Stochastic rate-dependent elasticity and failure of soft fibrous networks

Abstract

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.