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  Elasticity of 3D networks with rigid filaments and compliant crosslinks

Heidemann, K. M., Sharma, A., Rehfeldt, F., Schmidt, C. F., & Wardetzky, M. (2015). Elasticity of 3D networks with rigid filaments and compliant crosslinks. Soft Matter, 11(2), 343-354. doi:10.1039/C4SM01789G.

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Heidemann, Knut M.1, Author              
Sharma, Abhinav, Author
Rehfeldt, Florian, Author
Schmidt, Christoph F, Author
Wardetzky, Max, Author
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1Group Physics of social systems, Department of Dynamics of Complex Fluids, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society, ou_3171842              

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 Abstract: Disordered filamentous networks with compliant crosslinks exhibit a low linear elastic shear modulus at small strains, but stiffen dramatically at high strains. Experiments have shown that the elastic modulus can increase by up to three orders of magnitude while the networks withstand relatively large stresses without rupturing. Here, we perform an analytical and numerical study on model networks in three dimensions. Our model consists of a collection of randomly oriented rigid filaments connected by flexible crosslinks that are modeled as wormlike chains. Due to zero probability of filament intersection in three dimensions, our model networks are by construction prestressed in terms of initial tension in the crosslinks. We demonstrate how the linear elastic modulus can be related to the prestress in these networks. Under the assumption of affine deformations in the limit of infinite crosslink density, we show analytically that the nonlinear elastic regime in 1- and 2-dimensional networks is characterized by power-law scaling of the elastic modulus with the stress. In contrast, 3-dimensional networks show an exponential dependence of the modulus on stress. Independent of dimensionality, if the crosslink density is finite, we show that the only persistent scaling exponent is that of the single wormlike chain. We further show that there is no qualitative change in the stiffening behavior of filamentous networks even if the filaments are bending-compliant. Consequently, unlike suggested in prior work, the model system studied here cannot provide an explanation for the experimentally observed linear scaling of the modulus with the stress in filamentous networks.

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 Dates: 2015-10
 Publication Status: Published in print
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 Identifiers: DOI: 10.1039/C4SM01789G
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Title: Soft Matter
  Abbreviation : Soft Matter
Source Genre: Journal
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Publ. Info: Cambridge, UK : Royal Society of Chemistry
Pages: - Volume / Issue: 11 (2) Sequence Number: - Start / End Page: 343 - 354 Identifier: ISSN: 1744-683X
CoNE: https://pure.mpg.de/cone/journals/resource/1744-683X