Are there reliable constitutive laws for dynamic friction?

Conveyance of texture signals along a rat whisker

Neuronal activities underlying a percept are constrained by the physics of sensory signals. In the tactile sense such constraints are frictional stick-slip events, occurring, amongst other vibrotactile features, when tactile sensors are in contact with objects. We reveal new biomechanical phenomena about the transmission of these microNewton forces at the tip of a rat's whisker, where they occur, to the base where they engage primary afferents. Using high resolution videography and accurate measurement of axial and normal forces at the follicle, we show that the conical and curved rat whisker acts as a sign-converting amplification filter for moment to robustly engage primary afferents. Furthermore, we present a model based on geometrically nonlinear Cosserat rod theory and a friction model that recreates the observed whole-beam whisker dynamics. The model quantifies the relation between kinematics (positions and velocities) and dynamic variables (forces and moments). Thus, only videographic assessment of acceleration is required to estimate forces and moments measured by the primary afferents. Our study highlights how sensory systems deal with complex physical constraints of perceptual targets and sensors.

Health monitoring of bolted joints using modal-based vibrothermography

This article presents a novel modal-based vibrothermographic approach for health monitoring of loosening bolted joints in coupled structures. In this article, the theoretical background supporting this proposed approach is firstly presented. Through finite element analyses on a simple bolted structure with varying joint conditions achieved by adjustment of bolt loads, the relationship between the bolt load and the temperature increase in the vibrating bolted joint during vibrothermographic tests was revealed. Experimental vibrothermographic tests on a more complex structure were completed to verify the observations from the finite element analyses while demonstrating the viability of the vibrothermographic approach in a laboratory environment. It has been shown that this vibrothermographic approach was able to determine the stage of a bolted joint in its progression of failure by tracing the changes in the temperature increase in relevant regions during vibrothermographic tests. Moreover, additional tests have been performed to illustrate that this approach was effective even by using only the residual responses of the structure’s vibration that were away from the resonances, which indicates it is more applicable to structures with higher damping as such structures have stronger residual responses during vibration that can be utilized. In the concluding observations of the article, the procedure for practical application of this approach is summarized, and its potential for further development is discussed.

Spatiotemporal Dynamics of Frictional Systems: The Interplay of Interfacial Friction and Bulk Elasticity

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 a minimal 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.

A phase-plane analysis of localized frictional waves

Sliding frictional interfaces at a range of length scales are observed to generate travelling waves; these are considered relevant, for example, to both earthquake ground surface movements and the performance of mechanical brakes and dampers. We propose an explanation of the origins of these waves through the study of an idealized mechanical model: a thin elastic plate subject to uniform shear stress held in frictional contact with a rigid flat surface. We construct a nonlinear wave equation for the deformation of the plate, and couple it to a spinodal rate-and-state friction law which leads to a mathematically well-posed problem that is capable of capturing many effects not accessible in a Coulomb friction model. Our model sustains a rich variety of solutions, including periodic stick–slip wave trains, isolated slip and stick pulses, and detachment and attachment fronts. Analytical and numerical bifurcation analysis is used to show how these states are organized in a two-parameter state diagram. We discuss briefly the possible physical interpretation of each of these states, and remark also that our spinodal friction law, though more complicated than other classical rate-and-state laws, is required in order to capture the full richness of wave types.

The landscape of nonlinear structural dynamics: an introduction

Nonlinear behaviour is ever-present in vibrations and other dynamical motions of engineering structures. Manifestations of nonlinearity include amplitude-dependent natural frequencies, buzz, squeak and rattle, self-excited oscillation and non-repeatability. This article primarily serves as an extended introduction to a theme issue in which such nonlinear phenomena are highlighted through diverse case studies. More ambitiously though, there is another goal. Both the engineering context and the mathematical techniques that can be used to identify, analyse, control or exploit these phenomena in practice are placed in the context of a mind-map, which has been created through expert elicitation. This map, which is available in software through the electronic supplementary material, attempts to provide a practitioner's guide to what hitherto might seem like a vast and complex research landscape.