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Networks and dense suspensions frequently reside near a boundary between soft(or fluid-like) and rigid (or solid-like) regimes. Transitions between theseregimes can be driven by changes in structure, density, or applied stress orstrain. In general, near the onset or loss of rigidity in these systems,dissipation-limiting heterogeneous nonaffine rearrangements dominate themacroscopic viscoelastic response, giving rise to diverging relaxation timesand power-law rheology. Here, we describe a simple quantitative relationshipbetween nonaffinity and the excess viscosity. We test thisnonaffinity-viscosity relationship computationally and demonstrate itsrheological consequences in simulations of strained filament networks and densesuspensions. We also predict critical signatures in the rheology ofsemiflexible and stiff biopolymer networks near the strain stiffeningtransition.

Strain-controlled critical slowing down in the rheology of disordered networks