Léopoldès, Conrad and Jia (Phys. Rev. Lett. 110, 248301, 2013) showed that nonlinear shear ultrasound, regardless of polarization, triggers macroscopic sliding of weakly adhesive amorphous-film interfaces far below the static threshold, through a vibration-induced decrease of the apparent static friction coefficient μs→μs∗\mu_s\to\mu_s^* in which the oscillation acts like an effective temperature TeffT_{\mathrm{eff}} in an unjamming diagram. The mechanism-level problem they left open remains open. The standard rate-and-state laws of Dieterich and Ruina do not include an effective temperature built from the vibrational energy of imposed high-frequency oscillation, so the observed pre-sliding softening and threshold reduction are not predicted by them. It is not known when adhesion-area reduction (Johnson–Kendall–Roberts-type response, edge fracture of the soft film) governs the softening regime rather than interior frictional microslip. Finally, the extent to which this contact-scale mechanism accounts for the reduction of the yielding threshold of bulk granular layers and fault gouge by acoustic fluidization is undetermined. Follow-up work has demonstrated and modeled ultrasound-triggered avalanches and flows in granular layers, but has not supplied the mechanism-level account of the threshold reduction.

Background

When two elastic bodies are pressed together and then tangentially loaded below the threshold for gross sliding, the interface is not uniformly stuck. Mindlin's classical analysis of an elastic sphere on a flat substrate shows that an annulus near the contact edge slips while the center remains stuck; this partial, or 'microslip', response sets the tangential compliance of the contact and dissipates energy hysteretically, and it underlies the multicontact friction of rough and soft interfaces (reviewed by Baumberger and Caroli). For dry friction at such interfaces the standard phenomenology is the rate-and-state framework of Dieterich and Ruina, in which the friction coefficient depends on the instantaneous sliding rate and on a 'state variable' encoding the age and strength of the population of microcontacts; these laws are the workhorse of earthquake nucleation models. When the contacting solids are soft or adhesive, the contact area itself is set by surface energy through the Johnson–Kendall–Roberts (JKR) theory of adhesive elastic contact; under tangential loading the area can shrink and the contact can fail by edge cracks — a channel of apparent 'softening' that competes with interior microslip. In granular media and fault gouge (the crushed granular material filling fault zones), an analogous weakening is attributed to 'acoustic fluidization': elastic waves agitating grain contacts reduce the effective interparticle friction and the effective confinement, so that sheared granular material yields under loads well below its static threshold, a hypothesis invoked for earthquake remote triggering after Johnson and co-workers showed that acoustic waves modify stick-slip in granular gouge.

Léopoldès, Conrad and Jia connected these scales in a model experiment: an amorphous (polymer) film forming a weakly adhesive interface, sheared while a quartz-crystal ultrasonic resonator imposes high-frequency oscillatory shear directly across the contact, so that the interfacial shear stiffness and the onset of sliding — monitored through the angle of sliding, the inclination angle of the plane at which the interface starts to slide — could be measured simultaneously, building on their earlier resonator-based viscoelastic probing of thin polymer films. They found that the interfacial shear stiffness softens before sliding under either quasi-static or high-amplitude oscillatory shear; that nonlinear shear ultrasound triggers macroscopic sliding far below the static threshold whatever its polarization; and that the effect amounts to a vibration-induced reduction μs→μs∗\mu_s\to\mu_s^* of the apparent static friction coefficient, describable as an effective temperature TeffT_{\mathrm{eff}} in an unjamming diagram — a jammed assembly loses rigidity ('unjams') when thermal-like agitation, here supplied by ultrasound rather than heat, exceeds a threshold. Fits of the stiffness softening with Mindlin-type microslip gave contact-scale static friction coefficients that differ from the macroscopic angle-of-sliding values. The authors proposed this microslip-mediated route ('acoustic lubrication' of contacts) as a contact-scale mechanism for the acoustic fluidization that ultrasound was already known to produce in dense granular packs.

Problem Statement

Give a predictive, mechanism-level account of how high-frequency oscillatory (ultrasonic) shear, regardless of its polarization, lowers the static friction threshold of amorphous, weakly adhesive interfaces: account for the softening of the interfacial shear stiffness prior to sliding and for the vibration-induced reduction μs→μs∗\mu_s\to\mu_s^* of the apparent static friction coefficient as functions of oscillation amplitude and frequency, with μs∗\mu_s^* the vibration-reduced value of the apparent static friction coefficient μs\mu_s and with the vibrational (oscillation) energy playing the role of an effective temperature TeffT_{\mathrm{eff}} in an unjamming picture. Determine, as a function of oscillation amplitude and frequency, the relative contribution to this weakening of reduction of the adhesive contact area (Johnson–Kendall–Roberts-type contact response, with tangential-force-induced shrinkage and interfacial fracture of the soft adhesive contact) and of Mindlin-type interior frictional microslip, and state which of the two mechanisms dominates in which regime. And use this contact-scale mechanism to understand the reduction of the yielding threshold of granular media by acoustic fluidization.

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