Time-strain nonseparability in viscoelastic constitutive equations

Asymptotic analysis was carried out to verify that the time-strain separability implemented in viscoelastic models is the main origin of mathematically ill-posed behavior in these models. The hypothesis of time-strain separability caused the Hadamard-type instability of the Wagner, Luo-Tanner, Papanastasiou, and K-BKZ models with the Larson-Monroe or Mooney potential, and the dissipative instability of the Lodge model. The implicit relation between the Finger strain C^-1 and the geometric tensor Q allowed the same conclusion to be drawn for the Doi-Edwards model.