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Reentrant rigidity percolation in structurally correlated filamentous networks

Jonathan Michel1,*, Gabriel von Kessel1, Thomas Wyse Jackson2, Lawrence J. Bonassar3,4, Itai Cohen2, and Moumita Das1,†

  • 1School of Physics and Astronomy, Rochester Institute of Technology, Rochester, New York 14623-5603, USA
  • 2School of Physics, Cornell University, Ithaca, New York 14853, USA
  • 3Meinig School of Biomedical Engineering, Cornell University, Ithaca, New York 14853, USA
  • 4Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York 14853, USA

  • *Corresponding author should be addressed: jamsps@rit.edu
  • †Corresponding author should be addressed: modsps@rit.edu
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Phys. Rev. Research 4, 043152 – Published 30 November, 2022

DOI: https://doi.org/10.1103/PhysRevResearch.4.043152

Abstract

Many biological tissues feature a heterogeneous network of fibers whose tensile and bending rigidity contribute substantially to these tissues' elastic properties. Rigidity percolation has emerged as an important paradigm for relating these filamentous tissues' mechanics to the concentrations of their constituents. Past studies have generally considered tuning of networks by spatially homogeneous variation in concentration, while ignoring structural correlation. We introduce here a model in which dilute fiber networks are built in a correlated manner that produces alternating sparse and dense regions. Our simulations indicate that structural correlation consistently allows tissues to attain rigidity with less material. We further find that the percolation threshold varies nonmonotonically with the degree of correlation, such that it decreases with moderate correlation and once more increases for high correlation. We explain the eventual reentrance in the dependence of the rigidity percolation threshold on correlation as the consequence of large, stiff clusters that are too poorly coupled to transmit forces across the network. Our study offers deeper understanding of how spatial heterogeneity may enable tissues to robustly adapt to different mechanical contexts.

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Phys. Rev. Research 4, 043152– Published 30 November, 2022
  • Received 24 April 2022
  • Accepted 25 October 2022
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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