Anisotropy in granular media: classical elasticity and directed force chain network

TL;DR

This paper develops a unified framework for analyzing stress responses in anisotropic granular layers, revealing that classical elastic models can produce two-peak responses with linear growth, contrasting with hyperbolic models.

Contribution

It introduces a formalism that encompasses both classical anisotropic elasticity and directed force chain networks, clarifying their response behaviors in granular media.

Findings

Two-peak response functions can occur in classical anisotropic elastic materials.

Peak widths grow linearly with layer height, indicating diffusive spreading.

Directed force chain networks studied are in the elliptic regime, not hyperbolic.

Abstract

A general approach is presented for understanding the stress response function in anisotropic granular layers in two dimensions. The formalism accommodates both classical anisotropic elasticity theory and linear theories of anisotropic directed force chain networks. Perhaps surprisingly, two-peak response functions can occur even for classical, anisotropic elastic materials, such as triangular networks of springs with different stiffnesses. In such cases, the peak widths grow linearly with the height of the layer, contrary to the diffusive spreading found in `stress-only' hyperbolic models. In principle, directed force chain networks can exhibit the two-peak, diffusively spreading response function of hyperbolic models, but all models in a particular class studied here are found to be in the elliptic regime.