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Evaluation of the Toupin-Mindlin Theory for Predicting the Size Effects in the Buckling of the Carbon Nanotubes

Veturia Chiroiu1, Ligia Munteanu1, Pier Paolo Delsanto2
Institute of Solid Mechanics of Romanian Academy, Ctin Mille 15, 010141 Bucharest
Politecnico of Torino, Physics Department, Corso Duca degli Abruzzi 24, 10129 Torino

Computers, Materials & Continua 2010, 16(1), 75-100. https://doi.org/10.3970/cmc.2010.016.075

Abstract

Conventional continuum theories are unable to capture the observed indentation size effects, due to the lack of intrinsic length scales that represent the measures of nanostructure in the constitutive relations. In order to overcome this deficiency, the Toupin-Mindlin strain gradient theory of nanoindentation is formulated in this paper and the size dependence of the hardness with respect to the depth and the radius of the indenter for multiple walled carbon nanotubes is investigated. Results show a peculiar size influence on the hardness, which is explained via the shear resistance between the neighboring walls during the buckling of the multiwalled nanotubes.

Keywords

Toupin-Mindlin strain gradient theory, nanoindentation, size effects, buckling, carbon nanotubes.

Cite This Article

V. . Chiroiu, L. . Munteanu and P. P. . Delsanto, "Evaluation of the toupin-mindlin theory for predicting the size effects in the buckling of the carbon nanotubes," Computers, Materials & Continua, vol. 16, no.1, pp. 75–100, 2010.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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