Thermodynamics of non-local materials: extra fluxes and internal powers

TL;DR

This paper compares two approaches to formulating the Laws of Thermodynamics for non-local materials, advocating for an internal powers framework that is more general and directly based on constitutive equations.

Contribution

It introduces a formulation of thermodynamics for non-local materials based on internal powers, avoiding the need for ad hoc fluxes and clarifying internal power contributions.

Findings

Derived expressions for internal powers of non-local materials

Compared flux-based and internal power formulations

Highlighted advantages of the internal powers approach

Abstract

The most usual formulation of the Laws of Thermodynamics turns out to be suitable for local or simple materials, while for non-local systems there are two different ways: either modify this usual formulation by introducing suitable extra fluxes or express the Laws of Thermodynamics in terms of internal powers directly, as we propose in this paper. The first choice is subject to the criticism that the vector fluxes must be introduced a posteriori in order to obtain the compatibility with the Laws of Thermodynamics. On the contrary, the formulation in terms of internal powers is more general, because it is a priori defined on the basis of the constitutive equations. Besides it allows to highlight, without ambiguity, the contribution of the internal powers in the variation of the thermodynamic potentials. Finally, in this paper, we consider some examples of non-local materials and derive the proper expressions of their internal powers from the power balance laws.