Strain-induced critical slowing of stress relaxation in disordered networks

Common biological materials contain embedded fibrous networks that stiffen significantly in response to applied strain, a phenomenon that provides living tissues with enhanced mechanical resilience and enables long-range force transmission by cells. Prior work has shown that strain-induced stiffening in mechanically under-constrained elastic networks corresponds to the traversal of a “critical point” in strain, at which the energy-minimizing network configuration becomes marginally stable. Near this transition, various quantities measured via quasistatic deformation exhibit power law scaling with respect to the reduced strain. However, the dynamics of systems near this transition remain poorly understood. Here, we model the small-amplitude oscillatory shear and stress relaxation of under-constrained, fluid-immersed elastic networks subjected to applied extensional pre-strain (e.g. swelling and simple shear). We show that the rheology of these networks is controlled by a pre-strain-controlled correlation length and corresponding characteristic relaxation time that both diverge at a connectivity-controlled critical point, giving rise to weak power law scaling of the complex modulus with frequency and diverging strain fluctuations.