic model

    Heslot, F.; Baumberger, T.; Perrin, B.; Caroli, B.; Caroli, C. Creep, stick-slip, and dry-friction dynamics: Experiments and a heuristic model. Phys. Rev. E 1994, 49, 4973–4988. doi:10.1103/PhysRevE.49.4973

    1994 doi

  14. [22]

    Accelerated creep as a precursor of friction instability and earthquake prediction

    Popov, V.L.; Grzemba, B.; Starcevic, J.; Fabry, C. Accelerated creep as a precursor of friction instability and earthquake prediction. Phys. Mesomech. 2010, 13, 283–291. doi:10.1016/j.physme.2010.11.009

    2010 doi

  15. [23]

    A model for the nucleation of earthquake slip

    Dieterich, J.H. A model for the nucleation of earthquake slip. In Earthq. source Mech.; Wiley Online Library, 1986; pp. 37–47. doi:10.1029/GM037p0037

    1986 doi

  16. [24]

    The mechanics of earthquake rupture

    Rice, J.R. The mechanics of earthquake rupture. In Phys. Earth’s Inter. ; 1980; pp. 555–649. doi:10.1.1.161.3251

    1980

  17. [25]

    The Nature of the Static and Kinetic Coefficients of Friction

    Rabinowicz, E. The Nature of the Static and Kinetic Coefficients of Friction. J. Appl. Phys. 1951, 22, 1373–1379. doi:10.1063/1.1699869

    1951 doi

  18. [26]

    Direct observation of frictional contacts: New insights for state-dependent properties

    Dieterich, J.H.; Kilgore, B.D. Direct observation of frictional contacts: New insights for state-dependent properties. Pure Appl. Geophys. 1994, 143, 283–302. doi:10.1007/BF00874332

    1994 doi

  19. [27]

    Detachment fronts and the onset of dynamic friction

    Rubinstein, S.M.; Cohen, G.; Fineberg, J. Detachment fronts and the onset of dynamic friction. Nature 2004, 430, 1005–

    2004

  20. [28]

    Dynamics of Precursors to Frictional Sliding

    Rubinstein, S.M.; Cohen, G.; Fineberg, J. Dynamics of Precursors to Frictional Sliding. Phys. Rev. Lett. 2007, 98, 226103. doi:10.1103/PhysRevLett.98.226103

    2007 doi

  21. [29]

    Monitoring frictional strength with acoustic wave transmission

    Nagata, K.; Nakatani, M.; Yoshida, S. Monitoring frictional strength with acoustic wave transmission. Geophys. Res. Lett. 2008, 35, L06310. doi:10.1029/2007GL033146

    2008 doi

  22. [30]

    On a model of frictional sliding.Pure Appl

    Estrin, Y.; Br´ echet, Y. On a model of frictional sliding.Pure Appl. Geophys.1996, 147, 745–762. doi:10.1007/BF01089700

    1996 doi

  23. [31]

    Time-dependent friction in rocks

    Dieterich, J.H. Time-dependent friction in rocks. J. Geophys. Res. 1972, 77, 3690–3697. doi:10.1029/JB077i020p03690

    1972 doi

  24. [32]

    The roles of time and displacement in the evolution effect in rock friction, 1994

    Beeler, N.M.; Tullis, T.E.; Weeks, J.D. The roles of time and displacement in the evolution effect in rock friction, 1994. doi:10.1029/94GL01599

    1994 doi

  25. [33]

    Physical analysis of the state- and rate-dependent friction law: Static friction, 1999

    Berthoud, P.; Baumberger, T.; G’Sell, C.; Hiver, J.M. Physical analysis of the state- and rate-dependent friction law: Static friction, 1999. doi:10.1103/PhysRevB.59.14313

    1999 doi

  26. [34]

    Low-velocity friction between macroscopic solids

    Bureau, L.; Baumberger, T.; Caroli, C.; Ronsin, O. Low-velocity friction between macroscopic solids. Comptes Rendus l’Acad´ emie des Sci. - Ser. IV - Phys. 2001, 2, 699–707. doi:10.1016/S1296-2147(01)01212-4

