Issue 42, 2023

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.

Graphical abstract: Effective medium theory for mechanical phase transitions of fiber networks

Article information

Article type
Paper
Submitted
21 Jun 2023
Accepted
22 Sep 2023
First published
28 Sep 2023

Soft Matter, 2023,19, 8124-8135

Author version available

Effective medium theory for mechanical phase transitions of fiber networks

S. Chen, T. Markovich and F. C. MacKintosh, Soft Matter, 2023, 19, 8124 DOI: 10.1039/D3SM00810J

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