Mechanics of transient semi-flexible networks: Soft-elasticity, stress relaxation and remodeling

Abstract

Networks of semi-flexible (or athermal) filaments cross-linked by flexible chains are found in a variety of biopolymers such as soft connective tissues, the cell’s cytoskeleton or the wall of plant cells. They can also be synthetized in the lab to create liquid crystal elastomers-like gels as well as tissue mimetics. While the elasticity of these networks has been explored, the visco-elastic response that originate from the existence of reversible and dynamic cross-links is still poorly understood. We here develop a model for these networks by taking a multiscale, statistical mechanics approach where the network is decomposed into its most basic building blocks: elastic rods (to describe semi-flexible filaments) and the flexible chains used to cross-link them. The topology of this assembly is represented by a hairy rod model for which we express the non-affine kinematics, and evolution equations for both cross-linkers and rods conformation. The mechanical response of this hairy rod is then expressed by an elastic potential that is built as a function of the basic elasticity of its components. The resulting model is able to capture salient features of the mechanics of such networks, including nonlinear elasticity (and in particular a liquid crystal-like soft-elastic response), creep and stress relaxation, as well as rate- and history-dependent network remodeling. The theory can thus be potentially used to better understand the rich response of these complex, yet ubiquitous networks and guide their development in the laboratory.