Formulation of thermoelastic dissipative material behavior using GENERIC We show that the coupled balance equations for a large class of dissipative materials can be cast in the form of GENERIC (General Equations for Non-Equilibrium Reversible Irreversible Coupling). In dissipative solids (generalized standard materials), the state of a material point is described by dissipative internal variables in addition to the elastic deformation and the temperature. The framework GENERIC allows for an efficient derivation of thermodynamically consistent coupled field equations, while revealing additional underlying physical structures, like the role of the free energy as the driving potential for reversible effects and the role of the free entropy (Massieu potential) as the driving potential for dissipative effects. Applications to large and small-strain thermoplasticity are given. Moreover, for the quasistatic case, where the deformation can be statically eliminated, we derive a generalized gradient structure for the internal variable and the temperature with a reduced entropy as driving functional.

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  1. Fischer, Julian; Hopf, Katharina; Kniely, Michael; Mielke, Alexander: Global existence analysis of energy-reaction-diffusion systems (2022)
  2. Romero, Ignacio; Andrés, Eva M.; Ortiz-Toranzo, Ángel: Variational updates for general thermo-chemo-mechanical processes of inelastic solids (2021)
  3. Betsch, Peter; Schiebl, Mark: GENERIC-based formulation and discretization of initial boundary value problems for finite strain thermoelasticity (2020)
  4. Kraaij, Richard C.; Lazarescu, Alexandre; Maes, Christian; Peletier, Mark: Fluctuation symmetry leads to GENERIC equations with non-quadratic dissipation (2020)
  5. Mielke, Alexander; Roubíček, Tomáš: Thermoviscoelasticity in Kelvin-Voigt rheology at large strains (2020)
  6. Pavelka, Michal; Klika, Václav; Grmela, Miroslav: Generalization of the dynamical lack-of-fit reduction from GENERIC to GENERIC (2020)
  7. Jüngel, Ansgar; Stefanelli, Ulisse; Trussardi, Lara: Two structure-preserving time discretizations for gradient flows (2019)
  8. Kantner, Markus; Mielke, Alexander; Mittnenzweig, Markus; Rotundo, Nella: Mathematical modeling of semiconductors: from quantum mechanics to devices (2019)
  9. Embacher, Peter; Dirr, Nicolas; Zimmer, Johannes; Reina, Celia: Computing diffusivities from particle models out of equilibrium (2018)
  10. Haskovec, Jan; Hittmeir, Sabine; Markowich, Peter; Mielke, Alexander: Decay to equilibrium for energy-reaction-diffusion systems (2018)
  11. Kraaij, Richard; Lazarescu, Alexandre; Maes, Christian; Peletier, Mark: Deriving GENERIC from a generalized fluctuation symmetry (2018)
  12. Mielke, Alexander; Mittnenzweig, Markus: Convergence to equilibrium in energy-reaction-diffusion systems using vector-valued functional inequalities (2018)
  13. Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe: Global existence results for viscoplasticity at finite strain (2018)
  14. Mielke, Alexander (ed.); Peletier, Mark (ed.); Slepcev, Dejan (ed.): Variational methods for evolution. Abstracts from the workshop held November 12--18, 2017 (2017)
  15. Mittnenzweig, Markus; Mielke, Alexander: An entropic gradient structure for Lindblad equations and couplings of quantum systems to macroscopic models (2017)
  16. Auricchio, Ferdinando; Boatti, Elisa; Reali, Alessandro; Stefanelli, Ulisse: Gradient structures for the thermomechanics of shape-memory materials (2016)
  17. Düring, Bertram (ed.); Schönlieb, Carola-Bibiane (ed.); Wolfram, Marie-Therese (ed.): Gradient flows: from theory to application. Selected papers based on the presentations at the international workshop held at the International Centre for Mathematical Sciences (ICMS), Edinburgh, UK, April 20--24, 2015 (2016)
  18. Fathi, Max: A gradient flow approach to large deviations for diffusion processes (2016)
  19. Mariano, Paolo Maria: Trends and challenges in the mechanics of complex materials: a view (2016)
  20. Duong, Manh Hong: Formulation of the relativistic heat equation and the relativistic kinetic Fokker-Planck equations using GENERIC (2015)

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