On the entropy inequality and its exploitation in continuum physics

Abstract

The paper deals with the statement and the application of the entropy principle, through the Clausius–Duhem inequality, in continuum physics. The conceptual role is taken from the Coleman–Noll paper of 1963 thus leading to the physical admissibility of constitutive equations. The statement is generalized by letting the rate of entropy production be a constitutive property per se. This generalization proves essential in connection with the modelling of hysteretic phenomena. As to the application, the view of the Coleman–Noll procedure is maintained but a representation formula is shown to generalize the consequences of the entropy principle; as an example the modelling of heat conduction is investigated. Furthermore, while applying the entropy principle to magnetic materials, it is shown an interesting connection between the balance of angular momentum and the thermodynamic restrictions. Also, the modelling through rate-type equations shows the need of Lagrangian fields to obey objectivity and that of the entropy production as a constitutive function to account for the difference between loading and unloading processes.