On compatibility of the Natural configuration framework with GENERIC: Derivation of anisotropic rate-type models

TL;DR

This paper explores the compatibility between the natural configuration framework and GENERIC in continuum thermodynamics, demonstrating their connection through isotropic and anisotropic rate-type fluid models and proposing interpretative links.

Contribution

It shows the compatibility of natural configurations with GENERIC and provides a unified interpretation for both frameworks in modeling complex fluid behaviors.

Findings

Both frameworks are compatible across various models.

Natural configurations can be interpreted within GENERIC.

The approach is demonstrated on anisotropic rate-type fluid models.

Abstract

Within the framework of natural configurations developed by Rajagopal and Srinivasa, evolution within continuum thermodynamics is formulated as evolution of a natural configuration linked with the current configuration. On the other hand, withing the General Equation for Non-Equilibrium Reversible-Irreversible Coupling (GENERIC) framework, the evolution is split into Hamiltonian mechanics and (generalized) gradient dynamics. These seemingly radically different approaches have actually a lot in common and we show their compatibility on a wide range of models. Both frameworks are illustrated on~isotropic and anisotropic rate-type fluid models. We propose an interpretation of the natural configurations within GENERIC and vice versa (when possible).