A minimal model for the inelastic mechanics of biopolymer networks and cells

Live cells have ambiguous mechanical properties. They were often described as either elastic solids or viscoelastic fluids and have recently been classified as soft glassy materials characterized by weak power-law rheology. Nonlinear rheological measurements have moreover revealed a pronounced inelastic response indicative of a competition between stiffening and softening. It is an intriguing question whether these observations can be explained from the material properties of much simpler in-vitro reconstituted networks of biopolymers that serve as reduced model systems for the cytoskeleton. Here, we explore the mechanism behind the inelastic response of cells and biopolymer networks, theoretically. Our analysis is based on the model of the inelastic glassy wormlike chain that accounts for the nonlinear polymer dynamics and transient crosslinking in biopolymer networks. It explains how inelastic and kinematic-hardening type behavior naturally emerges from the antagonistic mechanisms of viscoelastic stress-stiffening due to the polymers and inelastic fluidization due to bond breaking. It also suggests a simple set of schematic constitutive equations which faithfully reproduce the rich inelastic phenomenology of biopolymer networks and cells.