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Issue 32, 2016
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Nonlinear elasticity of semiflexible filament networks

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Abstract

We develop a continuum theory for equilibrium elasticity of a network of crosslinked semiflexible filaments, spanning the full range between flexible entropy-driven chains to stiff athermal rods. We choose the 3-chain constitutive model of network elasticity over several plausible candidates, and derive analytical expressions for the elastic energy at arbitrary strain, with the corresponding stress–strain relationship. The theory fits well to a wide range of experimental data on simple shear in different filament networks, quantitatively matching the differential shear modulus variation with stress, with only two adjustable parameters (which represent the filament stiffness and the pre-tension in the network, respectively). The general theory accurately describes the crossover between the positive and negative Poynting effect (normal stress on imposed shear) on increasing the stiffness of filaments forming the network. We discuss the network stability (the point of marginal rigidity) and the phenomenon of tensegrity, showing that filament pre-tension on crosslinking into the network determines the magnitude of linear modulus G0.

Graphical abstract: Nonlinear elasticity of semiflexible filament networks

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Publication details

The article was received on 03 May 2016, accepted on 08 Jul 2016 and first published on 08 Jul 2016


Article type: Paper
DOI: 10.1039/C6SM01029F
Soft Matter, 2016,12, 6749-6756
  • Open access: Creative Commons BY license
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    Nonlinear elasticity of semiflexible filament networks

    F. Meng and E. M. Terentjev, Soft Matter, 2016, 12, 6749
    DOI: 10.1039/C6SM01029F

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