  The rheology of biological tissue is key to processes such as embryo
development, wound healing and cancer metastasis. Vertex models of confluent
tissue monolayers have uncovered a spontaneous liquid-solid transition tuned by
cell shape; and a shear-induced solidification transition of an initially
liquid-like tissue. Alongside this jamming/unjamming behaviour, biological
tissue also displays an inherent viscoelasticity, with a slow time and rate
dependent mechanics. With this motivation, we combine simulations and continuum
theory to examine the rheology of the vertex model in nonlinear shear across a
full range of shear rates from quastistatic to fast, elucidating its nonlinear
stress-strain curves after the inception of shear of finite rate, and its
steady state flow curves of stress as a function of strain rate. We formulate a
rheological constitutive model that couples cell shape to flow and captures
both the tissue solid-liquid transition and its rich linear and nonlinear
rheology.
