Fluid versus solid behaviour in a rheological constitutive model of tissue mechanics*

The deformation and flow properties of biological tissue are key to many important biological phenomena - including morphogenesis, wound healing and tumour metastasis - but remain poorly understood. In this work, we construct a continuum constitutive model of biological tissue rheology, aimed at describing the mechanics of a monolayer of confluent cells. The basic dynamical variables of the model comprise the cellular anisotropy and the degree of nematic alignment of elongated cells. We explore the model's rheological predictions, which include a yield stress in the solid phase. These predictions are compared with results from a mesoscopic vertex model of sheared biological tissue.