  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.
