Abstract
Concentrated colloidal suspensions and emulsions are amorphous soft solids, widespread in technological and industrial applications and studied as model systems in physics and materials sciences. They are easily fluidized by applying mechanical stress, undergoing a yielding transition that still lacks a unified description. Here we investigate yielding in three classes of repulsive soft solids and find that at the microscopic level, yielding consists of a transition between two distinct dynamical states. We rationalize this by proposing a lattice model with dynamical coupling between neighbouring sites, leading to a unified state diagram for yielding. Employing the analogy with van der Waals phase diagram for real gases, we show that distance from a critical point plays a major role in the emergence of first-order-like versus second-order-like features in yielding, thereby reconciling previously contrasting observations on the nature of the transition.