Elasticity of 3D networks with rigid filaments and compliant crosslinks

  • 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-dimensionalDisordered 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.show moreshow less

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Metadaten
Author:Knut M. Heidemann, Abhinav SharmaGND, Florian Rehfeldt, Christoph F. Schmidt, Max Wardetzky
URN:urn:nbn:de:bvb:384-opus4-1038377
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/103837
ISSN:1744-683XOPAC
ISSN:1744-6848OPAC
Parent Title (English):Soft Matter
Publisher:Royal Society of Chemistry (RSC)
Place of publication:London
Type:Article
Language:English
Year of first Publication:2015
Publishing Institution:Universität Augsburg
Release Date:2023/05/02
Tag:Condensed Matter Physics; General Chemistry
Volume:11
Issue:2
First Page:343
Last Page:354
DOI:https://doi.org/10.1039/c4sm01789g
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Physik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Physik / Lehrstuhl für Theoretische Physik II
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
Licence (German):CC-BY 3.0: Creative Commons - Namensnennung (mit Print on Demand)