The derivation of the FENE-P model within the context of a thermodynamic perspective for bodies with evolving natural configurations

Abstract

In this paper, we provide a method for developing the FENE-P constitutive relation and generalizations of such constitutive relations from a totally different perspective than that used to develop such constitutive relations. The thermodynamic framework within which the constitutive relations are generated is a generalization of the structure within which rate type fluid models to describe the viscoelastic response of fluids were developed (JNNFM, 88, 207–227 (2000)). It is interesting to note that widely different approaches such as those based on the notion of configuration tensors and the study carried out here are able to lead to the same classes of models, providing one basis for some conviction concerning the appropriateness of the model. Also, the fact that the general thermodynamic structure used here has also been used successfully to establish constitutive relations to describe the response of bodies in a wide range of areas in inelasticity, twinning, phase transitions, chemically reacting mixtures, shape memory alloys and polymers, etc., gives additional credibility to the construction of constitutive relations such as those obtained in this study.