An exact expression of three-body system for the complex shear modulus of frictional granular materials
Soft Condensed Matter
2023-04-04 v3 Statistical Mechanics
Abstract
We propose a simple model comprising three particles to study the nonlinear mechanical response of jammed frictional granular materials under oscillatory shear. Owing to the introduction of the simple model, we obtain an exact analytical expression of the complex shear modulus for a system including many mono-dispersed disks, which satisfies a scaling law in the vicinity of the jamming point. These expressions perfectly reproduce the shear modulus of the many-body system with low strain amplitudes and friction coefficients. Even for disordered many-body systems, the model reproduces results by introducing a single fitting parameter.
Keywords
Cite
@article{arxiv.2211.03294,
title = {An exact expression of three-body system for the complex shear modulus of frictional granular materials},
author = {Michio Otsuki and Hisao Hayakawa},
journal= {arXiv preprint arXiv:2211.03294},
year = {2023}
}