Effective Medium Theory for Mechanical Phase Transitions of Fiber Networks

Abstract

Networks of stiff fibers govern the elasticity of biological structures such as the extracellular matrix of collagen. These networks are known to stiffen nonlinearly under shear or extensional strain. Recently, it has been shown that such stiffening is governed by a strain-controlled athermal but critical phase transition, from a floppy phase below the critical strain to a rigid phase above the critical strain. While this phase transition has been extensively studied numerically and experimentally, a complete analytical theory for this transition remains elusive. Here, we present an effective medium theory (EMT) for this mechanical phase transition of fiber networks. We extend a previous EMT appropriate for linear elasticity to incorporate nonlinear effects via an anharmonic Hamiltonian. The mean-field predictions of this theory, including the critical exponents, scaling relations and non-affine fluctuations qualitatively agree with previous experimental and numerical results.

References in corpus (10)

• Strain-induced alignment in collagen gels
• Nonaffine rubber elasticity for stiff polymer networks
• Crosslinked networks of stiff filaments exhibit negative normal stress
• Effective medium theory of semiflexible filamentous networks
• Strain-driven criticality underlies nonlinear mechanics of fibrous networks
• Elasticity of Filamentous Kagome Lattice
• Geometry and the onset of rigidity in a disordered network
• Non-affine deformation of semiflexible polymer and fiber networks
• Mechanics of fiber networks under a bulk strain
• Partition sum of thermal, under-constrained systems

Cited by in corpus (2)

• Scaling theory of critical strain-stiffening in disordered elastic networks
• The strain-stiffening critical exponents in polymer networks and their universality