Nonlinear elasticity, and stability of semiflexible filament networks

Networks of semiflexible or stiff filament exhibit unique mechanic properties. We construct an analytic form of the free energy of a model semiflexible network, with its constitutive relation, by assuming 3-chain configuration of the network structure. There are only two parameters: stiffness of individual filaments, and pre-tension of these filaments in equilibrium network. The model fits nonlinear strain-stress experiments for numerous filament networks, such as actin, collagen, vimentin, fibrin, etc. This model successfully explains why networks of stiff filaments show negative Poynting effect (negative normal stress), which remained a mystery in this area since its observation. We also discuss the marginal rigidity of the network, and the phenomenon of tensegrity, where the pre-tension of the strands determines the linear shear modulus of the network. As a result, we present a ‘phase diagram’ in variables of filament stiffness and pre-tension, and identify the transitions between regions of stable/unstable network, and positive/negative normal stress. Curiously, all cytoskeletal or extra-cellular network we have examined lie very close to the marginal rigidity boundary. The model is portable and adaptable to meet specific demands in experiment and industrial applications.