An official website of the United States government
Abstract Disordered spring networks can exhibit rigidity transitions, due to either the removal of material in over-constrained networks or the application of strain in under-constrained ones. While an effective medium theory (EMT) exists for the former, there is none for the latter. We, therefore, formulate an EMT for random regular, under-constrained spring networks with purely geometrical disorder to predict their stiffness via the distribution of tensions. We find a linear dependence of stiffness on strain in the rigid phase and a nontrivial dependence on both the mean and standard deviation of the tension distribution. While EMT does not yield highly accurate predictions of shear modulus due to spatial heterogeneities, it requires only the distribution of tensions for an intact system, therefore making it an ideal starting point for experimentalists quantifying the mechanics of such networks.
more »
« less
Effective medium theory for mechanical phase transitions of fiber networks
Networks of stiff fibers govern the elasticity of biological structures such as the extracellular matrix of collagen.These networks are known to stiffen nonlinearly under shear or extensional strain. Recently, it has been shown that such stiffening is governed by a strain-controlled athermal but critical phase transition, from a floppy phase below the critical strain to a rigid phase above the critical strain. While this phase transition has been extensively studied numerically and experimentally, a complete analytical theory for this transition remains elusive. Here, we present an effective medium theory (EMT) for this mechanical phase transition of fiber networks. We extend a previous EMT appropriate for linear elasticity to incorporate nonlinear effects via an anharmonic Hamiltonian. The mean-field predictions of this theory, including the critical exponents, scaling relations and non-affine fluctuations qualitatively agree with previous experimental and numerical results.
more »
« less
- PAR ID:
- 10512011
- Publisher / Repository:
- Royal Society of Chemistry
- Date Published:
- Journal Name:
- Soft Matter
- Volume:
- 19
- Issue:
- 42
- ISSN:
- 1744-683X
- Page Range / eLocation ID:
- 8124 to 8135
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
At zero temperature, spring networks with connectivity below Maxwell's isostatic threshold undergo a mechanical phase transition from a floppy state at small strains to a rigid state for applied shear strain above a critical strain threshold. Disordered networks in the floppy mechanical regime can be stabilized by entropic effects at finite temperature. We develop a scaling theory for this mechanical phase transition at finite temperature, yielding relationships between various scaling exponents. Using Monte Carlo simulations, we verify these scaling relations and identify anomalous entropic elasticity with sublinear 𝑇 dependence in the linear elastic regime. While our results are consistent with prior studies of phase behavior near the isostatic point, the present work also makes predictions relevant to the broad class of disordered thermal semiflexible polymer networks for which the connectivity generally lies far below the isostatic threshold.more » « less
-
Fibrous networks such as collagen are common in physiological systems. One important function of these networks is to provide mechanical stability for cells and tissues. At physiological levels of connectivity, such networks would be mechanically unstable with only central-force interactions. While networks can be stabilized by bending interactions, it has also been shown that they exhibit a critical transition from floppy to rigid as a function of applied strain. Beyond a certain strain threshold, it is predicted that underconstrained networks with only central-force interactions exhibit a discontinuity in the shear modulus. We study the finite-size scaling behavior of this transition and identify both the mechanical discontinuity and critical exponents in the thermodynamic limit. We find both non-mean-field behavior and evidence for a hyperscaling relation for the critical exponents, for which the network stiffness is analogous to the heat capacity for thermal phase transitions. Further evidence for this is also found in the self-averaging properties of fiber networks.more » « less
-
The epithelial-mesenchymal transition (EMT) is a cellular process critical for wound healing, cancer metastasis and embryonic development. Recent efforts have identified the role of hybrid epithelial/mesenchymal states, having both epithelial and mesehncymal traits, in enabling cancer metastasis and resistance to various therapies. Also, previous work has suggested that NRF2 can act as phenotypic stability factor to help stablize such hybrid states. Here, we incorporate a phenomenological epigenetic feedback effect into our previous computational model for EMT signaling. We show that this type of feedback can stabilize the hybrid state as compared to the fully mesenchymal phenotype if NRF2 can influence SNAIL at an epigenetic level, as this link makes transitions out of hybrid state more difficult. However, epigenetic regulation on other NRF2-related links do not significantly change the EMT dynamics. Finally, we considered possible cell division effects in our epigenetic regulation model, and our results indicate that the degree of epigenetic inheritance does not appear to be a critical factor for the hybrid E/M state stabilizing behavior of NRF2.more » « less
-
Active nematic liquid crystals have the remarkable ability to spontaneously deform and flow in the absence of any external driving force. While living materials with orientational order, such as the mitotic spindle, can self-assemble in quiescent active phases, reconstituted active systems often display chaotic, periodic, or circulating flows under confinement. Quiescent active nematics are, therefore, quite rare, despite the prediction from active hydrodynamic theory that confinement between two parallel plates can suppress flows. This spontaneous flow transition—named the active FrĂ©edericksz transition by analogy with the conventional FrĂ©edericksz transition in passive nematic liquid crystals under a magnetic field—has been a cornerstone of the field of active matter. Here, we report experimental evidence that confinement in spherical droplets can stabilize the otherwise chaotic dynamics of a 3D extensile active nematics, giving rise to a quiescent—yet still out-of-equilibrium—nematic liquid crystal. The active nematics spontaneously flow when confined in larger droplets. The composite nature of our model system composed of extensile bundles of microtubules and molecular motors dispersed in a passive colloidal liquid crystal allows us to demonstrate how the interplay of activity, nematic elasticity, and confinement impacts the spontaneous flow transition. The critical diameter increases when motor concentration decreases or nematic elasticity increases. Experiments and simulations also demonstrate that the critical confinement depends on the confining geometry, with the critical diameter in droplets being larger than the critical width in channels. Biochemical assays reveal that neither confinement nor nematic elasticity impacts the energy-consumption rate, confirming that the quiescent active phase is the stable out-of-equilibrium phase predicted theoretically. Further experiments in dense arrays of monodisperse droplets show that fluctuations in the droplet composition can smooth the flow transition close to the critical diameter. In conclusion, our work provides experimental validation of the active FrĂ©edericksz transition in 3D active nematics, with potential applications in human health, ecology, and soft robotics. Published by the American Physical Society2024more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1039/d3sm00810j