    2001 doi

  27. [35]

    Slip-stick and the evolution of frictional strength

    Ben-David, O.; Rubinstein, S.M.; Fineberg, J. Slip-stick and the evolution of frictional strength. Nature 2010, 463, 76–9. doi:10.1038/nature08676

    2010 doi

  28. [36]

    Constitutive behavior and stability of frictional sliding of granite

    Tullis, T.E.; Weeks, J.D. Constitutive behavior and stability of frictional sliding of granite. Pure Appl. Geophys. 1986, 124, 383–414. doi:10.1007/BF00877209. 22

    1986 doi

  29. [37]

    Velocity dependent friction of granite over a wide range of conditions

    Kilgore, B.D.; Blanpied, M.L.; Dieterich, J.H. Velocity dependent friction of granite over a wide range of conditions. Geophys. Res. Lett. 1993, 20, 903–906. doi:10.1029/93GL00368

    1993 doi

  30. [38]

    Physical analysis of the state- and rate-dependent friction law

    Baumberger, T.; Berthoud, P. Physical analysis of the state- and rate-dependent friction law. II. Dynamic friction. Phys. Rev. B 1999, 60, 3928–3939. doi:10.1103/PhysRevB.60.3928

    1999 doi

  31. [39]

    Fault weakening and earthquake instability by powder lubrication

    Reches, Z.; Lockner, D.A. Fault weakening and earthquake instability by powder lubrication. Nature 2010, 467, 452–455. doi:10.1038/nature09348

    2010 doi

  32. [40]

    Rate and state dependent friction and the stability of sliding between elastically deformable solids

    Rice, J.R.; Lapusta, N.; Ranjith, K. Rate and state dependent friction and the stability of sliding between elastically deformable solids. J. Mech. Phys. Solids 2001, 49, 1865–1898. doi:10.1016/S0022-5096(01)00042-4

    2001 doi

  33. [41]

    Conceptual and physical clarification of rate and state friction: Frictional sliding as a thermally activated rheology

    Nakatani, M. Conceptual and physical clarification of rate and state friction: Frictional sliding as a thermally activated rheology. J. Geophys. Res. Solid Earth 2001, 106, 13347–13380. doi:10.1029/2000JB900453

    2001 doi

  34. [42]

    The instantaneous rate dependence in low temperature labo- ratory rock friction and rock deformation experiments

    Beeler, N.M.; Tullis, T.E.; Kronenberg, A.K.; Reinen, L.A. The instantaneous rate dependence in low temperature labo- ratory rock friction and rock deformation experiments. J. Geophys. Res. 2007, 112, B07310. doi:10.1029/2005JB003772

    2007 doi

  35. [43]

    On the velocity-strengthening behavior of dry friction

    Bar-Sinai, Y.; Spatschek, R.; Brener, E.A.; Bouchbinder, E. On the velocity-strengthening behavior of dry friction. J. Geophys. Res. Solid Earth 2014, 119, 1738–1748. doi:10.1002/2013JB010586

    2014 doi

  36. [44]

    Multimechanism friction constitutive model for ultrafine quartz gouge at hypocentral condi- tions

    Chester, F.M.; Higgs, N.G. Multimechanism friction constitutive model for ultrafine quartz gouge at hypocentral condi- tions. J. Geophys. Res. 1992, 97, 1859–1870. doi:10.1029/91JB02349

    1992 doi

  37. [45]

    Self-healing slip pulse on a frictional surface

    Perrin, G.; Rice, J.R.; Zheng, G. Self-healing slip pulse on a frictional surface. J. Mech. Phys. Solids 1995, 43, 1461–1495. doi:10.1016/0022-5096(95)00036-I

    1995 doi

  38. [46]

    Steady and transient sliding under rate-and-state friction

    Putelat, T.; Dawes, J.H. Steady and transient sliding under rate-and-state friction. J. Mech. Phys. Solids 2015, 78, 70–93. doi:10.1016/j.jmps.2015.01.016

