ON INSTABILITIES OF SINGLE-INTEGRAL CONSTITUTIVE-EQUATIONS FOR VISCOELASTIC LIQUIDS

Various types of instabilities are exposed in this paper for time-stra in separable single-integral viscoelastic constitutive equations (CE's ). They were distinguished into two groups and defined as Hadamard and dissipative type of instabilities. As for the Hadamard-type, previous ly obtained criteria are found to be necessary only. They are necessar y and sufficient only for thermodynamic stability. Improved, stricter Hadamard stability criteria are described briefly in this paper, and t hen applied to study of stability of several CE's. It is shown that th e Currie potential with the K-BKZ equation and the model proposed by P apanastasiou et al. are Hadamard unstable. In the case of dissipative stability, the necessary and sufficient condition for stress boundedne ss in any regular flow with a given history, is proved. Then, this cri terion was applied to the neo-Hookean, Mooney, and Yen and McIntire sp ecifications of the general K-BKZ model, to exhibit unbounded solution s. In addition, Larson-Monroe potential which is later proved to be Ha damard unstable but satisfies the above criterion of boundedness, is s hown to have unstable decreasing branch in steady simple shear flow. A t present, to the authors' knowledge, there is no viscoelastic single- integral CE of factorable type proposed in the literature which can sa tisfy all the Hadamard and dissipative stability criteria.