Nonlinear rate-dependent stick-slip phenomena: modeling and parameter estimation

2001 ◽  
Vol 38 (8) ◽  
pp. 1415-1431 ◽  
Author(s):  
Hoon Wee ◽  
Yoon Young Kim ◽  
Haeil Jung ◽  
Gwang Nam Lee
2003 ◽  
Vol 70 (2) ◽  
pp. 220-226 ◽  
Author(s):  
A. Cochard ◽  
L. Bureau ◽  
T. Baumberger

This paper presents the stability analysis of a system sliding at low velocities (<100 μm⋅s−1) under a periodically modulated normal load, preserving interfacial contact. Experiments clearly evidence that normal vibrations generally stabilize the system against stick-slip oscillations, at least for a modulation frequency much larger than the stick-slip one. The mechanical model of L. Bureau, T. Baumberger, and C. Caroli validated on the steady-state response of the system, is used to map its stability diagram. The model takes explicitly into account the finite shear stiffness of the load-bearing asperities, in addition to a classical state and rate-dependent friction force. The numerical results are in excellent quantitative agreement with the experimental data obtained from a multicontact frictional system between glassy polymer materials. Simulations at larger amplitude of modulation (typically 20 percent of the mean normal load) suggest that the nonlinear coupling between normal and sliding motion could have a destabilizing effect in restricted regions of the parameter space.


2015 ◽  
Vol 9 (4) ◽  
pp. 3617-3660 ◽  
Author(s):  
A. Damsgaard ◽  
D. L. Egholm ◽  
J. A. Piotrowski ◽  
S. Tulaczyk ◽  
N. K. Larsen ◽  
...  

Abstract. The dynamics of glaciers are to a large degree governed by processes operating at the ice–bed interface, and one of the primary mechanisms of glacier flow over soft unconsolidated sediments is subglacial deformation. However, it has proven difficult to constrain the mechanical response of subglacial sediment to the shear stress of an overriding glacier. In this study, we present a new methodology designed to simulate subglacial deformation using a coupled numerical model for computational experiments on grain-fluid mixtures. The granular phase is simulated on a per-grain basis by the discrete element method. The pore water is modeled as a compressible Newtonian fluid without inertia. The numerical approach allows close monitoring of the internal behavior under a range of conditions. The rheology of a water-saturated granular bed may include both plastic and rate-dependent dilatant hardening or weakening components, depending on the rate of deformation, the material state, clay mineral content, and the hydrological properties of the material. The influence of the fluid phase is negligible when relatively permeable sediment is deformed. However, by reducing the local permeability, fast deformation can cause variations in the pore-fluid pressure. The pressure variations weaken or strengthen the granular phase, and in turn influence the distribution of shear strain with depth. In permeable sediments the strain distribution is governed by the grain-size distribution and effective normal stress and is typically on the order of tens of centimeters. Significant dilatant strengthening in impermeable sediments causes deformation to focus at the hydrologically more stable ice–bed interface, and results in a very shallow cm-to-mm deformational depth. The amount of strengthening felt by the glacier depends on the hydraulic conductivity at the ice–bed interface. Grain-fluid feedbacks can cause complex material properties that vary over time, and which may be of importance for glacier stick-slip behavior.


2009 ◽  
Vol 7 (43) ◽  
pp. 259-269 ◽  
Author(s):  
Nick Gravish ◽  
Matt Wilkinson ◽  
Simon Sponberg ◽  
Aaron Parness ◽  
Noe Esparza ◽  
...  

Geckos owe their remarkable stickiness to millions of dry, hard setae on their toes. In this study, we discovered that gecko setae stick more strongly the faster they slide, and do not wear out after 30 000 cycles. This is surprising because friction between dry, hard, macroscopic materials typically decreases at the onset of sliding, and as velocity increases, friction continues to decrease because of a reduction in the number of interfacial contacts, due in part to wear. Gecko setae did not exhibit the decrease in adhesion or friction characteristic of a transition from static to kinetic contact mechanics. Instead, friction and adhesion forces increased at the onset of sliding and continued to increase with shear speed from 500 nm s −1 to 158 mm s −1 . To explain how apparently fluid-like, wear-free dynamic friction and adhesion occur macroscopically in a dry, hard solid, we proposed a model based on a population of nanoscopic stick–slip events. In the model, contact elements are either in static contact or in the process of slipping to a new static contact. If stick–slip events are uncorrelated, the model further predicted that contact forces should increase to a critical velocity ( V *) and then decrease at velocities greater than V *. We hypothesized that, like natural gecko setae, but unlike any conventional adhesive, gecko-like synthetic adhesives (GSAs) could adhere while sliding. To test the generality of our results and the validity of our model, we fabricated a GSA using a hard silicone polymer. While sliding, the GSA exhibited steady-state adhesion and velocity dependence similar to that of gecko setae. Observations at the interface indicated that macroscopically smooth sliding of the GSA emerged from randomly occurring stick–slip events in the population of flexible fibrils, confirming our model predictions.


