Acoustics of Unconsolidated Model Granular Media: An Overview of Recent Results and Several Open Problems

Unconsolidated model granular media, such as packings of elastic beads in non cohesive contact, belong maybe to the most complicated class of materials from the point of view of the acoustic wave propagation as they gather most of the existing features influencing mechanical waves: velocity dispersion, nonlinearities (classical, hysteretic, clapping for instance), scattering (by the beads, the contact disorder, the geometrical disorder, the force chains), anisotropy, memory, relaxation, thermo-elasticity, mode coupling (Biot waves, rotational waves), macroscopic inhomogeneity (elastic property gradient), spatial correlations, fragility, and so on. The relative importance of these phenomena on the actual acoustic waves depends drastically on the granular medium state (ordering, applied static pressure, compacity) and on the wave properties (amplitude, frequency). We summarize in this article the state of our understanding of the different medium configurations and wave parameters for which some of the processes dominate or in contrary play a negligible role on the acoustic linear and nonlinear propagation. Interpretations rely on experimental results obtained under various configurations.