Elastic regimes of sub-isostatic athermal fiber networks

TL;DR

This study compares lattice-based and off-lattice athermal fiber networks, revealing their similar elastic behaviors in sub-isostatic regimes and elucidating the nonlinear stiffening mechanisms driven by fiber bending and stress stabilization.

Contribution

It demonstrates the equivalence of lattice and off-lattice network mechanics in sub-isostatic conditions and characterizes the nonlinear elastic response in terms of stress-induced stabilization.

Findings

Lattice and off-lattice networks exhibit similar linear and nonlinear mechanics.

Nonlinear stiffening is dominated by fiber bending and stress stabilization.

A generalized relation links normal stresses to nonlinear stiffening behavior.

Abstract

Athermal models of disordered fibrous networks are highly useful for studying the mechanics of elastic networks composed of stiff biopolymers. The underlying network architecture is a key aspect that can affect the elastic properties of these systems, which include rich linear and nonlinear elasticity. Existing computational approaches have focused on both lattice-based and off-lattice networks obtained from the random placement of rods. It is not obvious, a priori, whether the two architectures have fundamentally similar or different mechanics. If they are different, it is not clear which of these represents a better model for biological networks. Here, we show that both approaches are essentially equivalent for the same network connectivity, provided the networks are sub-isostatic with respect to central force interactions. Moreover, for a given sub-isostatic connectivity, we even find that lattice-based networks in both 2D and 3D exhibit nearly identical nonlinear elastic response. We provide a description of the linear mechanics for both architectures in terms of a scaling function. We also show that the nonlinear regime is dominated by fiber bending and that stiffening originates from the stabilization of sub-isostatic networks by stress. We propose a generalized relation for this regime in terms of the self-generated normal stresses that develop under deformation. Different network architectures have different susceptibilities to the normal stress, but essentially exhibit the same nonlinear mechanics. Such stiffening mechanism has been shown to successfully capture the nonlinear mechanics of collagen networks.