An Expression for the Granular Elastic Energy

TL;DR

This paper proposes an improved elastic energy expression for granular media within GSH, addressing stability limits, wave velocity anisotropy, and multiple yield surfaces, enhancing the model's realism and applicability.

Contribution

It introduces a refined elastic energy formula that incorporates realistic stability angles, anisotropic wave propagation, and multiple yield criteria in granular media modeling.

Findings

Increased maximum stable angle from 26° to 30°.

Successfully reproduces directional differences in wave velocities.

Incorporates multiple yield surfaces, including Coulomb, Lade-Duncan, and Matsuoka-Nakai.

Abstract

Granular Solid Hydrodynamics (GSH) is a broad-ranged continual mechanical description of granular media capable of accounting for static stress distributions, yield phenomena, propagation and damping of elastic waves, the critical state, shear band, and fast dense flow. An important input of GSH is an expression for the elastic energy needed to deform the grains. The original expression, though useful and simple, has some draw-backs. Therefore, a slightly more complicated expression is proposed here that eliminates three of them: (1) The maximal angle at which an inclined layer of grains remains stable is increased from $26^\circ$ to the more realistic value of $30^\circ$. (2)Depending on direction and polarization, transverse elastic waves are known to propagate at slightly different velocities. The old expression neglects these differences, the new one successfully reproduces them. (3) Most importantly, the old expression contains only the Drucker-Prager yield surface. The new one contains in addition those named after Coulomb, Lade-Duncan and Matsuoka-Nakai -- realizing each, and interpolating between them, by shifting a single scalar parameter.