1993 ◽  
Vol 115 (3) ◽  
pp. 286-291 ◽  
Author(s):  
G. L. Povirk ◽  
A. Needleman

Fiber pull-out is simulated through a quasi-static analysis of a circular elastic cylinder with a rigid cylindrical fiber embedded in its center. The interface between the fiber and the matrix is characterized in terms of a rate dependent internal variable friction constitutive relation. The analysis is carried out in two steps; one simulating the residual stresses that develop while cooling the cylinder from its processing temperature and the other simulating the mechanical response during fiber pull-out. Depending on parameter values, fiber pull-out can occur smoothly or a stick-slip instability can occur. Numerical simulations of fiber pull-out are presented that explore the effects of loading device stiffness, loading rate, and friction law parameters on the predicted behavior. For example, the amplitude of the load fluctuations during stick-slip was found to decrease as the rate of pull-out increased.


2008 ◽  
Vol 33-37 ◽  
pp. 867-874 ◽  
Author(s):  
S. Ozaki ◽  
Koichi Hashiguchi ◽  
D.H. Chen

In this study, the rate-dependent subloading-friction model, which can rationally describe the reciprocal transition of static-kinetic frictions by the unified formulation, is proposed. Then, the one-dimensional model of spring-mass system is implemented by incorporating the present friction model, and is applied to simulations of stick-slip motion. Further, we verified the validity of the present approach for the stick-slip motion by numerical experiments under various dynamic conditions.


2020 ◽  
Author(s):  
Arcady Dyskin ◽  
Elena Pasternak

&lt;p&gt;Seismic events associated with pre-existing faults are traditionally assumed to be caused by rupture propagation, that is in-plane shear crack propagation. However what appears to be a shear crack is a sliding zone over a fault; it grows by overcoming friction (either in direct contact or in the gouge) rather than rock rupture. When modelling frictional sliding, two important factors need to be considered: (1) the elasticity of the surrounding rocks which causes self-oscillations resulting in the movement resembling stick-slip even in constant friction; (2) the rotation of real gouge particles which being non-spherical lead, in the presence of compression, to the effect of negative shear stiffness. The latter effectively works to transfer the elastic energy stored in the compressed rock into the energy of the sliding zone propagation.&lt;/p&gt;&lt;p&gt;This presentation introduces 1D models accounting for these factors. Both lead to the so-called telegraph equation which is a wave equation with a non-derivative term referring to the fact that the movement is considered against a stationary solid. The equation with respect to displacement corresponds to the case of apparent negative stiffness, while the equation with respect to the displacement rate corresponds to the pure frictional sliding. The rock elasticity leads to the sliding zone propagation speed equal to the p-wave velocity making the propagation speed intra-sonic [1]. The rate-dependent friction can slightly reduce the speed. It is interesting that the sliding zone propagation is related to p-wave rather than s- or Raylegh waves as one would anticipate. The results of this research contribute to the understanding of the mechanics of seismicity.&lt;/p&gt;&lt;ol&gt;&lt;li&gt;Karachevtseva, I, A.V. Dyskin and E. Pasternak, 2017. Generation and propagation of stick-slip waves over a fault with rate-independent friction. Nonlinear Processes in Geophysics (NPG), 24, 343-349.&lt;/li&gt; &lt;/ol&gt;&lt;p&gt;&lt;strong&gt;Acknowledgements&lt;/strong&gt;. AVD acknowledges the support from the School of Civil and Transportation, Faculty of Engineering, Beijing University of Civil Engineering and Architecture.&lt;/p&gt;


Author(s):  
T. Gulik-Krzywicki ◽  
M.J. Costello

Freeze-etching electron microscopy is currently one of the best methods for studying molecular organization of biological materials. Its application, however, is still limited by our imprecise knowledge about the perturbations of the original organization which may occur during quenching and fracturing of the samples and during the replication of fractured surfaces. Although it is well known that the preservation of the molecular organization of biological materials is critically dependent on the rate of freezing of the samples, little information is presently available concerning the nature and the extent of freezing-rate dependent perturbations of the original organizations. In order to obtain this information, we have developed a method based on the comparison of x-ray diffraction patterns of samples before and after freezing, prior to fracturing and replication.Our experimental set-up is shown in Fig. 1. The sample to be quenched is placed on its holder which is then mounted on a small metal holder (O) fixed on a glass capillary (p), whose position is controlled by a micromanipulator.


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