The recent development of algebraic explicit stress models (AESM) for viscoelastic fluids rests upon a general equilibrium assumption, by invoking a slow variation condition on the evolution of the viscoelastic anisotropy tensor (the normalized de-viatoric part of the extra-stress tensor [G. Mompean, R.L. Thompson, P.R. Souza Mendes, A general transformation procedure for differential viscoelas...