  The yield stress is a defining feature of amorphous materials which is
difficult to analyze theoretically, because it stems from the strongly
non-linear response of an arrested solid to an applied deformation.
Mode-coupling theory predicts the flow curves of materials undergoing a glass
transition, and thus offers predictions for the yield stress of amorphous
solids. We use this approach to analyse several classes of disordered solids,
using simple models of hard sphere glasses, soft glasses, and metallic glasses
for which the mode-coupling predictions can be directly compared to the outcome
of numerical measurements. The theory correctly describes the emergence of a
yield stress of entropic nature in hard sphere glasses, and its rapid growth as
density approaches random close packing at qualitative level. By contrast, the
emergence of solid behavior in soft and metallic glasses, which originates from
direct particle interactions is not well described by the theory. We show that
similar shortcomings arise in the description of the vibrational dynamics of
the glass phase at rest. We discuss the range of applicability of mode-coupling
theory to understand the yield stress and non-linear rheology of amorphous
materials.
