WIAS Preprint No. 2856, (2021)

On compatibility of the natural configuration framework with general equation for non-equilibrium reversible-irreversible coupling (GENERIC): Derivation of anisotropic rate-type models


Authors

  • Pelech, Petr
    ORCID: 0000-0002-2271-7147
  • Tůma, Karel
  • Pavelka, Michal
  • Šípka, Martin
  • Sýkora, Martin

2020 Mathematics Subject Classification

  • 76A02 76A05 76A10 76A15

Keywords

  • Complex fluids, mathematical foundations, general fluid mechanics, non-Newtonian flows, rheology, viscous flows

DOI

10.20347/WIAS.PREPRINT.2856

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).

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