On the Polar Nature and Invariance Properties of a Thermomechanical Theory for Continuum-on-Continuum Homogenization

TL;DR

This paper rigorously analyzes the polar nature and invariance properties of a thermomechanical continuum derived via homogenization, emphasizing contributions from microscopic states to macroscopic balances.

Contribution

It introduces the concept of a polar continuum in homogenized thermomechanics and examines invariance of stress and heat flux under transformations.

Findings

Homogenized continuum exhibits polar characteristics with body couples and couple stresses.

Macroscopic stress and heat flux are invariant under certain transformations.

Balance laws maintain form-invariance in the homogenized setting.

Abstract

This paper makes a rigorous case for considering the homogenized continuum derived by the Irving-Kirkwood procedure as a polar medium in which the balances of angular momentum and energy contain contributions due to body couples and couple stresses defined in terms of the underlying microscopic state. The paper also addresses the question of invariance of macroscopic stress and heat flux and form-invariance of the macroscopic balance laws.