Anomalous acoustic reflection on a sliding interface or a shear band

Abstract

We study the reflection of an acoustic plane wave from a steadily sliding planar interface with velocity strengthening friction or a shear band in a confined granular medium. The corresponding acoustic impedance is utterly different from that of the static interface. In particular, the system being open, the energy of an in-plane polarized wave is no longer conserved, the work of the external pulling force being partitioned between frictional dissipation and gain (of either sign) of coherent acoustic energy. Large values of the friction coefficient favor energy gain, while velocity strengthening tends to suppress it. An interface with infinite elastic contrast (one rigid medium) and V-independent (Coulomb) friction exhibits spontaneous acoustic emission, as already shown by M. Nosonovsky and G.G. Adams (Int. J. Ing. Sci., {\bf 39}, 1257 (2001)). But this pathology is cured by any finite elastic contrast, or by a moderately large V-strengthening of friction. We show that (i) positive gain should be observable for rough-on-flat multicontact interfaces (ii) a sliding shear band in a granular medium should give rise to sizeable reflection, which opens a promising possibility for the detection of shear localization.