Elasticity of Rigidly Cross-Linked Networks of Athermal Filaments

Žagar, Goran; Onck, Patrick; Giessen, E. van der

doi:10.1021/ma201257v

Cited by 45 publications

(43 citation statements)

References 29 publications

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“…It is seen that the curves overlap in both the small strain (which is expected since all these systems have same value of w) and the large deformations regimes. As previously observed for this type of networks [21,22], the large strain branch of the stress-strain curve is exponential and hence the tangent stiffness varies linearly with the stress. The data in Fig.…”

Section: Resultssupporting

confidence: 79%

Structure-properties relation for random networks of fibers with noncircular cross section

Deogekar

Picu

2017

Phys. Rev. E

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The mechanical behavior of 3D cross-linked random fiber networks composed from fibers of non-circular cross-section characterized by two principal moments of inertia is studied in this work. Such fibers store energy in the axial deformation mode and two bending modes of unequal stiffness. We show that the torsional stiffness of fibers becomes important as it determines the relative contribution of the two bending modes to the overall deformation. The scaling of the small strain modulus with the network parameters is established. The large strain deformation of these structures is less sensitive to the shape of the cross-section.

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Section: Resultssupporting

confidence: 79%

Structure-properties relation for random networks of fibers with noncircular cross section

Deogekar

Picu

2017

Phys. Rev. E

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“…The inset in Fig. 1(a) shows that this results in a master curve that is well represented by the scaling law K ∝ (τ/τ 0 ) 3/2 proposed byŽagar et al [20]. Figure 1(b) shows exemplar curves for case ii.…”

Section: Mapping the Overall Response In Terms Of Filament Propesupporting

confidence: 61%

Predictive maps for stochastic nonaffine stiffening and damage in fibrous networks

et al. 2014

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The macroscopic responses of synthetic and natural filamentous networks are determined by a combination of microstructure and filament properties. Biofilament networks such as those of actin and fibrin have become vehicles for studying important concepts in mechanics such as rigidity percolation, linearity and nonlinearity, isotropy and anisotropy, affinity and nonaffinity, hardening and softening, bending and stretching transitions, etc. In this work, we consider generic fibrous network architectures to map out their mechanical responses over a wide range of filament properties. Using the finite element method, we perform two-dimensional simulations of discrete networks subjected to shear deformation. These simulations encompass stochastic effects arising from network topology (filament arrangement, orientation, and length distribution) and the thermally activated crosslink scission. We study the mechanics of these random networks up to a strain of 10%, including damage that is induced by crosslink scission. The response is nonlinear and the initial elastic modulus alone is not sufficient to give an understanding about the overall response. We show that the nonlinear elastic response of the network can be captured using a few parameters that depend on some well known length scales in network mechanics. For networks with filament density above the rigidity percolation threshold, by increasing filament density and bending stiffness, we observe a crossover from the bending dominated elastically compliant stiffening regime to a stretching dominated rigid nonstiffening regime. We show that in the bending dominated regime there are large deviations from the predictions of affine continuum theories. We also give a simple qualitative model for describing the contours of the incubation strain which marks the onset of damage in networks.

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“…An alternative explanation for strain-stiffening based on filament bending and enthalpic stretching has also been proposed for stiff filament networks [30–32]. In this model, the amplitude of thermal undulation is negligible in stiff filaments, and it is easier to bend the stiff filaments than to stretch them.…”

Section: Mechanisms Of Strain Stiffeningmentioning

confidence: 99%

Effects of non-linearity on cell–ECM interactions

Wen

Janmey

2013

Experimental Cell Research

102

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Filamentous biopolymers such as F-actin, vimentin, fibrin and collagen that form networks within the cytoskeleton or the extracellular matrix have unusual rheological properties not present in most synthetic soft materials that are used as cell substrates or scaffolds for tissue engineering. Gels formed by purified filamentous biopolymers are often strain stiffening, with an elastic modulus that can increase an order of magnitude at moderate strains that are relevant to cell and tissue deformation in vivo. This review summarizes some experimental studies of nonlinear rheology in biopolymer gels, discusses possible molecular mechanisms that account for strain stiffening, and explores the possible relevance of non-linear rheology to the interactions between cell and extracellular matrices.

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Elasticity of Rigidly Cross-Linked Networks of Athermal Filaments

Cited by 45 publications

References 29 publications

Structure-properties relation for random networks of fibers with noncircular cross section

Structure-properties relation for random networks of fibers with noncircular cross section

Predictive maps for stochastic nonaffine stiffening and damage in fibrous networks

Effects of non-linearity on cell–ECM interactions

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