Stress Overshoots in Simple Yield Stress Fluids

TL;DR

This paper develops a continuum model to explain stress overshoots in soft glassy materials under shear, revealing power-law scalings and regimes linked to fluidization dynamics, thus providing a comprehensive understanding of their transient rheological response.

Contribution

It introduces a continuum model that predicts power-law scalings of stress overshoot parameters and identifies different regimes based on shear rate, connecting local dynamics to global rheology.

Findings

Stress maximum increases as a power law of shear rate.

Two regimes of response are identified at low and high shear rates.

Model links nucleation and growth of fluidized regions to stress overshoot.

Abstract

Soft glassy materials such as mayonnaise, wet clays, or dense microgels display under external shear a solid-to-liquid transition. Such a shear-induced transition is often associated with a non-monotonic stress response, in the form of a stress maximum referred to as "stress overshoot". This ubiquitous phenomenon is characterized by the coordinates of the maximum in terms of stress $\sigma_\text{M}$ and strain $\gamma_\text{M}$ that both increase as weak power laws of the applied shear rate. Here we rationalize such power-law scalings using a continuum model that predicts two different regimes in the limit of low and high applied shear rates. The corresponding exponents are directly linked to the steady-state rheology and are both associated with the nucleation and growth dynamics of a fluidized region. Our work offers a consistent framework for predicting the transient response of soft glassy materials upon start-up of shear from the local flow behavior to the global rheological observables.