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Concentrated colloidal suspensions and emulsions are amorphous soft solids,widespread in technological and industrial applications and studied as modelsystems in physics and material sciences. They are easily fluidized by applyinga mechanical stress, undergoing a yielding transition that still lacks aunified description. Here, we investigate yielding in three classes ofrepulsive soft solids, using analytical and numerical modelling and experimentsprobing the microscopic dynamics and mechanical response under oscillatoryshear. We find that at the microscopic level yielding consists in a transitionbetween two distinct dynamical states, which we rationalize by proposing alattice model with dynamical coupling between neighboring sites, leading to aunified state diagram for yielding. Leveraging the analogy with Wan der Waals'sphase diagram for real gases, we show that distance from a critical point playsa major role in the emergence of first-order-like vs second-order-like featuresin yielding, thereby reconciling previously contrasting observations on thenature of the transition.

A unified state diagram for the yielding transition of soft colloids