Microscopic and Macroscopic Stress with Gravitational and Rotational Forces

TL;DR

This paper investigates the validity of Irving and Kirkwood's atomistic stress expression by analyzing a fluid in a gravitational field and a rotating solid, confirming the approach's accuracy through analytic solutions.

Contribution

It clarifies the role of velocity-dependent forces in atomistic stress calculations by comparing analytic solutions with the Irving-Kirkwood tensor in specific physical scenarios.

Findings

Analytic solutions agree with Irving-Kirkwood stress tensor.

Potential and kinetic stress contributions are both significant.

Supports the validity of Irving-Kirkwood's approach in complex conditions.

Abstract

Many recent papers have questioned Irving and Kirkwood's atomistic expression for stress. In Irving and Kirkwood's approach both interatomic forces and atomic velocities contribute to stress. It is the velocity-dependent part that has been disputed. To help clarify this situation we investigate [1] a fluid in a gravitational field and [2] a steadily rotating solid. For both problems we choose conditions where the two stress contributions, potential and kinetic, are significant. The analytic force-balance solutions of both these problems agree very well with a smooth-particle interpretation of the atomistic Irving-Kirkwood stress tensor.