A nonlinear viscoelastic model and non-equilibrium entropies

• Alternative entropies for non-linear viscoelasticity are considered.
• Thermodynamic conjugate of stress tensor is a suitable independent variable.
• Conservation–dissipation formalism is applied to non-linear viscoelasticity.
• New result for non-isothermal case is obtained.

We show that the thermodynamic conjugate of the extra stress is a more suitable independent variable than the extra stress itself for the thermodynamic description of some nonlinear models of viscoelasticity. This brings more precision to the knowledge of non-equilibrium thermodynamic potentials, and provides an illustration of a recently proposed conservation–dissipation formalism which allows bringing extended irreversible thermodynamics to the nonlinear regime.