    2015 doi

  39. [47]

    Conditions under which velocity-weakening friction allows a self-healing versus a cracklike mode of rupture

    Zheng, G.; Rice, J.R. Conditions under which velocity-weakening friction allows a self-healing versus a cracklike mode of rupture. Bull. Seismol. Soc. Am. 1998, 88, 1466–1483

    1998

  40. [48]

    The effect of a tangential force on the contact of metallic bodies

    Courtney-Pratt, J.S.; Eisner, E. The effect of a tangential force on the contact of metallic bodies. Proc. R. Soc. Lond. A. 1957, 238, 529–550. doi:10.1098/rspa.1957.0016

    1957

  41. [49]

    Elastic Deformation and the Laws of Friction

    Archard, J.F. Elastic Deformation and the Laws of Friction. Proc. R. Soc. A Math. Phys. Eng. Sci. 1957, 243, 190–205. doi:10.1098/rspa.1957.0214

    1957

  42. [50]

    Shear stiffness of a solid-solid multicontact interface

    Berthoud, P.; Baumberger, T. Shear stiffness of a solid-solid multicontact interface. Proc. R. Soc. A Math. Phys. Eng. Sci. 1998, 454, 1615–1634. doi:10.1098/rspa.1998.0223

    1998

  43. [51]

    Shear response of a frictional interface to a normal load modulation

    Bureau, L.; Baumberger, T.; Caroli, C. Shear response of a frictional interface to a normal load modulation. Phys. Rev. E 2000, 62, 6810–6820. doi:10.1103/PhysRevE.62.6810

    doi

  44. [52]

    Transverse and normal interfacial stiffness of solids with randomly rough surfaces

    Campa˜ n´ a, C.; Persson, B.N.J.; M¨ user, M.H. Transverse and normal interfacial stiffness of solids with randomly rough surfaces. J. Phys. Condens. Matter 2011, 23, 085001. doi:10.1088/0953-8984/23/8/085001

    2011 doi

  45. [53]

    Finite Element Simulations of Fiber Pull-Out

    Povirk, G.L.; Needleman, A. Finite Element Simulations of Fiber Pull-Out. J. Eng. Mater. Technol. 1993, 115, 286. doi:10.1115/1.2904220

    1993 doi

  46. [54]

    Frictional sliding modes along an interface between identical elastic plates subject to shear impact loading

    Coker, D.; Lykotrafitis, G.; Needleman, A.; Rosakis, A.J. Frictional sliding modes along an interface between identical elastic plates subject to shear impact loading. J. Mech. Phys. Solids 2005, 53, 884–922. doi:10.1016/j.jmps.2004.11.003

    2005 doi

  47. [55]

    Properties of dynamic rupture and energy partition in a solid with a frictional interface

    Shi, Z.; Ben-Zion, Y.; Needleman, A. Properties of dynamic rupture and energy partition in a solid with a frictional interface. J. Mech. Phys. Solids 2008, 56, 5–24. doi:10.1016/j.jmps.2007.04.006

    2008 doi

  48. [56]

    Dynamics of Transition from Static to Kinetic Friction

    Braun, O.M.; Barel, I.; Urbakh, M. Dynamics of Transition from Static to Kinetic Friction. Phys. Rev. Lett. 2009, 103, 194301. doi:10.1103/PhysRevLett.103.194301

    2009 doi

  49. [57]

    Slip modes and partitioning of energy during dynamic frictional sliding between identical elasticviscoplastic solids

    Shi, Z.; Needleman, A.; Ben-Zion, Y. Slip modes and partitioning of energy during dynamic frictional sliding between identical elasticviscoplastic solids. Int. J. Fract. 2010, 162, 51–67. doi:10.1007/s10704-009-9388-6

    2010 doi

  50. [58]

