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

TL;DR

This paper develops a thermodynamic framework for modeling viscoelastic fluids lacking instantaneous elasticity, capturing fluid-like behavior and including Maxwell and Kelvin-Voigt models through specific potential and dissipation choices.

Contribution

It introduces a thermodynamic approach to create rate-type models for fluids without instantaneous elasticity, expanding the modeling capabilities for viscoelastic fluids.

Findings

Model exhibits fluid-like characteristics.

Includes Maxwell-like and Kelvin-Voigt-like behaviors.

Capable of representing creep and stress relaxation.

Abstract

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 model that is developed exhibits fluid-like characteristics and is incapable of instantaneous elastic response. It also includes Maxwell-like and Kelvin-Voigt-like viscoelastic materials (when certain material moduli take special values).