On thermodynamic functions in thermoelasticity without energy dissipation

•Thermodynamic functions in coupled nonlinear GN thermoelasticity are derived.•The alternative thermodynamic functions for GN model are derived.•General procedure based on Legendre transforms is used to derive constitutive relations.•Relations between the thermodynamic potentials and the thermal work are provided.•An example showing the relations with the classic thermoelastic model is presented.

Using a systematic procedure based on convex/concave functions and Legendre transforms, the consistent set of the thermodynamic functions in the framework of the Green and Naghdi (GN) thermoelasticity without energy dissipation is addressed. Starting from the free energy of GN, the thermodynamic potentials, i.e. internal energy, enthalpy and Gibbs free energy, are derived. Moreover it is shown that four more thermodynamic potentials, named alternative, can be provided. The relations between these functions are provided and the constitutive relations are obtained extending the general methodology used for the classical thermoelastic behaviour.