“Bending to Stretching” Transition in Disordered Networks

Buxton, Gavin A.; Clarke, Nigel

doi:10.1103/physrevlett.98.238103

Cited by 67 publications

(77 citation statements)

References 28 publications

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“…Different parameters have been proposed in the literature [2,3,6,24] to quantify the degree of (non-)affinity of a displacement field, but most of them are global measures of the affinity. We use instead the local affinity measure m i defined at every node (junction and midpoint) i as 2 , whereū i is the macroscopic, affine, displacement field of the node i.…”

Section: (B) Resultsmentioning

confidence: 99%

“…Many different elastic systems-such as polymer gels, protein networks, cytoskeletal structures [1][2][3][4][5][6], or wood and bones [7][8][9][10][11]-can be understood as networks of interconnected beams. On a length scale much larger than the typical beam length ('macroscopic' scale), such a network can be viewed as a continuous and homogeneous medium characterized by spatially constant elastic moduli.…”

Section: Introductionmentioning

confidence: 99%

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Stiffest elastic networks

Gurtner

Durand

2014

Proc. R. Soc. A.

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The rigidity of a network of elastic beams is closely related to its microstructure. We show both numerically and theoretically that there is a class of isotropic networks, which are stiffer than any other isotropic network of same density. The elastic moduli of these stiffest elastic networks are explicitly given. They constitute upper-bounds, which compete or improve the well-known Hashin-Shtrikman bounds. We provide a convenient set of criteria (necessary and sufficient conditions) to identify these networks and show that their displacement field under uniform loading conditions is affine down to the microscopic scale. Finally, examples of such networks with periodic arrangement are presented, in both two and three dimensions. In particular, we present an optimal and isotropic three-dimensional structure which, to our knowledge, is the first one to be presented as such.

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Section: (B) Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stiffest elastic networks

Gurtner

Durand

2014

Proc. R. Soc. A.

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“…In the absence of fiber bending resistance, such networks exhibit zero-energy deformation modes and hence, they do not resist shear stresses. Thus, there are reasons to question the existence of an affine limit in realistic 3D networks with fibers that are softer to bending than to stretching [12,18,19]. This is still subject of debate since studies in 3D have so far been limited to small systems [18] or to networks with high connectivities [6,19].…”

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confidence: 99%

Filament-Length-Controlled Elasticity in 3D Fiber Networks

2012

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We present a model for disordered 3D fiber networks to study their linear and nonlinear elasticity over a wide range of network densities and fiber lengths. In contrast to previous 2D models, these 3D networks with binary cross-links are under-constrained with respect to fiber stretching elasticity, suggesting that bending may dominate their response. We find that such networks exhibit a fiber length-controlled bending regime and a crossover to a stretch-dominated regime for lengths beyond a characteristic scale that depends on the fiber's elastic properties. Finally, by extending the model to the nonlinear regime, we show that these networks become intrinsically nonlinear with a vanishing linear response regime in the limit of floppy or long filaments.

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“…The cytoskeleton is composed of macromolecules (actin filaments, intermediate filaments, and microtubules) forming a disordered network of semifiexible polymers [1] due to both the bending and longitudinal stiffness of the filaments. Many authors have investigated the properties of the cytoskeleton by means of micromechanical models [2][3][4][5][6][7][8][9][10][11]. These are expected to be useful for the understanding, for instance, of mechanotransduction, tissue development, or anomalous behavior of ill cells in comparison with healthy ones [12][13][14].…”

Section: Introductionmentioning

confidence: 99%

“…The first one considers struts as simple strings [21], while in the second the bending stiffness of the struts is also taken into account [2, 8,10,11,[22][23][24][25][26][27]. In both groups it can be distinguished between affine and nonaffine regimes depending on whether the deformation is ideally homogeneous or not, respectively [3,4,8].…”

Section: Introductionmentioning

confidence: 99%

Energy distribution in disordered elastic networks

Plaza

2010

Phys. Rev. E

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Disordered networks are found in many natural and artificial materials, from gels or cytoskeletal structures to metallic foams or bones. Here, the energy distribution in this type of networks is modeled, taking into account the orientation of the struts. A correlation between the orientation and the energy per unit volume is found and described as a function of the connectivity in the network and the relative bending stiffness of the struts. If one or both parameters have relatively large values, the struts aligned in the loading direction present the highest values of energy. On the contrary, if these have relatively small values, the highest values of energy can be reached in the struts oriented transversally. This result allows explaining in a simple way remodeling processes in biological materials, for example, the remodeling of trabecular bone and the reorganization in the cytoskeleton. Additionally, the correlation between the orientation, the affinity, and the bending-stretching ratio in the network is discussed.

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“Bending to Stretching” Transition in Disordered Networks

Cited by 67 publications

References 28 publications

Stiffest elastic networks

Stiffest elastic networks

Filament-Length-Controlled Elasticity in 3D Fiber Networks

Energy distribution in disordered elastic networks

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