Speed of fast and slow rupture fronts along frictional interfaces

Deriving the slip-front propagation velocity with slip-dependent and slip-velocity-dependent friction laws via the use of the linear marginal stability hypothesis

We investigate analytically and numerically the determining factors of the slip front propagation (SFP) velocity. The slip front has two forms characterized by an intruding or extruding front. We assume a one-dimensional viscoelastic medium on a rigid and fixed substrate, and we employ the friction law depending on the slip and slip velocity. Despite this dependency potentially being nonlinear, we use the linear marginal stability hypothesis, which linearizes the governing equation for the slip, to investigate the intruding and extruding front velocities. The analytically obtained velocities are found to be consistent with the numerical computation where we assume the friction law depends nonlinearly on both the slip and slip velocity. This implies that the linearized friction law is sufficient to capture the dominant features of SFP behavior.

Polymerase chain reaction thermal cycling using the programmed tilt displacements of capillary tubes

A thermal cycling method, whereby capillary tubes holding polymerase chain reactions are subjected to programmed tilt displacements so that they are moved using gravity over three spatial regions (I, II, and III) kept at different constant temperatures to facilitate deoxyribonucleic acid (DNA) denaturation, annealing, and extension, is described. At tilt speeds in excess of 0.2 rad/s, the standard deviation of static coefficient of friction values was below 0.03, indicating in sync movement of multiple capillary tubes over the holding platform. The travel time during the acceleration phase and under constant velocity between adjacent regions (I to II and II to III) and distant regions (III to I) was 0.03 s and 0.31 s, respectively. The deviations in temperature did not exceed 0.05 °C from the average at the prescribed denaturing, annealing, and extension temperatures applied. DNA amplification was determined by optical readings, the fluorescence signal was found to increase twofold after 30 thermal cycles, and 1.16 × 10⁶ DNA copies/μl could be detected. The approach also overcomes problems associated with thermal inertia, sample adhesion, sample blockage, and handling of the reaction vessels encountered in the other thermal cycling schemes used.

How collective asperity detachments nucleate slip at frictional interfaces

Sliding at a quasi-statically loaded frictional interface can occur via macroscopic slip events, which nucleate locally before propagating as rupture fronts very similar to fracture. We introduce a microscopic model of a frictional interface that includes asperity-level disorder, elastic interaction between local slip events, and inertia. For a perfectly flat and homogeneously loaded interface, we find that slip is nucleated by avalanches of asperity detachments of extension larger than a critical radius [Formula: see text] governed by a Griffith criterion. We find that after slip, the density of asperities at a local distance to yielding [Formula: see text] presents a pseudogap [Formula: see text], where θ is a nonuniversal exponent that depends on the statistics of the disorder. This result makes a link between friction and the plasticity of amorphous materials where a pseudogap is also present. For friction, we find that a consequence is that stick-slip is an extremely slowly decaying finite-size effect, while the slip nucleation radius [Formula: see text] diverges as a θ-dependent power law of the system size. We discuss how these predictions can be tested experimentally.

Minimal model for slow, sub-Rayleigh, supershear, and unsteady rupture propagation along homogeneously loaded frictional interfaces

In nature and experiments, a large variety of rupture speeds and front modes along frictional interfaces are observed. Here, we introduce a minimal model for the rupture of homogeneously loaded interfaces with velocity strengthening dynamic friction, containing only two dimensionless parameters; τ[over ¯], which governs the prestress, and α[over ¯], which is set by the interfacial viscosity. This model contains a large variety of front types, including slow fronts, sub-Rayleigh fronts, supershear fronts, slip pulses, cracks, arresting fronts, and fronts that alternate between arresting and propagating phases. Our results indicate that this wide range of front types is an inherent property of frictional systems with velocity strengthening branches.

Nature of the high-speed rupture of the two-dimensional Burridge-Knopoff model of earthquakes

The nature of the high-speed rupture or the main shock of the Burridge-Knopoff spring-block model in two dimensions obeying the rate- and state-dependent friction law is studied by means of extensive computer simulations. It is found that the rupture propagation in larger events is highly anisotropic and irregular in shape on longer length scales, although the model is completely uniform and the emergent rupture-propagation velocity is nearly constant everywhere at the rupture front. The manner of the rupture propagation sometimes mimics the successive ruptures of neighbouring 'asperities' observed in real, large earthquakes. Large events tend to be unilateral, with its epicentre lying at the rim of its rupture zone. The epicentre site of a large event is also located next to the rim of the rupture zone of some past event. Event-size distributions are computed and discussed in comparison with those of the corresponding one-dimensional model. The magnitude distribution exhibits a power-law behaviour resembling the Gutenberg-Richter law for smaller magnitudes, which changes over to a more characteristic behaviour for larger magnitudes. For very large events, the rupture-length distribution exhibits mutually different behaviours in one dimension and in two dimensions, reflecting the difference in the underlying geometry.This article is part of the theme issue 'Statistical physics of fracture and earthquakes'.

Evolution of real contact area under shear and the value of static friction of soft materials

The frictional properties of a rough contact interface are controlled by its area of real contact, the dynamical variations of which underlie our modern understanding of the ubiquitous rate-and-state friction law. In particular, the real contact area is proportional to the normal load, slowly increases at rest through aging, and drops at slip inception. Here, through direct measurements on various contacts involving elastomers or human fingertips, we show that the real contact area also decreases under shear, with reductions as large as 30[Formula: see text], starting well before macroscopic sliding. All data are captured by a single reduction law enabling excellent predictions of the static friction force. In elastomers, the area-reduction rate of individual contacts obeys a scaling law valid from micrometer-sized junctions in rough contacts to millimeter-sized smooth sphere/plane contacts. For the class of soft materials used here, our results should motivate first-order improvements of current contact mechanics models and prompt reinterpretation of the rate-and-state parameters.

Steady-state propagation speed of rupture fronts along one-dimensional frictional interfaces

The rupture of dry frictional interfaces occurs through the propagation of fronts breaking the contacts at the interface. Recent experiments have shown that the velocities of these rupture fronts range from quasistatic velocities proportional to the external loading rate to velocities larger than the shear wave speed. The way system parameters influence front speed is still poorly understood. Here we study steady-state rupture propagation in a one-dimensional (1D) spring-block model of an extended frictional interface for various friction laws. With the classical Amontons-Coulomb friction law, we derive a closed-form expression for the steady-state rupture velocity as a function of the interfacial shear stress just prior to rupture. We then consider an additional shear stiffness of the interface and show that the softer the interface, the slower the rupture fronts. We provide an approximate closed form expression for this effect. We finally show that adding a bulk viscosity on the relative motion of blocks accelerates steady-state rupture fronts and we give an approximate expression for this effect. We demonstrate that the 1D results are qualitatively valid in 2D. Our results provide insights into the qualitative role of various key parameters of a frictional interface on its rupture dynamics. They will be useful to better understand the many systems in which spring-block models have proved adequate, from friction to granular matter and earthquake dynamics.