A few remarks on thermomechanics

TL;DR

This paper develops a comprehensive thermomechanical framework for modeling thermo-visco-elastic materials, unifying various models and highlighting thermodynamic consistency issues in classical complex fluid models.

Contribution

It introduces a general invariant setting for thermo-visco-elastic models, including new models with internal variables, and analyzes thermodynamic compliance of classical models.

Findings

Oldroyd B model does not satisfy the second thermodynamic principle.

A Zaremba-Jaumann derivative-based model does satisfy the second principle.

The framework encompasses many known solid and fluid models.

Abstract

We develop a global setting for modeling thermo-visco-elastic materials that satisfy the principles of thermodynamics and are properly invariant. This setting encompasses many known solid and fluid models, as well as new models with internal variables that generalize the Maxwell rheological model. Complex fluid models such as the Oldroyd B model are shown to belong to the above general family of models. The specific Oldroyd B model is however found to be seriously lacking in terms of satisfying the second principle of thermodynamics. On the contrary, a second complex fluid model based on the Zaremba-Jaumann derivative is shown to satisfy the second principle of thermodynamics.