The dynamics of unsteady frictional slip pulses

Abstract

Self-healing slip pulses are major spatiotemporal failure modes of frictional systems, featuring a characteristic size $L(t)$ and a propagation velocity $c_{\mathrm{p}}(t)$ ($t$ is time). Here, we develop a theory of slip pulses in realistic rate-and-state dependent frictional systems. We show that slip pulses are intrinsically unsteady objects -- in agreement with previous findings -- yet their dynamical evolution is closely related to their unstable steady-state counterparts. In particular, we show that each point along the time-independent $L^{\mbox{(0)}}(τ_{\rm d})\!-\!c^{\mbox{(0)}}_{\rm p}(τ_{\rm d})$ line, obtained from a family of steady-state pulse solutions parameterized by the driving shear stress ${\tau }_{\mathrm{d}}$, is unstable. Nevertheless, and remarkably, the $c^{\mbox{(0)}}_{\rm p}[L^{\mbox{(0)}}]$ line is a dynamic attractor such that the unsteady dynamics of slip pulses (when they exist) -- whether growing ($\dot{L}(t)>0$) or decaying ($\dot{L}(t)<0$) -- reside on the steady-state line. The unsteady dynamics along the line are controlled by a single slow unstable mode. The slow dynamics of growing pulses, manifested by $\dot{L}(t)/c_{\mathrm{p}}(t)\ll 1$, explain the existence of sustained pulses, i.e.~pulses that propagate many times their characteristic size without appreciably changing their properties. Our theoretical picture of unsteady frictional slip pulses is quantitatively supported by large-scale, dynamic boundary-integral method simulations.

arXiv commentNote an addition to v2: Literature results for the thermal pressurization constitutive relation are consistent with our findings and indicate the relevance of the emerging picture to strongly weakening frictional interfaces

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Cited by in corpus (1)

• Unsteady slip pulses under spatially-varying prestress