The modified indeterminate couple stress model: Why Yang et al.'s arguments motivating a symmetric couple stress tensor contain a gap and why the couple stress tensor may be chosen symmetric nevertheless

TL;DR

This paper critiques Yang et al.'s reasoning for a symmetric couple stress tensor, identifies a gap, and argues that the tensor can be symmetric and traceless based on physical hypotheses and properties of total stress.

Contribution

It clarifies the reasoning behind the symmetry of the couple stress tensor and proposes that it can be symmetric and traceless, challenging previous assumptions.

Findings

Identifies a gap in Yang et al.'s argument for symmetry

Proposes the couple stress tensor can be symmetric and traceless

Reframes the origin of couple stress based on total stress properties

Abstract

We show that the reasoning in favor of a symmetric couple stress tensor in Yang et al.'s introduction of the modified couple stress theory contains a gap, but we present a reasonable physical hypothesis, implying that the couple stress tensor is traceless and may be symmetric anyway. To this aim, the origin of couple stress is discussed on the basis of certain properties of the total stress itself. In contrast to classical continuum mechanics, the balance of linear momentum and the balance of angular momentum are formulated at an infinitesimal cube considering the total stress as linear and quadratic approximation of a spatial Taylor series expansion.