Do yield-stress materials flow prior to yielding?

The mechanical response of yield-stress materials below the yield point remains a subject of debate. Two of the most widely used constitutive models for these materials offer fundamentally conflicting views: one permits plastic flow at all stress levels, the other assumes entirely recoverable viscoelasticity below yield. Using parallel superposition rheometry, we test the sub-yield behaviour of a microgel and an emulsion. Both fluids exhibit bounded, periodic strain responses, offering compelling evidence that they do not flow in the studied regime. Our results indicate that the sub-yield regime is underpinned by nonlinear viscoelasticity and underscore the need for improved constitutive relations that capture such effects without treating yielding as a precursor for nonlinearity.