Evidence of Raleigh-Hertz surface waves and shear stiffness anomaly in granular media

TL;DR

This study experimentally demonstrates Rayleigh-Hertz surface waves in granular media and investigates shear stiffness anomalies near the jamming transition, revealing pressure-dependent acoustic behaviors and validating non-linear elastic models.

Contribution

The paper provides direct experimental evidence of surface acoustic modes in granular media and tests shear stiffness anomalies predicted by non-linear elasticity near jamming.

Findings

Detection of Rayleigh-Hertz surface waves in granular materials.

Observation of shear stiffness anomaly near the jamming transition.

Validation of non-linear elastic models with finite size effects.

Abstract

Due to the non-linearity of Hertzian contacts, the speed of sound in granular matter increases with pressure. Under gravity, the non-linear elastic description predicts that acoustic propagation is only possible through surface modes, called Rayleigh-Hertz modes and guided by the index gradient. Here we directly evidence these modes in a controlled laboratory experiment and use them to probe the elastic properties of a granular packing under vanishing confining pressure. The shape and the dispersion relation of both transverse and sagittal modes are compared to the prediction of non-linear elasticity that includes finite size effects. This allows to test the existence of a shear stiffness anomaly close to the jamming transition.