Stress - Strain Rate Relation in Plug-Free Flow of Dense Granular Matter

TL;DR

This paper derives a macroscopic stress-strain rate relation for dense granular flow, based on first-principles coarse-graining and the da Vinci Fluid model, enhancing existing models by explicitly incorporating normal contact forces and solid friction.

Contribution

It provides a new explicit form for the stress-strain rate relation in dense granular flow, improving the theoretical understanding and modeling of such systems.

Findings

Derived the macroscopic stress tensor from inter-granular forces.

Provided an explicit stress-strain rate relation for dense granular flow.

Enhanced existing models by explicitly including normal contact forces and solid friction.

Abstract

We derive the macroscopic stress tensor for plug-free dense granular flow, using a first-principles coarse-graining of the inter-granular forces. The derivation is based on the assumption, which defines the da Vinci Fluid model, that the inter-granular interactions are dominated by normal contact forces and solid friction. An explicit form for the stress -- strain rate relation is obtained, providing closure for the flow equations of dense granular fluids and improves on existing models, which are also based on solid friction as the dominant drag mechanism.