    Slow Cracklike Dynamics at the Onset of Frictional Sliding

    Bouchbinder, E.; Brener, E.A.; Barel, I.; Urbakh, M. Slow Cracklike Dynamics at the Onset of Frictional Sliding. Phys. Rev. Lett. 2011, 107, 235501. doi:10.1103/PhysRevLett.107.235501

    2011 doi

  51. [59]

    Slip Sequences in Laboratory Experiments Resulting from Inhomogeneous Shear as Analogs of Earthquakes Associated with a Fault Edge.Pure Appl

    Rubinstein, S.M.; Barel, I.; Reches, Z.; Braun, O.M.; Urbakh, M.; Fineberg, J. Slip Sequences in Laboratory Experiments Resulting from Inhomogeneous Shear as Analogs of Earthquakes Associated with a Fault Edge.Pure Appl. Geophys. 2011, 168, 2151–2166. doi:10.1007/s00024-010-0239-1

    2011 doi

  52. [60]

    Slow rupture of frictional interfaces

    Bar Sinai, Y.; Brener, E.A.; Bouchbinder, E. Slow rupture of frictional interfaces. Geophys. Res. Lett. 2012, 39, L03308. doi:10.1029/2011GL050554

    2012 doi

  53. [61]

    Instabilities at frictional interfaces: Creep patches, nucleation, and rupture fronts

    Bar-Sinai, Y.; Spatschek, R.; Brener, E.A.; Bouchbinder, E. Instabilities at frictional interfaces: Creep patches, nucleation, and rupture fronts. Phys. Rev. E 2013, 88, 060403. doi:10.1103/PhysRevE.88.060403

    2013 doi

  54. [62]

    Viscoelastic Properties of Polymers, 3rd Edition ; Wiley, 1980

    Ferry, J. Viscoelastic Properties of Polymers, 3rd Edition ; Wiley, 1980

    1980

  55. [63]

    On the Elasticity and Viscosity of Metals

    Thomson, W. On the Elasticity and Viscosity of Metals. Proc. R. Soc. London 1865, 14, 289–297. doi:10.1098/rspl.1865.0052

  56. [64]

    Elasticity and onset of frictional dissipation at a non-sliding multi-contact interface

    Bureau, L.; Caroli, C.; Baumberger, T. Elasticity and onset of frictional dissipation at a non-sliding multi-contact interface. Proc. R. Soc. A Math. Phys. Eng. Sci. 2003, 459, 2787–2805. doi:10.1098/rspa.2003.1146

    2003

  57. [65]

    Intrinsic and apparent short-time limits for fault healing: Theory, observations, and implica- tions for velocity-dependent friction

    Nakatani, M.; Scholz, C.H. Intrinsic and apparent short-time limits for fault healing: Theory, observations, and implica- tions for velocity-dependent friction. J. Geophys. Res. Solid Earth 2006, 111, 1–19. doi:10.1029/2005JB004096

    2006 doi

  58. [66]

    A revised rate- and state-dependent friction law obtained by constraining constitutive and evolution laws separately with laboratory data

    Nagata, K.; Nakatani, M.; Yoshida, S. A revised rate- and state-dependent friction law obtained by constraining constitutive and evolution laws separately with laboratory data. J. Geophys. Res. Solid Earth 2012, 117, B02314. doi:10.1029/2011JB008818

    2012 doi

  59. [67]

    The effect of loading rate on static friction and the rate of fault healing during the earthquake cycle

    Marone, C. The effect of loading rate on static friction and the rate of fault healing during the earthquake cycle. Nature 1998, 391, 69–72. doi:10.1038/34157

    1998 doi

  60. [68]

    Transition Between Frictional Slip and Ductile Flow for Halite Shear Zones at Room Temperature.Science 23 1986, 231, 711–714

    Shimamoto, T. Transition Between Frictional Slip and Ductile Flow for Halite Shear Zones at Room Temperature.Science 23 1986, 231, 711–714. doi:10.1126/science.231.4739.711

    1986 doi

  61. [69]

