Granular Solid Hydrodynamics

TL;DR

This paper develops a comprehensive hydrodynamic theory for granular media by extending elasticity to include plasticity and temperature effects, unifying static and dynamic behaviors within a jamming phase diagram.

Contribution

It introduces a unified hydrodynamic framework that incorporates both elastic and plastic responses, including temperature effects, for granular materials.

Findings

Reduces to hypoplasticity in stationary temperature conditions

Provides a full jamming phase diagram model

Integrates static stress distribution with dynamic behavior

Abstract

Granular elasticity, an elasticity theory useful for calculating static stress distribution in granular media, is generalized to the dynamic case by including the plastic contribution of the strain. A complete hydrodynamic theory is derived based on the hypothesis that granular medium turns transiently elastic when deformed. This theory includes both the true and the granular temperatures, and employs a free energy expression that encapsulates a full jamming phase diagram, in the space spanned by pressure, shear stress, density and granular temperature. For the special case of stationary granular temperatures, the derived hydrodynamic theory reduces to {\em hypoplasticity}, a state-of-the-art engineering model.