Spatiotemporal chaos of a one-dimensional thin elastic layer with the rate-and-state friction law

Abstract

Independent of specific local features, global spatiotemporal structures in diverse phenomena around bifurcation points are described by the complex Ginzburg-Landau equation (CGLE) derived using the reductive perturbation method, which includes prediction of spatiotemporal chaos. The generality in the CGLE scheme includes oscillatory instability in slip behavior between stable and unstable regimes. Such slip transitions accompanying spatiotemporal chaos is expected for frictional interfaces of a thin elastic layer made of soft solids, such as rubber or gel, where especially chaotic behavior may be easily discovered due to their compliance. Slow earthquakes observed in the aseismic-to-seismogenic transition zone along a subducting plate are also potential candidates. This article focuses on the common properties of slip oscillatory instability from the viewpoint of a CGLE approach by introducing a drastically simplified model of an elastic body with a thin layer, whose local expression in space and time allows us to employ conventional reduction methods. Special attention is paid to incorporate a rate-and-state friction law supported by microscopic mechanisms beyond the Coulomb friction law. We discuss similarities and discrepancies in the oscillatory instability observed or predicted in soft matter or a slow earthquake.