Experimental data on a cracked medium exhibiting high acoustic nonlinearity is a commonly observed phenomenon. Here a physical model of a medium with cracks is suggested to explain the observed phenomena. The model is based on the assumption of uniform stress that is valid for a low concentration of cracks. The crack behavior is described using the model in which a crack is represented as an elastic contact of two rough surfaces, pressed one to the other under the action of internal stresses in the surrounding solid. Linear and nonlinear acoustic constants of the fractured medium are calculated. It is shown that, in this medium, negative values of the Poisson’s ratio and anomalously high values of the nonlinear constants are possible.

Rectification (demodulation) of high-frequency shear acoustic bursts is applied to probe the distribution of contact forces in 3D granular media. Symmetry principles allow for rectification of the shear waves only with their conversion into longitudinal mode. The rectification is due to nonlinear dynamic dilatancy, which is found to follow a quadratic or Hertzian power law in the shear wave amplitude. Evidence is given that a significant portion of weak contact forces is localized below 10(-2) of the mean force-a range previously inaccessible by experiment. Strong anisotropy of nonlinearity for shear waves with different polarization is observed.

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