    Velocity-strengthening friction significantly affects interfacial dynamics, strength and dissipation

    Bar-Sinai, Y.; Spatschek, R.; Brener, E.A.; Bouchbinder, E. Velocity-strengthening friction significantly affects interfacial dynamics, strength and dissipation. Sci. Rep. 2015, 5, 7841. doi:10.1038/srep07841

    2015 doi

  62. [70]

    Friction falls towards zero in quartz rock as slip velocity approaches seismic rates

    Di Toro, G.; Goldsby, D.L.; Tullis, T.E. Friction falls towards zero in quartz rock as slip velocity approaches seismic rates. Nature 2004, 427, 436–439. doi:10.1038/nature02249

    2004 doi

  63. [71]

    Flash Heating Leads to Low Frictional Strength of Crustal Rocks at Earthquake Slip Rates

    Goldsby, D.L.; Tullis, T.E. Flash Heating Leads to Low Frictional Strength of Crustal Rocks at Earthquake Slip Rates. Science 2011, 334, 216–218. doi:10.1126/science.1207902

    2011 doi

  64. [72]

    Unstable slippage across a fault that separates elastic media of different elastic constants

    Weertman, J. Unstable slippage across a fault that separates elastic media of different elastic constants. J. Geophys. Res. Solid Earth 1980, 85, 1455–1461. doi:10.1029/JB085iB03p01455

    1980 doi

  65. [73]

    Frictional Sliding without Geometrical Reflection Symmetry

    Aldam, M.; Bar-Sinai, Y.; Svetlizky, I.; Brener, E.A.; Fineberg, J.; Bouchbinder, E. Frictional Sliding without Geometrical Reflection Symmetry. Phys. Rev. X 2016, 6, 041023. doi:10.1103/PhysRevX.6.041023

    2016 doi

  66. [74]

    Poroelastic effects destabilize mildly rate-strengthening friction to generate stable slow slip pulses

    Heimisson, E.R.; Dunham, E.M.; Almquist, M. Poroelastic effects destabilize mildly rate-strengthening friction to generate stable slow slip pulses. J. Mech. Phys. Solids 2019, 130, 262–279. doi:10.1016/j.jmps.2019.06.007

    2019 doi

  67. [75]

    A spectral method for three-dimensional elastodynamic fracture problems

    Geubelle, P.; Rice, J.R. A spectral method for three-dimensional elastodynamic fracture problems. J. Mech. Phys. Solids 1995, 43, 1791–1824. doi:10.1016/0022-5096(95)00043-I

    1995 doi

  68. [76]

    A numerical scheme for mode III dynamic fracture problems

    Morrissey, J.W.; Geubelle, P.H. A numerical scheme for mode III dynamic fracture problems. Int. J. Numer. Methods Eng. 1997, 40, 1181–1196. doi:10.1002/(SICI)1097-0207(19970415)40:7¡1181::AID-NME108¿3.0.CO;2-X

    1997 doi

  69. [77]

    Numerical analysis of dynamic debonding under 2D in-plane and 3D loading

    Breitenfeld, M.S.; Geubelle, P.H. Numerical analysis of dynamic debonding under 2D in-plane and 3D loading. Int. J. Fract. 1998, 93, 13–38. doi:10.1023/A:1007535703095

    1998 doi

  70. [78]

    Slip patterns and earthquake populations along different classes of faults in elastic solids

    Ben-Zion, Y.; Rice, J.R. Slip patterns and earthquake populations along different classes of faults in elastic solids. J. Geophys. Res. Solid Earth 1995, 100, 12959–12983. doi:10.1029/94JB03037

    1995 doi

  71. [79]

    The role of radiation damping in the modeling of repeated earthquake events

    Crupi, P.; Bizzarri, A. The role of radiation damping in the modeling of repeated earthquake events. Ann. Geophys. 2013, 56, R0111. doi:10.4401/ag-6200

    2013 doi

  72. [80]

