Shear-induced phase transition and critical exponents in three-dimensional fiber networks

When subject to applied strain, fiber networks exhibit nonlinear elastic stiffening. Recent theory and experiments 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 three dimensions. By performing a 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.

Automated summary

The research reveals that fiber networks exhibit nonlinear elastic stiffening when subjected to applied strain, which is controlled by an underlying critical mechanical phase transition. Simulation results show non-mean-field behavior for this transition, with a proposed hyperscaling relation connecting the corresponding critical exponents. The study suggests that the strain-controlled phase transition may have an upper critical dimension above three, contrasting with the jamming transition representing another athermal, mechanical phase transition.