Length-Controlled Elasticity in 3D Fiber Networks

TL;DR

This paper introduces a 3D fiber network model to analyze their elastic behavior, revealing a fiber length-controlled bending regime and a transition to stretch-dominated response, with intrinsic nonlinearity in the nonlinear regime.

Contribution

It extends previous 2D models to 3D, highlighting the role of fiber length and elasticity in network mechanics and nonlinear behavior.

Findings

Networks exhibit a fiber length-controlled bending regime.

Transition to stretch-dominated regime occurs beyond a characteristic length.

Networks become intrinsically nonlinear with vanishing linear response in certain limits.

Abstract

We present a model for disordered 3D fiber networks to study their linear and nonlinear elasticity over a wide range of network densities and fiber lengths. In contrast to previous 2D models, these 3D networks with binary cross-links are under-constrained with respect to fiber stretching elasticity, suggesting that bending may dominate their response. We find that such networks exhibit a fiber length-controlled bending regime and a crossover to a stretch-dominated regime for lengths beyond a characteristic scale that depends on the fiber's elastic properties. Finally, by extending the model to the nonlinear regime, we show that these networks become intrinsically nonlinear with a vanishing linear response regime in the limit of floppy or long filaments.