    Relationship between displacements on a free surface and the stress on a fault

    Weertman, J. Relationship between displacements on a free surface and the stress on a fault. Bulletin of the Seismological Society of America 1965, 55, 945–953

    1965

  73. [81]

    Elementary fluid dynamics ; Oxford University Press, 1990

    Acheson, D.J. Elementary fluid dynamics ; Oxford University Press, 1990

    1990

  74. [82]

    Self-similar slip instability on interfaces with rate- and state-dependent friction

    Viesca, R.C. Self-similar slip instability on interfaces with rate- and state-dependent friction. Proc. R. Soc. A Math. Phys. Eng. Sci. 2016, 472, 20160254. doi:10.1098/rspa.2016.0254

    2016

  75. [83]

    Using fast vibrations to quench friction-induced oscillations

    Thomsen, J. Using fast vibrations to quench friction-induced oscillations. J. Sound Vib. 1999, 228, 1079–1102. doi:10.1006/jsvi.1999.2460

    1999

  76. [84]

    The role of friction film in friction, wear and noise of automotive brakes

    Rhee, S.; Jacko, M.; Tsang, P. The role of friction film in friction, wear and noise of automotive brakes. Wear 1991, 146, 89–97. doi:10.1016/0043-1648(91)90226-K

    1991 doi

  77. [85]

    Stick-Slip as a Mechanism for Earthquakes

    Brace, W.F.; Byerlee, J.D. Stick-Slip as a Mechanism for Earthquakes. Science 1966, 153, 990–992. doi:10.1126/science.153.3739.990

    1966 doi

  78. [86]

    Model for earthquake precursers based on premonitory fault slip

    Dieterich, J.H. Model for earthquake precursers based on premonitory fault slip. Trans. Geophys. Union 1975, 56, 1059– 1060

    1975

  79. [87]

    Critical Nucleation Length for Accelerating Frictional Slip

    Aldam, M.; Weikamp, M.; Spatschek, R.; Brener, E.A.; Bouchbinder, E. Critical Nucleation Length for Accelerating Frictional Slip. Geophys. Res. Lett. 2017, 44, 11,390–11,398. doi:10.1002/2017GL074939

    2017 doi

  80. [88]

    Earthquake nucleation on faults with rate-and state-dependent strength

    Dieterich, J.H. Earthquake nucleation on faults with rate-and state-dependent strength. Tectonophysics 1992, 211, 115–

    1992

  81. [89]

    Dynamic instabilities of frictional sliding at a bimaterial interface

    Brener, E.A.; Weikamp, M.; Spatschek, R.; Bar-Sinai, Y.; Bouchbinder, E. Dynamic instabilities of frictional sliding at a bimaterial interface. J. Mech. Phys. Solids 2016, 89, 149–173. doi:10.1016/j.jmps.2016.01.009

    2016 doi

  82. [90]

    Nucleation and early seismic propagation of small and large events in a crustal earthquake model

    Lapusta, N.; Rice, J.R. Nucleation and early seismic propagation of small and large events in a crustal earthquake model. J. Geophys. Res. Solid Earth 2003, 108, 2205. doi:10.1029/2001JB000793

    2003 doi

  83. [91]

    Earthquake nucleation on (aging) rate and state faults

    Rubin, A.M.; Ampuero, J.P. Earthquake nucleation on (aging) rate and state faults. J. Geophys. Res. Solid Earth 2005, 110, B11312. doi:10.1029/2005JB003686

    2005 doi

  84. [92]

    Earthquake nucleation on rate and state faults Aging and slip laws

    Ampuero, J.P.; Rubin, A.M. Earthquake nucleation on rate and state faults Aging and slip laws. J. Geophys. Res. Solid Earth 2008, 113, B01302. doi:10.1029/2007JB005082

    2008 doi

  85. [93]

    On the Propagation of Slip Fronts at Frictional Interfaces

    Kammer, D.S.; Yastrebov, V.A.; Spijker, P.; Molinari, J.F. On the Propagation of Slip Fronts at Frictional Interfaces. Tribol. Lett. 2012, 48, 27–32. doi:10.1007/s11249-012-9920-0

