The acoustic properties of granular materials are inherently non-linear and complex, reflecting the highly heterogeneous structure and history-dependence of particle interactions. Of particular interest is the Density of Vibrational Modes, which has been shown to be related to the rigidity of jammed, disordered solids [1,2,3]. In [prior work] we've established a technique with which to measure the density of modes for static, granular systems without detailed knowledge of the particle interactions or structure.
We are now extending this methodology to characterize the acoustic emissions from granular systems which exhibit stick-slip behavior under shear. Our apparatus is an annular shear cell with a dozen acoustic probes, as well as precision stress and strain sensors. Our granular material is photoelastic, which facilitates the measurement of contact forces between grains. Examples of experimental images (top) of the contact force network, timestamped relative to the time of a slip event, along with the associated difference images (bottom) are provided above. Images such as these allow us to see the structure and dynamics of a given event. By studying the time evolution of the Density of Modes, we hope to better understand the mechanics that dictate wait times between slip events, as well as the duration and spatial extent of the associated deformation.
We've also begun to study the shape dependence of the Density of Modes (with undergraduates Alex Mauney [now a doctoral student at Cornell], and senior Rebekah Lee). Besides simply reducing the symmetry of the system or introducing rotational coupling between grains, particles with angular shape, or with concave faces can introduce qualitatively different modes of contact, as illustrated above. Understanding the effect shape has on the acoustic properties of granular packings may facilitate effective design of acoustic metamaterials.