Scaling theory for mechanical critical behavior in fiber networks

Abstract

As a function of connectivity, spring networks exhibit a critical transition between floppy and rigid phases at an isostatic threshold. For connectivity below this threshold, fiber networks were recently shown theoretically to exhibit a rigidity transition with corresponding critical signatures as a function of strain. Experimental collagen networks were also shown to be consistent with these predictions. We develop a scaling theory for this strain-controlled transition. Using a real-space renormalization approach, we determine relations between the critical exponents governing the transition, which we verify for the strain-controlled transition using numerical simulations of both triangular lattice-based and packing-derived fiber networks.

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Cited by in corpus (16)

• A minimal-length approach unifies rigidity in under-constrained materials
• Finite size effects in critical fiber networks
• Nonlinear Poisson effect governed by mechanical critical transition
• Athermal Fracture of Elastic Networks: How Rigidity Challenges the Unavoidable Size-Induced Brittleness
• 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
• Strain-controlled critical slowing down in the rheology of disordered networks
• Mechanics of fiber networks under a bulk strain
• Evidences of conformal invariance in 2d rigidity percolation
• Scaling theory of critical strain-stiffening in disordered elastic networks
• Mechanical criticality of fiber networks at a finite temperature
• Effective Medium Theory for Mechanical Phase Transitions of Fiber Networks
• The strain-stiffening critical exponents in polymer networks and their universality
• Criticality enhances the reinforcement of disordered networks by rigid inclusions
• Spatial patterning of force centers controls folding pathways of active elastic networks