Stochastic rate-dependent elasticity and failure of soft fibrous networks

This work focuses on modeling the rate-sensitive stiffening-to-softening transition in fibrous architectures mimicking crosslinked fibrous actin (F-actin) networks induced by crosslink unbinding. Using finite element based discrete network (DN) modeling combined with stochastic crosslink scission kinetics, we correlate the microstructural damage evolution with the macroscopic stress-strain responses of these networks as a function of applied deformation rate. Simulations of multiple DN realizations for fixed filament density indicate that an incubation strain exists, which characterizes the minimum macroscopic deformation that a network should accrue before damage initiates. This incubation strain exhibits a direct relationship with the applied strain rate. Simulations predict that the critical damage fraction corresponding to colossal softening is quite low, which may be ascribed to the network non-affinity and filament reorientation. Furthermore, this critical fraction appears to be independent of applied strain rate. Based on these characteristics, we propose a phenomenological damage evolution law mimicking scission kinetics in an average sense. This law is embedded within an existing continuum model that is extended to include non-affine effects induced by filament bending.