Granular Packings: Nonlinear elasticity, sound propagation and collective relaxation dynamics

TL;DR

This study investigates the elastic properties of granular packings under compression, revealing limitations of classical elasticity theory and emphasizing the importance of collective relaxation mechanisms for accurate modeling.

Contribution

The paper provides a comprehensive experimental, numerical, and theoretical analysis of granular elasticity, highlighting discrepancies with classical models and proposing the significance of nonaffine relaxations.

Findings

Elastic moduli increase faster than 1/3 power law under compression.

Elasticity theory partially explains compressional responses but fails under shear.

Collective relaxation mechanisms are crucial for understanding granular dynamics.

Abstract

Experiments on isotropic compression of a granular assembly of spheres show that the shear and bulk moduli vary with the confining pressure faster than the 1/3 power law predicted by Hertz-Mindlin effective medium theories (EMT) of contact elasticity. Moreover, the ratio between the moduli is found to be larger than the prediction of the elastic theory by a constant value. The understanding of these discrepancies has been a longstanding question in the field of granular matter. Here we perform a test of the applicability of elasticity theory to granular materials. We perform sound propagation experiments, numerical simulations and theoretical studies to understand the elastic response of a deforming granular assembly of soft spheres under isotropic loading. Our results for the behavior of the elastic moduli of the system agree very well with experiments. We show that the elasticity partially describes the experimental and numerical results for a system under compressional loads. However, it drastically fails for systems under shear perturbations, particularly for packings without tangential forces and friction. Our work indicates that a correct treatment should include not only the purely elastic response but also collective relaxation mechanisms related to structural disorder and nonaffine motion of grains.