Do solids flow?

TL;DR

This paper explores whether solids can flow like liquids, revealing that solids are time-scale dependent and can flow under infinitesimal stress with diverging viscosity, and predicts a dynamic phase transition under oscillatory shear.

Contribution

It demonstrates that solids can flow under infinitesimal stress with diverging viscosity and introduces a dynamic phase transition line under oscillatory shear.

Findings

Solids flow under infinitesimal stress with diverging viscosity.

Shear stress decreases ultra-slowly with shear rate.

A predicted dynamic phase transition under oscillatory shear.

Abstract

Are solids intrinsically different from liquids? Must a finite stress be applied in order to induce flow? Or, instead, do all solids only look rigid on some finite timescales and eventually flow if an infinitesimal shear stress is applied? Surprisingly, these simple questions are a matter of debate and definite answers are still lacking. Here we show that solidity is only a time-scale dependent notion: equilibrium states of matter that break spontaneously translation invariance, e.g. crystals, flow if even an infinitesimal stress is applied. However, they do so in a way inherently different from ordinary liquids since their viscosity diverges for vanishing shear stress with an essential singularity. We find an ultra-slow decrease of the shear stress as a function of the shear rate, which explains the apparent yield stress identified in rheological flow curves. Furthermore, we suggest that an alternating shear of frequency $\omega$ and amplitude $\gamma$ should lead to a dynamic phase transition line in the ($\omega$,$\gamma$) plane, from a 'flowing' to a 'non-flowing' phase. Finally, we apply our results to crystals, show the corresponding microscopic process leading to flow and discuss possible experimental investigations.