Quantification of plasticity via particle dynamics above and below yield in a 2D jammed suspension

Abstract

Failure of amorphous materials is characterized by the emergence of dissipation. The connection between particle dynamics, dissipation, and overall material rheology, however, has still not been elucidated. Here, we take a new approach relating trajectories to yielding, using a custom built interfacial stress rheometer, which allows for measurement of shear moduli (G',G'') of a dense athermal suspension's microstructure while simultaneously tracking particle trajectories undergoing cyclic shear. We find an increase in total area traced by particle trajectories as the system is stressed well below to well above yield. Trajectories may be placed into three categories: reversibly elastic paths; reversibly plastic paths, associated with smooth limit cycles; and irreversibly plastic paths, in which particles do not return to their original position. We find that above yield, reversibly plastic trajectories are predominantly found near to the shearing surface, whereas reversibly elastic paths are more prominent near the stationary wall. This spatial transition between particles acting as solids to those acting as liquids is characteristic of a 'melting front', which is observed to shift closer to the wall with increasing strain. We introduce a non-dimensional measure of plastic dissipation based on particle trajectories that scales linearly with strain amplitude both above and below yield, and that is unity at the rheological yield point. Surprisingly, this relation collapses for three systems of varying degrees of disorder.