Finite size effects in critical fiber networks

Abstract

Fibrous networks such as collagen are common in physiological systems. One important function of these networks is to provide mechanical stability for cells and tissues. At physiological levels of connectivity, such networks would be mechanically unstable with only central-force interactions. While networks can be stabilized by bending interactions, it has also been shown that they exhibit a critical transition from floppy to rigid as a function of applied strain. Beyond a certain strain threshold, it is predicted that underconstrained networks with only central-force interactions exhibit a discontinuity in the shear modulus. We study the finite-size scaling behavior of this transition and identify both the mechanical discontinuity and critical exponents in the thermodynamic limit. We find both non-mean-field behavior and evidence for a hyperscaling relation for the critical exponents, for which the network stiffness is analogous to the heat capacity for thermal phase transitions. Further evidence for this is also found in the self-averaging properties of fiber networks.

References in corpus (29)

• Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder
• Jamming, Force Chains and Fragile Matter
• Random Packings of Frictionless Particles
• The origin of stiffening in cross-linked semiflexible networks
• Stress controls the mechanics of collagen networks
• Elasticity of Stiff Polymer Networks
• Deformation of crosslinked semiflexible polymer networks
• Criticality and isostaticity in fiber networks
• On the Rigidity of Amorphous Solids
• A coordination-based approach to elasticity of floppy and stiff random networks
• Strain-controlled criticality governs the nonlinear mechanics of fibre networks
• Finite-Size Scaling at the Jamming Transition
• Lack of Self-Averaging in Critical Disordered Systems
• Self-Averaging, Distribution of Pseudo-Critical Temperatures and Finite Size Scaling in Critical Disordered Systems
• The Statistical Physics of Athermal Materials
• Jamming in finite systems: stability, anisotropy, fluctuations and scaling
• A minimal-length approach unifies rigidity in under-constrained materials
• Stiff Polymers, Foams and Fiber Networks
• Size-dependent rheology of type-I collagen networks
• Nonlinear effective medium theory of disordered spring networks
• Strain-driven criticality underlies nonlinear mechanics of fibrous networks
• Fluctuation-stabilized marginal networks and anomalous entropic elasticity
• Scaling theory for mechanical critical behavior in fiber networks
• Geometry and the onset of rigidity in a disordered network
• Disorder Averaging and Finite Size Scaling
• Stress-stabilized sub-isostatic fiber networks in a rope-like limit
• Normal stresses, contraction, and stiffening in sheared elastic networks
• Normal stress anisotropy and marginal stability in athermal elastic networks
• Elastic collapse in disordered isostatic networks

Cited by in corpus (10)

• Non-affine deformation of semiflexible polymer and fiber networks
• Shear-induced phase transition and critical exponents in 3D fiber networks
• Stiffening of under-constrained spring networks under isotropic strain
• Rigidity of Epithelial Tissues as a Double Optimization Problem
• Mechanics of fiber networks under a bulk strain
• Mechanical criticality of fiber networks at a finite temperature
• Towards understanding structure-function relationships in random fiber networks
• Effective Medium Theory for Mechanical Phase Transitions of Fiber Networks
• Building rigid networks with prestress and selective pruning
• Criticality enhances the reinforcement of disordered networks by rigid inclusions