Interparticle interaction-dependent critical point(s) govern yielding in soft particulate systems

Soft particulate materials exhibit a solid–fluid transition under shear. In the non-inertial regime, yielding is generically a two-step transition process that organizes a universal rheology across these systems. Using natural Soft-Earth suspensions as a model system, we identify: (i) an elastic-to-plastic transition at a lower critical shear rate, where an amorphous solid deforms and initiates flow, and (ii) a plastic to viscous transition at a higher critical shear rate where hydrodynamic dissipation dominates and a high-shear Newtonian limit emerges. We classify particulate systems by dominant interactions at the constituent particle scale. Frictional (granular) systems concentrate the two transitions to a single critical point, producing Bingham-like behavior and abrupt failure akin to Coulomb friction. Non-frictional systems (colloids, emulsions, and gels) generically possess two distinct critical points and exhibit a mix of Bingham and Herschel-Bulkley type flow, where the effective exponent reflects the distance between critical points and the underlying interparticle interactions in the system. By unifying granular rheology with elastoplastic models, the grain-scale interaction dependent two-point critical picture provides predictive control of plastic yielding across soft matter, relevant to manufacturing, geophysical hazard prediction, and complex fluids design.