  We develop a constitutive model allowing for the description of the rheology
of two-dimensional soft dense suspensions above jamming. Starting from a
statistical description of the particle dynamics, we derive, using a set of
approximations, a non-linear tensorial evolution equation linking the
deviatoric part of the stress tensor to the strain-rate and vorticity tensors.
The coefficients appearing in this equation can be expressed in terms of the
packing fraction and of particle-level parameters. This constitutive equation
rooted in the microscopic dynamic qualitatively reproduces a number of salient
features of the rheology of jammed soft suspensions, including the presence of
yield stresses for the shear component of the stress and for the normal stress
difference. More complex protocols like the relaxation after a preshear are
also considered, showing a smaller stress after relaxation for a stronger
preshear.
