Shear-induced phase transition and critical exponents in 3D fiber networks

TL;DR

This study investigates the critical behavior of shear-induced phase transitions in 3D fiber networks through simulations, revealing non-mean-field exponents and suggesting an upper critical dimension above three.

Contribution

It provides the first finite-size scaling analysis of the critical exponents in 3D fiber networks, testing hyperscaling and challenging existing mean-field assumptions.

Findings

Critical exponents deviate from mean-field predictions.

Hyperscaling relation appears valid in 3D networks.

Upper critical dimension for the transition exceeds three.

Abstract

When subject to applied strain, fiber networks exhibit nonlinear elastic stiffening. Recent theory and experiements have shown that this phenomenon is controlled by an underlying mechanical phase transition that is critical in nature. Growing simulation evidence points to non-mean-field behavior for this transition and a hyperscaling relation has been proposed to relate the corresponding critical exponents. Here, we report simulations on two distinct network structures in 3D. By performing finite-size scaling analysis, we test hyperscaling and identify various critical exponents. From the apparent validity of hyperscaling, as well as the non-mean-field exponents we observe, our results suggest that the upper critical dimension for the strain-controlled phase transition is above three, in contrast to the jamming transition that represents another athermal, mechanical phase transition.