Elasto-frictional reduced model of a cyclically sheared container filled with particles

TL;DR

This paper develops and validates a simplified elasto-frictional model to describe the hysteretic and damping behavior of granular media under cyclic shear, capturing key nonlinear responses across various conditions.

Contribution

It introduces a reduced single degree-of-freedom model that reliably predicts granular response under cyclic shear, linking parameters to granular rheology and effective medium theory.

Findings

Model accurately describes nonlinear granular response.

Mechanical behavior depends on a dimensionless parameter similar to Coulomb threshold.

Optimal damping occurs at the transition between unjammed and elastic regimes.

Abstract

This article explores the hysteretic behavior and the damping features of sheared granular media using discrete element method (DEM) simulations. We consider polydisperse non-cohesive frictional spherical particles, enclosed in a container with rigid but moving walls, submitted to a cyclic simple shear superimposed to a confining pressure. The mechanical response of the grains is analyzed in the permanent regime, by fitting the macroscopic stress-strain relation applied to the box with a Dahl-like elasto-frictional model. The influence of several parameters such as the amplitude of the strain, the confining pressure, the elasticity, the friction coefficient, the size and the number of particles are explored. We find that the fitted parameters of our macroscopic Ansatz qualitatively rely on both a well-established effective medium theory of confined granular media and a well-documented rheology of granular flow. Quantitatively, we demonstrate that the single degree-of-freedom elasto-frictional reduced model reliably describes the nonlinear response of the granular layer over a wide range of operating conditions. In particular, we show that the mechanical response of a granular slab under simple shear depends on an unique dimensionless parameter, akin to an effective Coulomb threshold, at low shear/high pressure. Further, exploring higher shear/lower pressure, we evidence an optimal damping at the crossover between a loose unjammed regime and a dense elastic regime.