On the Formulation of Continuum Thermodynamic Models for Solids as General Equations for Non-equilibrium Reversible-Irreversible Coupling

The purpose of this work is the comparison of some aspects of the formulation of material models in the context of continuum thermodynamics (e.g., ilhavA1/2 in The mechanics and thermodynamics of continuous media, Springer, Berlin, 1997) with their formulation in the form of a General Equation for Non-Equilibrium Reversible-Irreversible Coupling (GENERIC: e.g., Grmela and A-ttinger in Phys. Rev. E 56: 6620-6632, 1997; A-ttinger and Grmela in Phys. Rev. E 56: 6633-6655, 1997; A-ttinger in Beyond equilibrium thermodynamics, Wiley, New York, 2005; Grmela in J. Non-Newton. Fluid Mech. 165: 980-998, 2010). A GENERIC represents a generalization of the Ginzburg-Landau model for the approach of non-equilibrium systems to thermodynamic equilibrium. Originally developed to formulate non-equilibrium thermodynamic models for complex fluids, it has recently been applied to anisotropic inelastic solids in a Eulerian setting (Hutter and Tervoort in J. Non-Newton. Fluid Mech. 152: 45-52, 2008; 53-65, 2008; Adv. Appl. Mech. 42: 254-317, 2009) as well as to damage mechanics (Hutter and Tervoort in Acta Mech. 201: 297-312, 2008). In the current work, attention is focused for simplicity on the case of thermoelastic solids with heat conduction and viscosity in a Lagrangian setting (e.g., ilhavA1/2 in The mechanics and thermodynamics of continuous media, Springer, Berlin, 1997, Chaps. 9-12). In the process, the relation of the two formulations to each other is investigated in detail. A particular point in this regard is the concept of dissipation and its model representation in both contexts.