ArticleProceedings of the National Academy of Sciences of the United States of America2019
A minimal-length approach unifies rigidity in underconstrained materials.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2019. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 19 papers.
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Who cites it
19 citing papers in PubMed.
- Article
- Vertex models capturing subcellular scales in epithelial tissues.PLoS computational biology · 2025Review
- Epithelial Layer Fluidization by Curvature-Induced Unjamming.Physical review letters · 2025Article
- Cell-Level Modelling of Homeostasis in Confined Epithelial Monolayers.Journal Of Elasticity · 2025Article
- Regulation of epithelial cell jamming transition by cytoskeleton and cell-cell interactions.Biophysics reviews · 2024Review
- Jamming of nephron-forming niches in the developing mouse kidney creates cyclical mechanical stresses.Nature materials · 2024Article
- E-cadherin tunes tissue mechanical behavior before and during morphogenetic tissue flows.Current biology : CB · 2024Article
- Article
- Collective chemotaxis in a Voronoi model for confluent clusters.Biophysical journal · 2022Article
- Interplay between substrate rigidity and tissue fluidity regulates cell monolayer spreading.Soft matter · 2022Article
- Linear viscoelastic properties of the vertex model for epithelial tissues.PLoS computational biology · 2022Article
- Moduli and modes in the Mikado model.Soft matter · 2021Article
- The structural, vibrational, and mechanical properties of jammed packings of deformable particles in three dimensions.Soft matter · 2021Article
- The Cell Adaptation Time Sets a Minimum Length Scale for Patterned Substrates.Biophysical journal · 2020Article
- Anisotropy links cell shapes to tissue flow during convergent extension.Proceedings of the National Academy of Sciences of the United States of America · 2020Article
- Force networks, torque balance and Airy stress in the planar vertex model of a confluent epithelium.Proceedings. Mathematical, physical, and engineering sciences · 2020Article
- Linear and nonlinear mechanical responses can be quite different in models for biological tissues.Soft matter · 2020Article
- Rigidity and auxeticity transitions in networks with strong bond-bending interactions.The European physical journal. E, Soft matter · 2019Article
- Article
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4 authors.
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Abstract
We present an approach to understand geometric-incompatibility-induced rigidity in underconstrained materials, including subisostatic 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 [Formula: see text], 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 3. We propose that this factor of 3 is a general hallmark of geometrically induced rigidity in underconstrained materials and could be used to distinguish this effect from nonlinear mechanics of single components in experiments. Finally, our results may lay important foundations for ways to estimate [Formula: see text] from measurements of local geometric structure and thus help develop methods to characterize large-scale mechanical properties from imaging data.
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