Constitutive Relations of Jammed Frictionless Granular Materials under Oscillatory Shear

TL;DR

This study uses simulations to explore how jammed frictionless granular materials respond to oscillatory shear, revealing different rheological behaviors depending on shear amplitude and frequency.

Contribution

It introduces a phenomenological constitutive model that describes the rheology of granular materials under large amplitude oscillatory shear.

Findings

Small amplitude shear exhibits visco-elastic behavior modeled by Kelvin-Voigt.

Large amplitude shear results in yield stress liquid behavior.

Rheology depends strongly on shear amplitude and frequency.

Abstract

We numerically investigate the rheological properties of jammed frictionless granular materials under an oscillatory shear in terms of our simulation of the distinct element method. It is demonstrated that the constitutive relation between the shear stress and the shear strain of grains strongly depends on the amplitude and the frequency of the oscillatory shear. For a small amplitude region, the granular material behaves as a visco-elastic material characterized by the Kelvin-Voigt model, while it behaves as a yield stress liquid for a large amplitude region. We find that the rheology of grains under the large amplitude oscillatory shear can be described by a phenomenological constitutive model.