WIAS Preprint No. 3178, (2025)

Reference map approach to Eulerian thermomechanics using GENERIC


Authors

  • Peschka, Dirk
    ORCID: 0000-0002-3047-1140
  • Thomas, Marita
    ORCID: 0000-0001-9172-014X
  • Zafferi, Andrea
    ORCID: 0000-0003-4012-7666

2020 Mathematics Subject Classification

  • 74A15 74F10 74B20 65M60

Keywords

  • Reference map, Eulerian thermomechanics, GENERIC

DOI

10.20347/WIAS.PREPRINT.3178

Abstract

An Eulerian GENERIC model for thermo-viscoelastic materials with diffusive components is derived based on a transformation framework that maps a Lagrangian formulation to corresponding Eulerian coordi- nates. The key quantity describing the deformation in Eulerian coordinates is the inverse of the deformation, i.e. the reference map. The Eulerian model is formally constructed, and by reducing the GENERIC system to a damped Hamiltonian system, the isothermal limit is derived. A structure-preserving weak formulation is developed. As an example, the coupling of finite strain viscoelasticity and diffusion in a multiphase system governed by Lagrangian indicator functions is demonstrated.

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