Dynamical behavior of disordered spring networks

Abstract

We study the dynamical rheology of spring networks with a percolation model constructed by bond dilution in a two-dimensional triangular lattice. Hydrodynamic interactions are implemented by a Stokesian viscous coupling between the network nodes and a uniformly deforming liquid. Our simulations show that in a critical connectivity regime, these systems display weak power law rheology in which the complex shear modulus scales with frequency as G^* ~ (i * omega)^Delta where Delta = 0.41, in discord with a mean field prediction of Delta = 1/2. The weak power law rheology in the critical regime can be understood from a simple scaling relation between the macroscopic rheology and the nonaffine strain fluctuations, which diverge with vanishing frequency for isostatic networks. We expand on a dynamic effective medium theory, showing that it quantitatively describes the rheology of a diluted triangular lattice far from isostaticity; although the EMT correctly predicts the scaling form for the rheology of near-isostatic networks, there remains a quantitative disparity due to the mean-field nature of the EMT. Surprisingly, by connecting this critical scaling of the rheology with that of the strain fluctuations, we find that the dynamical behavior of disordered spring networks is fully determined by the critical exponents that govern the behavior of elastic network in the absence of viscous interactions.

7 pages, 6 figures

References in corpus (19)

• Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder
• Elasticity of Stiff Polymer Networks
• Deformation of crosslinked semiflexible polymer networks
• Criticality and isostaticity in fiber networks
• A coordination-based approach to elasticity of floppy and stiff random networks
• A unified framework for non-Brownian suspension flows and soft amorphous solids
• The jamming transition as probed by quasistatic shear flow
• Floppy modes and non-affine deformations in random fiber networks
• Scaling of phononic transport with connectivity in amorphous solids
• Non-affine response: jammed packings versus spring networks
• Relaxations and rheology near jamming
• Shear flow of non-Brownian suspensions close to jamming
• Effective medium theory of semiflexible filamentous networks
• Nonlinear effective medium theory of disordered spring networks
• Phonon gap and localization lengths in floppy materials
• Redundancy and cooperativity in the mechanics of compositely crosslinked filamentous networks
• Actively stressed marginal networks
• Toward a microscopic description of flow near the jamming threshold
• Floppiness, cutting, and freezing: Dynamic critical scaling near isostaticity

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• Non-affine deformation of semiflexible polymer and fiber networks
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• Jamming as a Multicritical Point
• Strain-controlled critical slowing down in the rheology of disordered networks
• Importance of non-affine viscoelastic response in disordered fibre networks
• Scaling behavior of non-equilibrium measures in internally driven elastic assemblies
• Non-affinity and fluid-coupled viscoelastic plateau for immersed fiber networks
• Universal scaling for disordered viscoelastic matter near the onset of rigidity
• Criticality enhances the reinforcement of disordered networks by rigid inclusions
• Viscoelastic scaling regimes for marginally-rigid fractal spring networks