Stochastic, rate-dependent elasticity and failure of soft, fibrous networks
Filamentous networks are subscale motifs ubiquitous in biopolymers and synthetic polymers. They provide structural stiffness that can be modulated actively (e.g. in actin networks) or passively (e.g. in synthetic polymers) by mechanical stimuli. In this work, we develop a finite element based approach to model such discrete filament networks. The approach is motivated by the recent progress in biopolymers that exhibit rate-dependent mechanical characteristics including elastic and inelastic behaviors, ascribed to the role of crosslinks. The model comprises discrete filaments representing actin filaments modeled by beam finite elements that are connected at intersections via nonlinear springs representing the actin binding proteins (crosslinks). The crosslink dissociation due to exerted force is modeled via Kinetic Monte Carlo (KMC) procedure. The resulting macroscopic response is highly nonlinear and rate-dependent. The stiffness characteristics depend on the initial topology for a fixed cross-link density and evolve with deformation exhibiting strong stiffening (filament stretching) followed by rapid degradation (crosslink scission). We compare the rate-dependent behavior of these networks with experiments and discuss the variability arising from the stochastic effects. Although the model is motivated by the mechanics of biopolymeric materials, the strategy may be adopted for a variety of systems that exhibit similar architectures at different length-scales.