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Shear banding, discontinuous shear thickening, and rheological phase transitions in athermally sheared frictionless disks

Daniel Vågberg, Peter Olsson, and S. Teitel
Phys. Rev. E 95, 052903 – Published 30 May 2017

Abstract

We report on numerical simulations of simple models of athermal, bidisperse, soft-core, massive disks in two dimensions, as a function of packing fraction ϕ, inelasticity of collisions as measured by a parameter Q, and applied uniform shear strain rate γ̇. Our particles have contact interactions consisting of normally directed elastic repulsion and viscous dissipation, as well as tangentially directed viscous dissipation, but no interparticle Coulombic friction. Mapping the phase diagram in the (ϕ,Q) plane for small γ̇, we find a sharp first-order rheological phase transition from a region with Bagnoldian rheology to a region with Newtonian rheology, and show that the system is always Newtonian at jamming. We consider the rotational motion of particles and demonstrate the crucial importance that the coupling between rotational and translational degrees of freedom has on the phase structure at small Q (strongly inelastic collisions). At small Q, we show that, upon increasing γ̇, the sharp Bagnoldian-to-Newtonian transition becomes a coexistence region of finite width in the (ϕ,γ̇) plane, with coexisting Bagnoldian and Newtonian shear bands. Crossing this coexistence region by increasing γ̇ at fixed ϕ, we find that discontinuous shear thickening can result if γ̇ is varied too rapidly for the system to relax to the shear-banded steady state corresponding to the instantaneous value of γ̇.

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  • Received 3 March 2017

DOI:https://doi.org/10.1103/PhysRevE.95.052903

©2017 American Physical Society

Physics Subject Headings (PhySH)

Polymers & Soft Matter

Authors & Affiliations

Daniel Vågberg1, Peter Olsson2, and S. Teitel3

  • 1Laboratoire Charles Coulomb, UMR 5221 CNRS, Université Montpellier, Montpellier, France
  • 2Department of Physics, Umeå University, 901 87 Umeå, Sweden
  • 3Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA

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Issue

Vol. 95, Iss. 5 — May 2017

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