A microscopic theory for discontinuous shear thickening of frictional granular materials

TL;DR

This paper develops a microscopic theoretical framework for understanding discontinuous shear thickening in frictional granular materials, extending previous models for frictionless systems and capturing hysteresis phenomena.

Contribution

It introduces a microscopic derivation of rheological equations for frictional disks, accounting for shear stress hysteresis and discontinuous thickening.

Findings

The theory reproduces flow curves and shear stress hysteresis.

Numerical solutions match experimental signatures of shear thickening.

The model extends prior frictionless theories to frictional granular systems.

Abstract

We extend a recent theory for the rheology of frictionless granular materials [K. Suzuki and H. Hayakawa, Phys. Rev. Lett. 2015, 115, 098001] to the case of frictional disks in two dimensions. Employing a frictional contact model for molecular dynamics simulations, we derive difference equations of the shear stress, the granular temperature, and the spin temperature from the generalized Green-Kubo formula, where all the terms are given by microscopic expressions. The numerical solutions of the difference equations not only describe the flow curve, but also reproduce the hysteresis of shear stress, which can be the signature of discontinuous shear thickening of frictional disks.