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Issue 29, 2013
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Dynamical behavior of disordered spring networks

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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* ∼ ()Δ where Δ = 0.41, in discord with a mean field prediction of Δ = 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.

Graphical abstract: Dynamical behavior of disordered spring networks

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Article information


Submitted
16 Jan 2013
Accepted
27 Mar 2013
First published
25 Apr 2013

Soft Matter, 2013,9, 7000-7006
Article type
Paper

Dynamical behavior of disordered spring networks

M. G. Yucht, M. Sheinman and C. P. Broedersz, Soft Matter, 2013, 9, 7000
DOI: 10.1039/C3SM50177A

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