Strain-stiffening and strain-softening responses in random viscoelastic fibrous networks: interplay between fiber orientation and viscoelastic softening

Abstract

ABSTRACT Collagen networks are usually modeled as an inelastic material that accentuates the role of bond dynamics in their viscoelastic response. However, permanent cross-links can be used to fix these fibers to a large degree. Here, we model a network in which the fibers are assumed to maintain their viscoelasticity nature while the cross-linking bonds between them are fixed. Our models show that the interplay between fiber orientation and energy dissipation due to the viscoelasticity of fibers gives rise to a rich mechanical response. The network can stiffen, soften, or have an approximately constant stiffness as a function of strain when different loading rates are imposed. Using the order parameters of Q-tensor, we verify that the stiffening is due to the orientation of fibers, which is a well-established behavior in fibrous networks. In contrast to inelastic networks where there is always a linear initial response, the present network exhibits a constant stiffness only for a small range of loading rates. Also, it is shown that this duality is independent of the fiber concentration and only depends on the loading rate. Consequently, the existence of both strain-softening and strain-stiffening responses is a general behavior that is in common in fibrous networks with viscoelastic components and permanent cross-links.