Abstract
This paper studies the Hadamard-type stability of viscoelastic constitutive equations (VECEs) of single-integral type by the analysis of local linear stability against extremely short and fast disturbances. The analysis is quite similar to that previously considered for Maxwell-like VECEs of differential type. The necessary and sufficient conditions for the global stability (i.e. stability for any type of flow and any value of velocity gradient) are obtained in algebraic form for the time-strain separable single-integral VECEs with instantaneous elasticity. These conditions are then applied to the analysis of the stability for some single-integral VECEs proposed in the literature: Oldroyd-Lodge model, some specifications of the Kaye-BK-Z model and two modifications of the VECEs proposed by Wagner. It is shown that apart from very particular cases, both Wagner's VECEs are unstable in the Hadamard-type sense, seemingly due to poor (or the absence of any) relations to thermodynamic description.
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