Dynamic instabilities of frictional sliding at a bimaterial interface

Abstract

We study the 2D linear stability analysis of a deformable solid of a finite height $H$, steadily sliding on top of a rigid solid within a generic rate-and-state friction type constitutive framework, fully accounting for elastodynamic effects. We derive the linear stability spectrum, quantifying the interplay between stabilization related to the frictional constitutive law and destabilization related both to the elastodynamic bi-material coupling between normal stress variations and interfacial slip, and to finite size effects. The stabilizing effects related to the frictional constitutive law include velocity-strengthening friction (i.e.~an increase in frictional resistance with increasing slip velocity, both instantaneous and under steady-state conditions) and a regularized response to normal stress variations. We first consider the small wave-number $k$ limit and demonstrate that homogeneous sliding in this case is universally unstable, independently of the details of the friction law. This universal instability is mediated by propagating waveguide-like modes, whose fastest growing mode is characterized by a wave-number satisfying $kH\sim \mathcal{O}(1)$ and by a growth rate that scales with $H^{-1}$. We then consider the limit $kH\to \infty$ and derive the stability phase diagram in this case. We show that the dominant instability mode travels at nearly the dilatational wave-speed in the opposite direction to the sliding direction. Instability modes which travel at nearly the shear wave-speed in the sliding direction also exist in some range of physical parameters. Finally, we show that a finite-time regularized response to normal stress variations, within the framework of generalized rate-and-state friction models, tends to promote stability.

37 pages, 9 figures

References in corpus (4)

• On the velocity-strengthening behavior of dry friction
• Instabilities at Frictional Interfaces: Creep Patches, Nucleation and Rupture Fronts
• Velocity-strengthening friction significantly affects interfacial dynamics, strength and dissipation
• Destabilization of long-wavelength Love and Stoneley waves in slow sliding

Cited by in corpus (6)

• Finite element modeling of dynamic frictional rupture with rate and state friction
• Critical nucleation length for accelerating frictional slip
• Velocity-driven frictional sliding: Coarsening and steady-state pulse trains
• Frictional sliding without geometrical reflection symmetry
• Nonlinear self-adapting wave patterns
• Non-monotonicity of the frictional bimaterial effect