Stress-Stiffening Biopolymer Network

Biopolymer stress-stiffening: Networks of semiflexible filaments (actin, collagen, fibrin) exhibit dramatic strain-stiffening: the differential modulus K = dσ/dγ grows as K ~ σ^(3/2) (MacKintosh-Käs-Janmey 1995). Unlike rubber elasticity (entropic, linear), semiflexible filaments are nearly inextensible. Under tension, thermal undulations are pulled taut — enthalpic backbone stiffness kicks in, causing K to rise orders of magnitude. The onset strain scales as γ* ~ (l_p/L)^(1/2) for tightly cross-linked networks.