Coupled thermodynamic orhogonality in non-linear models of type-III thermoelasticity

The present study is devoted to a derivation of non-linear constitutive equations for the non-linear Green-Naghdi type-III thermoelastic model on the basis of the principle of thermodynamic (or thermomechanical) orthogonality. The latter was proposed by Ziegler as an extention to the Onsager linear irreversible thermodynamics. It states that the irreversible constituent parts of thermodynamic currents (velocities) are orthogonal to the convex dissipation potential level surface in the space of thermodynamic forces for any process of heat propagation in a solid. Non-linear constitutive laws of the heat propagation complying with the principle of thermomechanical orthogonality are obtained and discussed.