A Gibbs-potential-based formulation for obtaining the response functions for a class of viscoelastic materials

Abstract

In this article, we demonstrate the use of a Gibbs-potential-based formulation as a means for developing a thermodynamically consistent model for a class of viscoelastic fluids of the rate type. Since one cannot always use a formulation based on a Helmholtz potential to model rate-type models, the formulation takes on added significance. The salient features of this approach are the following: — this approach provides a thermodynamical rationalization of many commonly used models that are developed on purely phenomenological grounds; furthermore, the study provides a framework for generating other classes of models and allows for a relatively straightforward means for the inclusion of thermal effects, — the approach provides a simple means for including anisotropic effects without the need for directors or other new internal variables, and — the approach does not use any additional variables (such as conformation tensors or elastic strains measured from stress free configurations) other than the current (or Cauchy) stress, the current mass density and the velocity gradient. We also show how the entire structure of the theory is obtained from just two scalar functions, the Gibbs potential and the rate of dissipation function.