Continuum modeling of soft glassy materials under shear

Soft Glassy Materials (SGM) consist in dense amorphous assemblies of colloidal par-ticles of multiple shapes, elasticity, and interactions, which confer upon them solid-like properties at rest. They are ubiquitously encountered in modern engineering, including additive manufactur-ing, semi-solid flow cells, dip coating, adhesive locomotion, where they are subjected to complex mechanical histories. Such processes often include a solid-to-liquid transition induced by large enough shear, which results in complex transient phenomena such as non-monotonic stress re-sponses, i.e., stress overshoot, and spatially heterogeneous flows, e.g., shear banding or brittle failure. In the present article, we propose a pedagogical introduction to a continuum model based on a spatially resolved fluidity approach that we recently introduced to rationalize shear-induced yielding in SGMs. Our model, which relies upon non-local effects, quantitatively captures salient features associated with such complex flows, including the rate dependence of the stress overshoot, as well as transient shear-banded flows together with non-trivial scaling laws for fluidization times. This approach offers a versatile framework to account for subtle effects, such as avalanche-like phe-nomena, or the impact of boundary conditions, which we illustrate by including in our model the elasto-hydrodynamic slippage of soft particles compressed against solid surfaces.