Extended Coleman–Noll procedure and thermodynamics of viscoelastic solids revisited

In the classical Coleman–Noll approach to the exploitation of second law of thermodynamics, the balance laws of mass, linear momentum and energy are regarded as differential bilateral constraints to be included in the entropy inequality. In recent years, the classical Coleman–Noll procedure has been generalized by considering also the gradients of the fundamental balance equations as constraints in the entropy inequality. In the present paper, a generalized Coleman–Noll procedure is applied to analyze viscoelastic solids with and without relaxation of the heat flux. It is proved that the relaxation of the heat flux does not ensure the hyperbolicity of the system of balance laws. An overview of the generalized exploitation procedures is provided as well.