  We explore the rheology predicted by a recently proposed constitutive model
for jammed suspensions of soft elastic particles derived from particle-level
dynamics [Cuny et al., Phys. Rev. Lett. 127, 218003 (2021)]. Our model predicts
that the orientation of the anisotropy of the microstructure, governed by an
interplay between advection and contact elasticity, plays a key role at
yielding and in flow. It generates normal stress differences contributing
significantly to the yield criterion and Trouton ratio. It gives rise to
non-trivial transients such as stress overshoots in step increases of shear
rate, residual stresses after flow cessation and power-law decay of the shear
rate in creep. Finally, it explains the collapse of storage modulus as measured
in parallel superposition for a yielded suspension.
