Numerical Instability at the Edge of a Dynamic Fracture

Knopoff, L.; Ni, Xueqian

doi:10.1046/j.1365-246x.2001.01567.x

Cited by 19 publications

(19 citation statements)

References 12 publications

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“…Classical ways to reduce them significantly are either to regularize the AC friction law (see e.g. [5] and references therein) or to introduce a viscous damping in the system [9,17,20,34,35]. Both are physically sound, but we choose to adopt the second approach.…”

Section: Introducing a Relative Viscous Dampingmentioning

confidence: 99%

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1D Model of Precursors to Frictional Stick-Slip Motion Allowing for Robust Comparison with Experiments

et al. 2011

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In this article, we study the dynamic behaviour of 1D spring-block models of friction when the external loading is applied from a side, and not on all blocks like in the classical Burridge-Knopoff-like models. Such a change in the loading yields specific difficulties, both from numerical and physical viewpoints. To address some of these difficulties and clarify the precise role of a series of model parameters, we start with the minimalistic model by Maegawa et al. (Tribol. Lett. 38: 313, 2010) which was proposed to reproduce their experiments about precursors to frictional sliding in the stick-slip regime. By successively adding an (i) internal viscosity, (ii) interfacial stiffness and (iii) initial tangential force distribution at the interface, we manage to (i) avoid the model's unphysical stress fluctuations, (ii) avoid its unphysical dependence on the spatial resolution and (iii) improve its agreement with the experimental results, respectively. Based on the behaviour of this improved 1D model, we develop an analytical prediction for the length of precursors as a function of the applied tangential load. We also discuss the relationship between the microscopic and macroscopic friction coefficients in the model.

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Section: Introducing a Relative Viscous Dampingmentioning

confidence: 99%

“…Physically, such viscosity is a way to model the energy dissipation that any material undergoes during deformation. After Knopoff and Ni [17], we consider the following form for the viscous force F n g :…”

Section: Introducing a Relative Viscous Dampingmentioning

confidence: 99%

1D Model of Precursors to Frictional Stick-Slip Motion Allowing for Robust Comparison with Experiments

et al. 2011

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“…From numerical simulations, Wang (2007Wang ( , 2016bWang ( , 2017 stressed the viscous effect on faulting. Noted that several researchers (Knopoff et al, 1973;Cohen, 1979;Xu and Knopoff, 1994;Knopoff and Ni, 2001;Dragoni and Santini, 2015) took viscosity as a factor in causing seismic radiation to reduce energy during faulting. The viscosity coefficient, υ, of rocks is mainly controlled by temperature, T .…”

Section: Viscositymentioning

confidence: 99%

Multistable slip of a one-degree-of-freedom spring-slider model in the presence of thermal-pressurized slip-weakening friction and viscosity

Wang

2017

Nonlin. Processes Geophys.

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Abstract. This study is focused on multistable slip of earthquakes based on a one-degree-of-freedom spring-slider model in the presence of thermal-pressurized slip-weakening friction and viscosity by using the normalized equation of motion of the model. The major model parameters are the normalized characteristic displacement, U c , of the friction law and the normalized viscosity coefficient, η, between the slider and background plate. Analytic results at small slip suggest that there is a solution regime for η and γ (= 1/U c ) to make the slider slip steadily. Numerical simulations exhibit that the time variation in normalized velocity, V /V max (V max is the maximum velocity), obviously depends on U c and η. The effect on the amplitude is stronger due to η than due to U c . In the phase portrait of V /V max versus the normalized displacement, U/U max (U max is the maximum displacement), there are two fixed points. The one at large V /V max and large U/U max is not an attractor, while that at small V /V max and small U/U max can be an attractor for some values of η and U c . When U c <0.55, unstable slip does not exist. When U c ≥ 0.55, U c and η divide the solution domain into three regimes: stable, intermittent, and unstable (or chaotic) regimes. For a certain U c , the three regimes are controlled by a lower bound, η l , and an upper bound, η u , of η. The values of η l , η u , and η u − η l all decrease with increasing U c , thus suggesting that it is easier to yield unstable slip for larger U c than for smaller U c or for larger η than for smaller η. When U c <1, the Fourier spectra calculated from simulation velocity waveforms exhibit several peaks, thus suggesting the existence of nonlinear behavior of the system. When U c >1, the related Fourier spectra show only one peak, thus suggesting linear behavior of the system.

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“…Quartz plasticity could lubricate the fault plane at higher T and yield viscous stresses to resist slip at lower T. Some researchers have already investigated the effect of viscosity in springblock system [e.g., Shaw, 1994;Yoshino, 1998;Hainzl et al, 1999;Wang, 2016a]. On the other hand, several researchers [Knopoff et al, 1973;Cohen, 1979;Xu and Knopoff, 1994;Knopoff and Ni, 2001] took the viscous effect as a factor in causing seismic radiation to reduce energy during earthquake ruptures.…”

Section: Introductionmentioning

confidence: 99%

Slip of a Two-degree-of-freedom Spring-slider Model in the Presence of Slip-dependent Friction and Viscosity

Wang

2017

Annals of Geophysics

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Numerical Instability at the Edge of a Dynamic Fracture

Cited by 19 publications

References 12 publications

1D Model of Precursors to Frictional Stick-Slip Motion Allowing for Robust Comparison with Experiments

1D Model of Precursors to Frictional Stick-Slip Motion Allowing for Robust Comparison with Experiments

Multistable slip of a one-degree-of-freedom spring-slider model in the presence of thermal-pressurized slip-weakening friction and viscosity

Slip of a Two-degree-of-freedom Spring-slider Model in the Presence of Slip-dependent Friction and Viscosity

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