A thermodynamic framework to develop rate-type models for fluids without instantaneous elasticity

In this paper, we apply the thermodynamic framework recently put into place by Rajagopal and co-workers, to develop rate-type models for viscoelastic fluids which do not possess instantaneous elasticity. To illustrate the capabilities of such models, we make a specific choice for the specific Helmholtz potential and the rate of dissipation and consider the creep and stress relaxation response associated with the model. Given specific forms for the Helmholtz potential and the rate of dissipation, the rate of dissipation is maximized with the constraint that the difference between the stress power and the rate of change of Helmholtz potential is equal to the rate of dissipation and any other constraint that may be applicable such as incompressibility. We show that the class of models that are developed exhibit fluid-like characteristics, when none of the material moduli that appear in the model are not zero, and are incapable of instantaneous elastic response. They also include Maxwell-like and Kelvin-Voigt-like viscoelastic materials (when certain material moduli take special values).

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