Transitional nonlinear elastic behaviour in dense granular media

Nonlinear sound propagation in a stressed glass bead pack is investigated via amplitude measurements of harmonic generation. We evidence two distinct regimes of sound-matter interaction: reversible and irreversible, as a function of the ratio r(s) between dynamic strain and static one. In the reversible regime, the higher harmonics generated agree well with a mean-field model based on the Hertz contact theory, and the coefficient of nonlinearity beta deduced from the measured amplitude of second-harmonic is consistent with that deduced from the acoustoelastic measurement. Beyond a certain threshold (r(s) > 3%), the interaction of sound wave with granular matter becomes irreversible, accompanied by a small compaction of the medium.