On the Second Law of Thermodynamics in Continuum Physics

The paper revisits the formulation of the second law in continuum physics and investigates new methods of exploitation. Both the entropy flux and the entropy production are taken to be expressed by constitutive equations. In three-dimensional settings, vectors and tensors are in order and they occur through inner products in the inequality representing the second law; a representation formula, which is quite uncommon in the literature, produces the general solution whenever the sought equations are considered in rate-type forms. Next, the occurrence of the entropy production as a constitutive function is shown to produce a wider set of physically admissible models. Furthermore the constitutive property of the entropy production results in an additional, essential term in the evolution equation of rate-type materials, as is the case for Duhem-like hysteretic models. This feature of thermodynamically consistent hysteretic materials is exemplified for elastic–plastic materials. The representation formula is shown to allow more general non-local properties while the constitutive entropy production proves essential for the modeling of hysteresis.