  Soft Glassy Materials (SGM) consist in dense amorphous assemblies of
colloidal particles of multiple shapes, elasticity, and interactions, which
confer upon them solid-like properties at rest. They are ubiquitously
encountered in modern engineering, including additive manufacturing, 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 responses, 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 nontrivial scaling laws for
fluidization times. This approach offers a versatile framework to account for
subtle effects, such as avalanche-like phenomena, 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.
