Elastic regimes of sub-isostatic athermal fiber networks

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.

14 pages, 14 figures

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Cited by in corpus (14)

• Biopolymers: life's mechanical scaffolds
• A minimal-length approach unifies rigidity in under-constrained materials
• Strain-driven criticality underlies nonlinear mechanics of fibrous networks
• Stress-stabilized sub-isostatic fiber networks in a rope-like limit
• Nonlinear Poisson effect governed by mechanical critical transition
• Non-affine deformation of semiflexible polymer and fiber networks
• Normal stress anisotropy and marginal stability in athermal elastic networks
• Stiffening of under-constrained spring networks under isotropic strain
• Mechanics of fiber networks under a bulk strain
• Mechanical criticality of fiber networks at a finite temperature
• Scaling theory of critical strain-stiffening in disordered elastic networks
• Effective Medium Theory for Mechanical Phase Transitions of Fiber Networks
• The strain-stiffening critical exponents in polymer networks and their universality
• A new open source framework for multiscale modeling of fibrous materials on heterogeneous supercomputers