Preprint Article Version 1 This version is not peer-reviewed

An Assessment of Couple Stress Theories

Version 1 : Received: 8 November 2018 / Approved: 9 November 2018 / Online: 9 November 2018 (04:01:56 UTC)

How to cite: Hadjesfandiari, A.R.; Dargush, G.F. An Assessment of Couple Stress Theories. Preprints 2018, 2018110236 (doi: 10.20944/preprints201811.0236.v1). Hadjesfandiari, A.R.; Dargush, G.F. An Assessment of Couple Stress Theories. Preprints 2018, 2018110236 (doi: 10.20944/preprints201811.0236.v1).

Abstract

In this paper, we examine the mathematical and physical consistencies of the three primary couple stress theories: original Mindlin-Tiersten-Koiter couple stress theory (MTK-CST), modified couple stress theory (M-CST) and consistent couple stress theory (C-CST).  As has been known for many years, MTK-CST suffers from some fundamental inconsistencies, such as the indeterminacy of the couple-stress tensor.  Therefore, despite the fact that MTK-CST has a fundamental position in the evolution of size-dependent continuum mechanics, it is not a reliable theory within continuum mechanics, for example, in developing new size-dependent multi-physics formulations.  We also observe that M-CST not only inherits all inconsistences from the original MTK-CST, but also suffers from new additional inconsistencies, such as the introduction of a new non-physical governing equation.  These inconsistencies refute the claim of those who state that the couple-stress tensor may be chosen symmetric.  Therefore, the apparent success of MTK-CST and M-CST in describing a size-effect for some problems, such as two-dimensional plate and beam bending, is not enough to justify these theories as suitable for general cases.  In fact, the symmetric couple-stresses in M-CST create torsional or anticlastic deformation, not bending.  On the other hand, C-CST, with a skew-symmetric couple-stress tensor, is the consistent continuum mechanics suitable for solving different size-dependent solid, fluid and multi-physics problems. 

Subject Areas

couple stress theory; size-dependent mechanics; indeterminacies; curvature tensor; torsion tensor

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