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

Neff, Patrizio; Münch, Ingo von; Ghiba, Ionel–Dumitrel; Madeo, Angela

doi:10.1016/j.ijsolstr.2015.11.028

Cited by 60 publications

(44 citation statements)

References 34 publications

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“…In that model the non-local force stress tensor τ is skew-symmetric as before, but the couple stress tensor m is assumed to be completely skew-symmetric as well. Their reasoning, based on a certain restricted understanding of boundary conditions, is critically discussed in Neff et al [42].…”

Section: Related Models In Isotropic Second Gradient Elasticitymentioning

confidence: 99%

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

et al. 2017

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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.

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Section: Related Models In Isotropic Second Gradient Elasticitymentioning

confidence: 99%

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

et al. 2017

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“…It seems, to us, however, that the state of the art in general strain gradient theories [59,86,47,72,75,6,56,55,44,64] is much more advanced as far as boundary conditions are concerned. This paper has been motivated by our reading of [42,40,41,39,38,43], in which the form of traction boundary conditions in the indeterminate couple stress model, together with an apparently plausible physical postulate lead to unacceptable conclusions, see [73]. Therefore, there had to be an underlying problem which we believe to have tracked down to the hitherto accepted format of boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

A new view on boundary conditions in the Grioli–Koiter–Mindlin–Toupin indeterminate couple stress model

Madeo

Ghiba

Neff

et al. 2016

European Journal of Mechanics - A/Solids

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In this paper we consider the Grioli-Koiter-Mindlin-Toupin linear isotropic indeterminate couple stress model. Our main aim is to show that, up to now, the boundary conditions have not been completely understood for this model. As it turns out, and to our own surprise, restricting the well known boundary conditions stemming from the strain gradient or second gradient models to the particular case of the indeterminate couple stress model, does not always reduce to the Grioli-Koiter-Mindlin-Toupin set of accepted boundary conditions. We present, therefore, a proof of the fact that when specific "mixed" kinematical and traction boundary conditions are assigned on the boundary, no "a priori" equivalence can be established between Mindlin's and our approach.

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“…We also have to mention recently published papers [26,33,37] where have been proposed modified couple stress theories which use only one additional constant that takes into account the microstructure of a material at micro and nano scale. These theories have some differences in a 3-D case which are analyzed and discussed in [41]. In the 2-D case they give the differences disappear, therefore we will not analyze them here and use the equations presented in [26,37] for development of the curved rods theories.…”

Section: Introductionmentioning

confidence: 99%

Couple stress theory of curved rods. 2-D, high order, Timoshenko’s and Euler-Bernoulli models

Zozulya

2017

Curved and Layered Structures

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New models for plane curved rods based on linear couple stress theory of elasticity have been developed. 2-D theory is developed from general 2-D equations of linear couple stress elasticity using a special curvilinear system of coordinates related to the middle line of the rod as well as special hypothesis based on assumptions that take into account the fact that the rod is thin. High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First, stress and strain tensors, vectors of displacements and rotation along with body forces have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate. Thereby, all equations of elasticity including Hooke's law have been transformed to the corresponding equations for Fourier coefficients. Then, in the same way as in the theory of elasticity, a system of differential equations in terms of displacements and boundary conditions for Fourier coefficients have been obtained. Timoshenko's and EulerBernoulli theories are based on the classical hypothesis and the 2-D equations of linear couple stress theory of elasticity in a special curvilinear system. The obtained equations can be used to calculate stress-strain and to model thin walled structures in macro, micro and nano scales when taking into account couple stress and rotation effects.

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

Cited by 60 publications

References 34 publications

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

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

A new view on boundary conditions in the Grioli–Koiter–Mindlin–Toupin indeterminate couple stress model

Couple stress theory of curved rods. 2-D, high order, Timoshenko’s and Euler-Bernoulli models

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