Open Access

ARTICLE

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

by Veturia Chiroiu¹, Ligia Munteanu¹, Pier Paolo Delsanto²

1 Institute of Solid Mechanics of Romanian Academy, Ctin Mille 15, 010141 Bucharest
2 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.

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