Strain-driven criticality underlies nonlinear mechanics of fibrous networks

TL;DR

This paper investigates the critical behavior of fibrous networks under strain, demonstrating divergence in strain fluctuations at a critical point, confirmed experimentally in collagen networks, and highlighting the universality of this phenomenon across dimensions.

Contribution

It provides a quantitative analysis of strain-driven criticality in subisostatic networks, linking critical exponents to mechanical response and confirming universality through experiments and simulations.

Findings

Divergence of strain fluctuations at critical strain

Experimental validation in collagen networks

Critical slowing down observed in models

Abstract

Networks with only central force interactions are floppy when their average connectivity is below an isostatic threshold. Although such networks are mechanically unstable, they can become rigid when strained. It was recently shown that the transition from floppy to rigid states as a function of simple shear strain is continuous, with hallmark signatures of criticality (Nat. Phys. 12, 584 (2016)). The nonlinear mechanical response of collagen networks was shown to be quantitatively described within the framework of such mechanical critical phenomenon. Here, we provide a more quantitative characterization of critical behavior in subisostatic networks. Using finite size scaling we demonstrate the divergence of strain fluctuations in the network at well-defined critical strain. We show that the characteristic strain corresponding to the onset of strain stiffening is distinct from but related to this critical strain in a way that depends on critical exponents. We confirm this prediction experimentally for collagen networks. Moreover, we find that the apparent critical exponents are largely independent of the spatial dimensionality. In a highly simplified computational model of network dynamics, we also observe critical slowing down in the vicinity of the critical strain. With subisostaticity as the only required condition, strain-driven criticality is expected to be a general feature of biologically relevant fibrous networks.