Anomalous acoustic reflection on a sliding interface or a shear band.

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 Nosonovsky and Adams [Int. J. Eng. Sci. 39, 1257 (2001)]. But this pathology is cured by a moderately large V strengthening of friction, or, for systems with not too large friction coefficients, by any finite elastic contrast. We show that (i) positive gain should be observable for rough-on-flat multicontact interfaces and (ii) a sliding shear band in a granular medium should give rise to sizable reflection, which opens a promising possibility for the detection of shear localization.

Pressure dependence of the sound velocity in a two-dimensional lattice of Hertz-Mindlin balls: mean-field description.

We study the dependence on the external pressure P of the velocities v(L,T) of long wavelength sound waves in a confined two-dimensional hexagonal close-packed lattice of 3D elastic frictional balls interacting via one-sided Hertz-Mindlin contact forces, whose diameters exhibit mild dispersion. The presence of an underlying long range order enables us to build an effective medium description, which incorporates the radial fluctuations of the contact forces acting on a single site. Due to the nonlinearity of Hertz elasticity, self-consistency results in a highly nonlinear differential equation for the "equation of state" linking the effective stiffness of the array with the applied pressure, from which sound velocities are then obtained. The results are in excellent agreement with existing experimental results and simulations in the high- and intermediate-pressure regimes. It emerges from the analysis that the departure of v(L)(P) from the ideal P(1/6) Hertz behavior must be attributed primarily to the fluctuations of the stress field, rather than to the pressure dependence of the number of contacts.