Reentrant Rigidity Percolation in Structurally Correlated Filamentous Networks

TL;DR

This study investigates how structural correlations in filamentous networks influence rigidity percolation, revealing that heterogeneity can reduce material requirements and cause non-monotonic thresholds due to cluster interactions.

Contribution

It introduces a correlated fiber network model and uncovers the non-monotonic relationship between correlation degree and rigidity percolation threshold.

Findings

Correlated networks achieve rigidity with less material.

Percolation threshold varies non-monotonically with correlation.

Large, stiff clusters can hinder force transmission at high correlation.

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 a 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 here introduce 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 non-monotonically 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.