  We derive from particle-level dynamics a constitutive model describing the
rheology of two-dimensional dense soft suspensions below the jamming
transition, in a regime where hydrodynamic interactions between particles are
screened. Based on a statistical description of particle dynamics, we obtain
through a set of physically plausible approximations a non-linear tensorial
evolution equation for the deviatoric part of the stress tensor, involving the
strain-rate and vorticity tensors. This tensorial evolution equation involves
singular terms usually not taken into account in phenomenological constitutive
models, which most often assume a regular expansion in terms of the stress
tensor. All coefficients appearing in the equation have known expressions in
terms of the microscopic parameters of the model. The predictions of this
microscopically grounded constitutive model have several qualitative features
that are specific to the rheology of soft suspensions measured in experiments
or simulations. The model shows a typical behavior of polymeric visco-elastic
materials, such as normal stress differences quadratic in the shear rate
$\dot\gamma$, as well as typical behaviors of suspensions of stiff particles,
such as a particle pressure linear in $\dot\gamma$ and a zero-shear viscosity
diverging at the jamming transition. The model also predicts a sharper shear
thinning than other visco-elastic models at small shear rates, in qualitative
agreement with experimental observations. Furthermore the shear thinning
follows a critical scaling close to the jamming transition.
