Stick-slip dynamics in the relaxation of stresses in a continuous elastic medium

Debonding waves in gel thin films

We develop a mathematical model for the sliding of a gel sheet adhered to a moving substrate. The sliding takes place by the motion of detached region between the gel sheet and the substrates, i.e. the propagation of a Schallamach wave. Efficient numerical methods are developed to solve the problem. Numerical examples illustrate that the model can describe the Schallamach wave and are consistent with the existing experiments qualitatively.

Slip dynamics at a patterned rubber/glass interface during stick-slip motions

We report on an experimental study of heterogeneous slip instabilities generated during stick-slip motions at a contact interface between a smooth rubber substrate and a patterned glass lens. Using a sol-gel process, the glass lens is patterned with a lattice of parallel ridges (wavelength, 1.6 μm, amplitude 0.35 μm). Friction experiments using this patterned surface result in the systematic occurrence of stick-slip motions over three orders of magnitude in the imposed driving velocity while stable friction is achieved with a smooth surface. Using a contact imaging method, real-time displacement fields are measured at the surface of the rubber substrate. Stick-slip motions are found to involve the localized propagation of transverse interface shear cracks whose velocity is observed to be remarkably independent on the driving velocity.

Observation of spatio-temporal structure in stick-slip motion of an adhesive gel sheet

We studied the sliding friction between an adhesive gel sheet and a glass substrate. In this system, the probability distribution of the force drop obeys a power law similar to that found in earthquakes and granular systems. We observed the motion of the slip regions at the frictional interfaces and obtained the spatial distributions of shear strain by image analysis. The frictional force evaluated by the image analysis is in good agreement with the actual force measured by a load cell. This indicates that the present method provides a powerful tool to study the spatio-temporal structure in the heterogeneous stick-slip motions in sliding friction.

Regular to chaotic transition of stick-slip motion in sliding friction of an adhesive gel-sheet

Spatio-temporal pattern of the stick-slip motion of a gel-sheet pulled on a glass substrate is observed. The sliding takes place via the propagation of the wave of detachment (Schallamach wave). At large pull velocity, the detached region is a stripe which moves regularly with constant speed and the frictional force shows a periodic time dependence. As the pull velocity is decreased, the detached region is separated into bubbles which move around irregularly. In the irregular state, the frictional force shows chaotic time dependence and the statistics of the event of the force drop obeys a power law similar to the Gutenberg-Richter law known in earthquakes. In the regular region, the detachment wave is analyzed theoretically and the velocity and lengths are obtained as a function of the pull velocity. The transition from the regular to chaotic behavior is shown to be related to the spontaneous wetting of the gel.

Fracture and friction: Stick-slip motion

We discuss the stick-slip motion of an elastic block sliding along a rigid substrate. We argue that for a given external shear stress this system shows a discontinuous nonequilibrium transition from a uniform stick state to uniform sliding at some critical stress which is nothing but the Griffith threshold for crack propagation. An inhomogeneous mode of sliding occurs when the driving velocity is prescribed instead of the external stress. A transition to homogeneous sliding occurs at a critical velocity, which is related to the critical stress. We solve the elastic problem for a steady-state motion of a periodic stick-slip pattern and derive equations of motion for the tip and resticking end of the slip pulses. In the slip regions we use the linear friction law and do not assume any intrinsic instabilities even at small sliding velocities. We find that, as in many other pattern forming system, the steady-state analysis itself does not select uniquely all the internal parameters of the pattern, especially the primary wavelength. Using some plausible analogy to first-order phase transitions we discuss a "soft" selection mechanism. This allows to estimate internal parameters such as crack velocities, primary wavelength and relative fraction of the slip phase as functions of the driving velocity. The relevance of our results to recent experiments is discussed.

Self-healing slip pulses along a gel/glass interface

We present experimental evidence of self-healing shear cracks at a gel/glass interface. This system exhibits two dynamical regimes depending on the driving velocity: steady sliding at high velocity (>V(c) approximately 100--125 microm/s), characterized by a shear-thinning rheology, and periodic stick-slip dynamics at low velocity. In this last regime, slip occurs by propagation of pulses that restick via a "healing instability" occurring when the local sliding velocity reaches the macroscopic transition velocity V(c). At driving velocities close below V(c), the system exhibits complex spatiotemporal behavior.

Discrete Burridge-Knopoff model, with exact solitonic or compactlike traveling wave solution

We have explored the dynamics of two versions of a Burridge-Knopoff model: with linear or nonlinear interactions between adjacent blocks. We have shown that by properly choosing the analytical form of the discrete solitary wave solution of the model we can calculate analytically the form of the friction function. In both cases our analytical results show that the friction force naturally presents the behavior of a simple weakening friction law first introduced qualitatively by Burridge and Knopoff [Bull. Seismol. Soc. Am. 57, 3411 (1967)] and quantitatively by Carlson and Langer [Phys. Rev. Lett. 62, 2632 (1989)]. With such a force function the discrete solitonic or compactlike wave-front solutions are exact and stable solutions. In the case of linear coupling our numerical simulations show that an irregular initial state evolves into kink pairs (large-amplitude events), that can recombine or not, plus nonlinear localized modes and small linear oscillations (small-amplitude events) that disperse with time, owing to dispersion. For nonlinear coupling one observes compactlike kink pairs or shocks, and a background of robust incoherent nonlinear oscillations (small amplitude events) that persist with time. Our results show that discreteness is a necessary ingredient to observe a rich and complex dynamical behavior. Nonlinearity allows the existence of strictly localized shocks.

Slip pulses at a sheared frictional viscoelastic/nondeformable interface

We study the possibility for a semi-infinite block of linear viscoelastic material, in homogeneous frictional contact with a nondeformable one, to slide under shear via a periodic set of "self-healing pulses," i.e., a set of drifting slip regions separated by stick ones. We show that, contrary to existing experimental indications, such a mode of frictional sliding is impossible for an interface obeying a simple local Coulomb law of solid friction. We then discuss possible physical improvements of the friction model which might open the possibility of such dynamics, among which slip weakening of the friction coefficient, and stress the interest of developing systematic experimental investigations of this question.