Linear rheology of reversibly cross-linked biopolymer networks

Amuasi, Henry; Fischer, Andreas; Zippelius, Annette; Heussinger, Claus

doi:10.48550/arxiv.1808.05407

Cited by 1 publication

(1 citation statement)

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“…Second, while we studied here the vicinity of one local minimum of ¯ min depending e.g. on γ, it would be interesting to study the behavior of the system beyond that, by including higher order terms in ¯ min, and by also explicitly taking plastic events into account (61). In the case of biological tissues, plastic events typically correspond to so-called T1 transitions (62), which in our approach would correspond to changing to a different ¯ min "branch".…”

Section: R a F Tmentioning

confidence: 99%

A minimal-length approach unifies rigidity in underconstrained materials

Merkel

Baumgarten

Tighe

et al. 2019

Proc. Natl. Acad. Sci. U.S.A.

107

155

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We present a novel approach to understand geometricincompatibility-induced rigidity in under-constrained materials, including sub-isostatic 2D spring networks and 2D and 3D vertex models for dense biological tissues. We show that in all these models a geometric criterion, represented by a minimal length min , determines the onset of prestresses and rigidity. This allows us to predict not only the correct scalings for the elastic material properties, but also the precise magnitudes for bulk modulus and shear modulus discontinuities at the rigidity transition as well as the magnitude of the Poynting effect. We also predict from first principles that the ratio of the excess shear modulus to the shear stress should be inversely proportional to the critical strain with a prefactor of three, and propose that this factor of three is a general hallmark of geometrically induced rigidity in under-constrained materials and could be used to distinguish this effect from nonlinear mechanics of single components in experiments. Lastly, our results may lay important foundations for ways to estimate¯ min from measurements of local geometric structure, and thus help develop methods to characterize large-scale mechanical properties from imaging data. M.M., B.P.T., and M.L.M. designed the research, M.M. performed the research and analyzed the data, K.B. provided important simulation data, M.M., B.P.T., and M.L.M. wrote the paper.The authors declare no conflict of interest.

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Section: R a F Tmentioning

confidence: 99%