# Spatiotemporal dynamics of frictional systems: The interplay of interfacial friction and bulk elasticity

## TL;DR

This paper explores how the interaction between interfacial friction laws and bulk elasticity influences complex spatiotemporal behaviors in frictional systems, emphasizing the importance of their coupled dynamics.

## Contribution

It provides a comprehensive analysis of the coupling between macroscopic friction laws and bulk elasticity, including extensions supported by experimental data and implications for frictional dynamics.

## Key findings

- Coupling leads to diverse frictional phenomena like rupture fronts and slip pulses.
- Extensions to the rate-and-state friction framework improve experimental alignment.
- System geometry significantly affects the range and nature of elastic interactions.

## Abstract

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 the 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.