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. Embacher, Peter; Dirr, Nicolas; Zimmer, Johannes; Reina, Celia: Computing diffusivities from particle models out of equilibrium (2018)
  2. Haskovec, Jan; Hittmeir, Sabine; Markowich, Peter; Mielke, Alexander: Decay to equilibrium for energy-reaction-diffusion systems (2018)
  3. Kraaij, Richard; Lazarescu, Alexandre; Maes, Christian; Peletier, Mark: Deriving GENERIC from a generalized fluctuation symmetry (2018)
  4. Mielke, Alexander; Mittnenzweig, Markus: Convergence to equilibrium in energy-reaction-diffusion systems using vector-valued functional inequalities (2018)
  5. Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe: Global existence results for viscoplasticity at finite strain (2018)
  6. Mielke, Alexander (ed.); Peletier, Mark (ed.); Slepcev, Dejan (ed.): Variational methods for evolution. Abstracts from the workshop held November 12--18, 2017 (2017)
  7. Mittnenzweig, Markus; Mielke, Alexander: An entropic gradient structure for Lindblad equations and couplings of quantum systems to macroscopic models (2017)
  8. 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)
  9. Fathi, Max: A gradient flow approach to large deviations for diffusion processes (2016)
  10. Mariano, Paolo Maria: Trends and challenges in the mechanics of complex materials: a view (2016)
  11. Grandi, Diego; Stefanelli, Ulisse: The Souza-Auricchio model for shape-memory alloys (2015)
  12. Mielke, A.; Peletier, M. A.; Renger, D. R. M.: On the relation between gradient flows and the large-deviation principle, with applications to Markov chains and diffusion (2014)
  13. Duong, Manh Hong; Peletier, Mark A.; Zimmer, Johannes: GENERIC formalism of a Vlasov-Fokker-Planck equation and connection to large-deviation principles (2013)
  14. Grmela, Miroslav: Extensions of nondissipative continuum mechanics toward complex fluids and complex solids (2013)
  15. Liero, Matthias; Mielke, Alexander: Gradient structures and geodesic convexity for reaction-diffusion systems (2013)
  16. Mielke, Alexander: Thermomechanical modeling of energy-reaction-diffusion systems, including bulk-interface interactions (2013)
  17. Mielke, Alexander: Dissipative quantum mechanics using GENERIC (2013)
  18. Colli, Pierluigi; Krejčí, Pavel; Rocca, Elisabetta; Sprekels, Jürgen: A nonlocal quasilinear multi-phase system with nonconstant specific heat and heat conductivity (2011)
  19. Mielke, Alexander: Formulation of thermoelastic dissipative material behavior using GENERIC (2011)
  20. Mielke, Alexander: A gradient structure for reaction-diffusion systems and for energy-drift-diffusion systems (2011)

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