Effects of inertia on the steady-shear rheology of disordered solids

TL;DR

This study uses molecular dynamics simulations to explore how inertia and damping influence the steady-shear rheology of disordered solids, revealing distinct flow regimes and the impact of temperature and damping on flow behavior.

Contribution

It identifies two flow regimes in disordered solids under shear, showing how inertia and damping alter rheological laws and flow characteristics in a systematic way.

Findings

Overdamped regime follows Herschel-Bulkley law with positive yield stress.

Underdamped regime exhibits non-monotonic flow curves at low damping.

Rheology depends on kinetic temperature and shear rate, scaled by vibration frequency.

Abstract

We study the finite-shear-rate rheology of disordered solids by means of molecular dynamics simulations in two dimensions. By systematically varying the damping magnitude $\zeta$ in the low-temperature limit, we identify two well defined flow regimes, separated by a thin (temperature-dependent) crossover region. In the overdamped regime, the athermal rheology is governed by the competition between elastic forces and viscous forces, whose ratio gives the Weissenberg number $Wi= \zeta \dot\gamma$ (up to elastic parameters); the macroscopic stress $\Sigma$ follows the frequently encountered Herschel-Bulkley law $\Sigma= \Sigma\_0 + k \sqrt{Wi}$, with yield stress $\Sigma\_0\textgreater{}0$. In the underdamped (inertial) regime, dramatic changes in the rheology are observed for low damping: the flow curve becomes non-monotonic. This change is not caused by longer-lived correlations in the particle dynamics at lower damping; instead, for weak dissipation, the sample heats up considerably due to, and in proportion to, the driving. By suitably thermostatting more or less underdamped systems, we show that their rheology only depends on their kinetic temperature and the shear rate, rescaled with Einstein's vibration frequency.