Virial Theorems and Virial Stresses of Micropolar Media

TL;DR

This paper extends virial theorems and virial stresses to micropolar continuum mechanics, linking kinetic energies and stresses with molecular dynamics concepts, and introduces formulas for virial force and couple-stresses.

Contribution

It generalizes virial theorems to micropolar media, providing new formulas for virial force-stress and couple-stress in continuum mechanics.

Findings

Derived first and second virial theorems for micropolar media.

Established formulas for virial force-stress and couple-stress.

Connected virial stresses with Reynolds and turbulent stresses.

Abstract

A generalization of virial theorems and virial stresses to micropolar continuum mechanics is explored. The linear momentum balance in dyadic product with translation leads to (i) the first virial theorem of micropolar continuum mechanics involving the infinite-time limit of the kinetic translational energy and (ii) a classical formula for computing the virial force-stress known in molecular dynamics. The angular momentum balance in dyadic product with rotation leads to (i) the second virial theorem of micropolar continuum mechanics involving the infinite-time limit of the kinetic rotational energy and (ii) a virial couple-stress along with a formula for its computation. The latter stress is also uncovered in the dyadic product of linear momentum balance with rotation. The virial force-stress and virial couple-stress contain, respectively, the Reynolds force-stress and turbulent couple-stress.