On some fundamental misunderstandings in the indeterminate couple stress model. A comment on recent papers of A.R. Hadjesfandiari and G.F. Dargush

TL;DR

This paper critiques recent claims that the second-order couple stress tensor must be skew-symmetric, showing that their boundary condition choices are incomplete and contain errors, but their model remains mathematically consistent.

Contribution

It clarifies misunderstandings in the indeterminate couple stress model by analyzing boundary conditions and the implications of prior assumptions.

Findings

The boundary condition choices are incomplete and contain errors.

The model remains well-posed despite the errors.

The skew-symmetry claim is not universally valid.

Abstract

In a series of papers which are either published [A.R. Hadjesfandiari and G.F. Dargush, Couple stress theory for solids, Int. J. Solids Struct. 48, 2496-2510, 2011; A.R. Hadjesfandiari and G.F. Dargush, Fundamental solutions for isotropic size-dependent couple stress elasticity, Int. J. Solids Struct. 50, 1253-1265, 2013] or available as preprints Hadjesfandiari and Dargush have reconsidered the linear indeterminate couple stress model. They are postulating a certain physically plausible split in the virtual work principle. Based on this postulate they claim that the second-order couple stress tensor must always be skew-symmetric. Since they use an incomplete set of boundary conditions in their virtual work principle their statement contains unrecoverable errors. This is shown by specifying their development to the isotropic case. However, their choice of constitutive parameters is mathematically possible and still yields a well-posed boundary value problem.