  The vertex model is widely used to describe the dynamics of epithelial
tissues, because of its simplicity and versatility and the direct inclusion of
biophysical parameters. Here, it is shown that quite generally, when cells
modify their equilibrium perimeter due to their activity, or the tissue is
subject to external stresses, the tissue becomes unstable with deformations
that couple pure-shear or deviatoric modes, with rotation and expansion modes.
For short times, these instabilities deform cells increasing their ellipticity
while, at longer times, cells become non-convex, indicating that the vertex
model ceases to be a valid description for tissues under these conditions. The
agreement between the analytic calculations performed for a regular hexagonal
tissue and the simulations of disordered tissues is excellent due to the
homogenization of the tissue at long wavelengths.