    2012 doi

  86. [94]

    Classical shear cracks drive the onset of dry frictional motion

    Svetlizky, I.; Fineberg, J. Classical shear cracks drive the onset of dry frictional motion. Nature 2014, 509, 205–208. doi:10.1038/nature13202

    2014 doi

  87. [95]

    Fracture and friction: Stick-slip motion

    Brener, E.A.; Malinin, S.V.; Marchenko, V.I. Fracture and friction: Stick-slip motion. Eur. Phys. J. E 2005, 17, 101–113. doi:10.1140/epje/i2004-10112-3

    2005 doi

  88. [96]

    On the slip-weakening behavior of rate- and state dependent constitutive laws

    Cocco, M.; Bizzarri, A. On the slip-weakening behavior of rate- and state dependent constitutive laws. Geophys. Res. Lett. 2002, 29, 1516. doi:10.1029/2001GL013999

    2002 doi

  89. [97]

    Dynamic Fracture Mechanics; Cambridge university press: Cambridge, 1998

    Freund, L.B. Dynamic Fracture Mechanics; Cambridge university press: Cambridge, 1998

    1998

  90. [98]

    The Dynamics of the Onset of Frictional Slip

    Ben-David, O.; Cohen, G.; Fineberg, J. The Dynamics of the Onset of Frictional Slip. Science 2010, 330, 211–214. doi:10.1126/science.1194777

    2010 doi

  91. [99]

    Slow Earthquakes, Preseismic Velocity Changes, and the Origin of Slow Frictional Stick-Slip

    Kaproth, B.M.; Marone, C. Slow Earthquakes, Preseismic Velocity Changes, and the Origin of Slow Frictional Stick-Slip. Science 2013, 341, 1229–1232. doi:10.1126/science.1239577

    2013 doi

  92. [100]

    The geophysics, geology and mechanics of slow fault slip

    B¨ urgmann, R. The geophysics, geology and mechanics of slow fault slip. Earth Planet. Sci. Lett. 2018, 495, 112–134. doi:10.1016/j.epsl.2018.04.062

    2018 doi

  93. [101]

    A phase-plane analysis of localized frictional waves

    Putelat, T.; Dawes, J.H.; Champneys, A.R. A phase-plane analysis of localized frictional waves. Proc. R. Soc. A Math. 24 Phys. Eng. Sci. 2017, 473, 20160606. doi:10.1098/rspa.2016.0606

    2017

  94. [102]

    Unstable Slip Pulses and Earthquake Nucleation as a Nonequilibrium First-Order Phase Transition

    Brener, E.A.; Aldam, M.; Barras, F.; Molinari, J.F.; Bouchbinder, E. Unstable Slip Pulses and Earthquake Nucleation as a Nonequilibrium First-Order Phase Transition. Phys. Rev. Lett. 2018, 121, 234302. doi:10.1103/PhysRevLett.121.234302

    2018 doi

  95. [103]

    Evidence for and implications of self-healing pulses of slip in earthquake rupture

    Heaton, T.H. Evidence for and implications of self-healing pulses of slip in earthquake rupture. Phys. Earth Planet. Inter. 1990, 64, 1–20. doi:10.1016/0031-9201(90)90002-F

    1990 doi

  96. [104]

    Earthquake ruptures with thermal weakening and the operation of major faults at low overall stress levels

    Noda, H.; Dunham, E.M.; Rice, J.R. Earthquake ruptures with thermal weakening and the operation of major faults at low overall stress levels. J. Geophys. Res. Solid Earth 2009, 114, B07302. doi:10.1029/2008JB006143

    2009 doi

  97. [105]

    Universal nucleation length for slip-weakening rupture instability under nonuniform fault loading

    Uenishi, K.; Rice, J.R. Universal nucleation length for slip-weakening rupture instability under nonuniform fault loading. J. Geophys. Res. Solid Earth 2003, 108, 2042. doi:10.1029/2001JB001681

