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Nonlinear elasticity of semiflexible filament networks

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Publication Date: 2016-07-08

Journal Title: Soft Matter

Publisher: Royal Society of Chemistry

Volume: 12

Number: 6749

Language: English

Type: Article

This Version: VoR

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Citation: Meng, F., & Terentjev, E. M. (2016). Nonlinear elasticity of semiflexible filament networks. Soft Matter, 12 (6749)

Description: This is the final version of the article. It first appeared from RSC at

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 G$_{0}$.

Sponsorship: This work has been funded by the TCM Critical Mass Grant from EPSRC (EP/J017639).


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Rights: Attribution 4.0 International

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Autor: Meng, FanlongTerentjev, Eugene M.



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