Strain-controlled criticality governs the nonlinear mechanics of fibre networks

TL;DR

This study combines computational modeling and experiments to reveal that the nonlinear mechanics of collagen fiber networks are governed by a strain-controlled critical phase transition, with critical behavior consistent across various conditions.

Contribution

It introduces a theoretical and experimental framework showing strain-controlled criticality in fibre networks, extending understanding of their nonlinear mechanical behavior.

Findings

Rigidity develops via a strain-controlled continuous phase transition.

Experimental data confirms critical exponents predicted by the model.

Scaling theory accurately describes the nonlinear mechanics of collagen networks.

Abstract

Disordered fibrous networks are ubiquitous in nature as major structural components of living cells and tissues. The mechanical stability of networks generally depends on the degree of connectivity: only when the average number of connections between nodes exceeds the isostatic threshold are networks stable (Maxwell, J. C., Philosophical Magazine 27, 294 (1864)). Upon increasing the connectivity through this point, such networks undergo a mechanical phase transition from a floppy to a rigid phase. However, even sub-isostatic networks become rigid when subjected to sufficiently large deformations. To study this strain-controlled transition, we perform a combination of computational modeling of fibre networks and experiments on networks of type I collagen fibers, which are crucial for the integrity of biological tissues. We show theoretically that the development of rigidity is characterized by a strain-controlled continuous phase transition with signatures of criticality. Our experiments demonstrate mechanical properties consistent with our model, including the predicted critical exponents. We show that the nonlinear mechanics of collagen networks can be quantitatively captured by the predictions of scaling theory for the strain-controlled critical behavior over a wide range of network concentrations and strains up to failure of the material.