Exotic rheology of materials with active rearrangements

The flow of biological tissues during development is controlled through the active stresses generated by cells interacting with their mechanical environment in the tissue. Many developmental processes are driven by convergence-extension flows where the tissue has an emergent negative shear modulus and viscosity. This exotic rheology is generated through active T1 transitions where rearrangements are opposite the applied stress direction. Here, we introduce a mean-field elasto-plastic model which shows convergence-extension, based on the Hebraud-Lequeux model, that includes both passive and active elastic elements with opposite stress responses. We find that the introduction of active elements profoundly changes the rheology. Beyond a threshold fraction of active elements, it gives rise to non-monotonic flow curves and negative stresses at positive strain rates. Controlled by the active fraction and the stress diffusion rate, we find both yield stress materials and fluids, with either a positive or negative yield stress or viscosity. These features are characteristic of metamaterials, and highlight how biology uses disordered, active materials with exotic rheology.