Anisotropic elastic theory of preloaded granular media

TL;DR

This paper develops a macroscopic elastic theory for static preloaded granular media, linking microscopic contact elasticity and network texture to macroscopic stress responses.

Contribution

It systematically derives an elastic description from microscopic contact elasticity, incorporating fabric tensors and grain reorientation effects.

Findings

The theory accounts for normal and tangential forces at contacts.

Reorientation of grains influences stress response.

Fabric tensors encode the system's preparation history.

Abstract

A macroscopic elastic description of stresses in static, preloaded granular media is derived systematically from the microscopic elasticity of individual inter-grain contacts. The assumed preloaded state and friction at contacts ensure that the network of inter-grain contacts is not altered by small perturbations. The texture of this network, set by the preparation of the system, is encoded in second and fourth order fabric tensors. A small perturbation generates both normal and tangential inter-grain forces, the latter causing grains to reorient. This reorientation response and the incremental stress are expressed in terms of the macroscopic strain.