Small and Large Scale Granular Statics

TL;DR

This paper reviews recent experimental findings on granular materials' static response, discussing the applicability of traditional elastic models versus alternative hyperbolic or diffusive models, and emphasizes the importance of grain-scale descriptions and friction effects.

Contribution

It highlights the limitations of continuum elasticity in granular systems and advocates for grain-scale and nonlinear elastic models, incorporating friction and anisotropy, to better interpret experimental results.

Findings

Elasticity can describe some large-scale properties of granular assemblies.

Friction significantly influences the contact network and system anisotropy.

Nonlinear, stress-history dependent elastic models are useful for complex granular behaviors.

Abstract

Recent experimental results on the static or quasistatic response of granular materials have been interpreted to suggest the inapplicability of the traditional engineering approaches, which are based on elasto-plastic models (which are elliptic in nature). Propagating (hyperbolic) or diffusive (parabolic) models have been proposed to replace the `old' models. Since several recent experiments were performed on small systems, one should not really be surprised that (continuum) elasticity, a macroscopic theory, is not directly applicable, and should be replaced by a grain-scale (``microscopic'') description. Such a description concerns the interparticle forces, while a macroscopic description is given in terms of the stress field. These descriptions are related, but not equivalent, and the distinction is important in interpreting the experimental results. There are indications that at least some large scale properties of granular assemblies can be described by elasticity, although not necessarily its isotropic version. The purely repulsive interparticle forces (in non-cohesive materials) may lead to modifications of the contact network upon the application of external forces, which may strongly affect the anisotropy of the system. This effect is expected to be small (in non-isostatic systems) for small applied forces and for pre-stressed systems (in particular for disordered systems). Otherwise, it may be accounted for using a nonlinear, incrementally elastic model, with stress-history dependent elastic moduli. Although many features of the experiments may be reproduced using models of frictionless particles, results demonstrating the importance of accounting for friction are presented.