# Effects of {Inertia} on the {Steady}-{Shear} {Rheology} of {Disordered} {Solids}

Publication Type
Journal Article
Year of Publication
2016
Authors
Nicolas, Alexandre
Barrat, Jean-Louis
Rottler, Jörg
Name of Publication
Physical Review Letters
Volume
16
Pagination
058303
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 strength ζ 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∝ζγ˙; the macroscopic stress Σ follows the frequently encountered Herschel-Bulkley law Σ=Σ0+kWi−−−√, with yield stress Σ0{\textgreater}0. In the underdamped (inertial) regime, dramatic changes in the rheology are observed for low damping: the flow curve becomes nonmonotonic. 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 thermostating more or less underdamped systems, we are able to link quantitatively the rheology to the kinetic temperature and the shear rate, rescaled with Einstein’s vibration frequency.