Techniques for the Thermodynamic Consistency of Constitutive Equations

Abstract

The paper investigates the techniques associated with the exploitation of the second law of thermodynamics as a restriction on the physically admissible processes. Though the exploitation consists of the use of the arbitrariness occurring in the Clausius–Duhem inequality, the approach emphasizes two uncommon features within the thermodynamic analysis: the representation formula, of vectors and tensors, and the entropy production. The representation is shown to be fruitful whenever more terms of the Clausius–Duhem inequality are not independent. Among the examples developed to show this feature, the paper yields the constitutive equation for hypo-elastic solids and for Maxwell–Cattaneo-like equations of heat conduction. The entropy production is assumed to be given by a constitutive function per se and not merely the expression inherited by the other constitutive functions. This feature results in more general expressions of the representation formulae and is crucial for the compact description of hysteretic phenomena.