    2003 doi

  98. [106]

    The emergence of crack-like behavior of frictional rupture: The origin of stress drops

    Barras, F.; Aldam, M.; Roch, T.; Brener, E.A.; Bouchbinder, E.; Molinari, J.F. The emergence of crack-like behavior of frictional rupture: The origin of stress drops. arXiv 2019, arXiv:1906.11533. [1906.11533]

    2019 arXiv

  99. [107]

    The emergence of crack-like behavior of frictional rupture: Edge singularity and energy balance

    Barras, F.; Aldam, M.; Roch, T.; Brener, E.A.; Bouchbinder, E.; Molinari, J.F. The emergence of crack-like behavior of frictional rupture: Edge singularity and energy balance. arXiv 2019, arXiv:1907.04376. [1907.04376]

    2019 arXiv

  100. [108]

    Rupture modes in laboratory earthquakes: Effect of fault prestress and nucleation conditions

    Lu, X.; Rosakis, A.J.; Lapusta, N. Rupture modes in laboratory earthquakes: Effect of fault prestress and nucleation conditions. J. Geophys. Res. Solid Earth 2010, 115, 1–25. doi:10.1029/2009JB006833

    2010 doi

  101. [109]

    Cohesive force across the tip of a longitudinal-shear crack and Griffith’s specific surface energy

    Ida, Y. Cohesive force across the tip of a longitudinal-shear crack and Griffith’s specific surface energy. J. Geophys. Res. 1972, 77, 3796–3805. doi:10.1029/JB077i020p03796

    1972 doi

  102. [110]

    The growth of slip surfaces in the progressive failure of over-consolidated clay

    Palmer, A.C.; Rice, J.R. The growth of slip surfaces in the progressive failure of over-consolidated clay. Proc. R. Soc. A Math. Phys. Eng. Sci. 1973, 332, 527–548. doi:10.1098/rspa.1973.0040

    1973

  103. [111]

    Are there reliable constitutive laws for dynamic friction? Philos

    Woodhouse, J.; Putelat, T.; McKay, A. Are there reliable constitutive laws for dynamic friction? Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 2015, 373, 20140401. doi:10.1098/rsta.2014.0401

    2015

  104. [112]

    Survival of Heterogeneous Stress Distributions Created by Precursory Slip at Frictional Interfaces

    Radiguet, M.; Kammer, D.S.; Gillet, P.; Molinari, J.F. Survival of Heterogeneous Stress Distributions Created by Precursory Slip at Frictional Interfaces. Phys. Rev. Lett. 2013, 111, 164302. doi:10.1103/PhysRevLett.111.164302

    2013 doi

  105. [113]

    The role of viscoelasticity on heterogeneous stress fields at frictional interfaces

    Radiguet, M.; Kammer, D.S.; Molinari, J.F. The role of viscoelasticity on heterogeneous stress fields at frictional interfaces. Mech. Mater. 2015, 80, 276–287. doi:10.1016/j.mechmat.2014.03.009

    2015 doi

  106. [114]

    Earthquake cycle simulations with rate-and-state friction and power-law viscoelasticity

    Allison, K.L.; Dunham, E.M. Earthquake cycle simulations with rate-and-state friction and power-law viscoelasticity. Tectonophysics 2017. doi:10.1016/j.tecto.2017.10.021

    2017 doi

  107. [115]

    Earthquake slip between dissimilar poroelastic materials

    Dunham, E.M.; Rice, J.R. Earthquake slip between dissimilar poroelastic materials. J. Geophys. Res. Solid Earth 2008, 113, B09304. doi:10.1029/2007JB005405

    2008 doi

  108. [116]

    New development in freefem++

    Hecht, F. New development in freefem++. J. Numer. Math. 2012, 20. doi:10.1515/jnum-2012-0013

    2012 doi

  109. [134]

    doi:10.1016/0040-1951(92)90055-B

    1951 doi

  110. [1009]

    doi:10.1038/nature02830

    doi

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.