Effective Medium Theory for Mechanical Phase Transition of Fiber Networks

Disordered fiber networks, such like extracellular matrix of collagen, are responsible for the mechanical properties for cells and tissues. With an average connectivity between 3 to 4 in 3 dimensions, fiber networks do not meet the Maxwell threshold for mechanically stable networks. Such networks are floppy under small deformation, with linear elasticity governed by the bending energy. However, these sub-isostatic networks can become rigid under large strain via a critical phase transition. In this talk we present an effective medium theory (EMT) for this strain-controlled critical phase transition. Our theory describes the non-affine deformation of the disordered networks and predicts the mechanical phase transition using a Landau-type elastic energy. Our theory qualitatively captures the critical behavior with predictions of mean-field critical exponents.