Mechanical criticality of fiber networks at a finite temperature

Abstract

At zero temperature, spring networks with connectivity below Maxwell's isostatic threshold undergo a mechanical phase transition from a floppy state at small strains to a rigid state for applied shear strain above a critical strain threshold. Disordered networks in the floppy mechanical regime can be stabilized by entropic effects at finite temperature. We develop a scaling theory based on a real-space renormalization approach for this mechanical phase transition at finite temperature, yielding relationships between various scaling exponents. Using Monte Carlo simulations, we verify these scaling relations and identify anomalous entropic elasticity with sub-linear $T$-dependence in the linear elastic regime. While our results are consistent prior studies of phase behavior near the isostatic point, the present work also makes predictions relevant to the broad class of disordered thermal semiflexible polymer networks for which the connectivity generally lies far below the isostatic threshold.

References in corpus (23)

• Modeling semiflexible polymer networks
• Elasticity of Stiff Polymer Networks
• Deformation of crosslinked semiflexible polymer networks
• Criticality and isostaticity in fiber networks
• Approximate analytical description of the nonaffine response 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
• Force-Extension Relation and Plateau Modulus for Wormlike Chains
• A minimal-length approach unifies rigidity in under-constrained materials
• Effective medium theory of semiflexible filamentous networks
• Nonlinear elasticity of disordered fiber networks
• Elastic regimes of sub-isostatic athermal fiber networks
• Actively stressed marginal 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
• Micromechanical theory of strain-stiffening of biopolymer networks
• Finite size effects in critical fiber networks
• Finite temperature mechanical instability in disordered lattices
• Shear-induced phase transition and critical exponents in 3D fiber networks
• Anomalous linear elasticity of disordered networks
• Stability and anomalous entropic elasticity of sub isostatic random-bond networks

Cited by in corpus (1)

• Spatial patterning of force centers controls folding pathways of active elastic networks