Nonlinear stiffening in strain ramps with a rate of 0.1/s. The derivative of the stress-strain curve, K, normalized by its initial value, Ko, as a function of strain. (A) Filamin with RF = 0.01 and L = 15 (short dash), 10 (long dash), 7 (dash-dot), 5 (solid), and 2 (dot) μm. For the network with L = 15 μm, K/Ko = 1 at small strains before beginning to stiffen above γc = 0.06. Networks with shorter filaments initially display weakening behavior, where K/Ko decreases below 1, due to their lower network connectivity, but stiffen at higher strains where the slope of the curve becomes positive. The value γc increases with decreasing L. (B) Rigid cross-links with RB = 0.01 and L = 10 (dash), 5 (solid), and 2 (dot) μm. Networks with long filaments display stiffening behavior that is independent of L, while networks with short filaments display weakening behavior. (Insets) Same data plotted versus stress.