We study the linear stability of Plane Poiseuille flow of an
elastoviscoplastic fluid using a revised version of the model proposed by Putz
and Burghelea (Rheol. Acta (2009)48:673-689). The evolution of the
microstructure upon a gradual increase of the external forcing is governed by a
structural variable (the concentration of solid material elements) which decays
smoothly from unity to zero as the stresses are gradually increased beyond the
yield point. Stability results are in close conformity with the ones of a
pseudo-plastic fluid. Destabilizing effects are related to the presence of an
intermediate transition zone where elastic solid elements coexist with fluid
elements. This region brings an elastic contribution which does modify the
stability of the flow
