Torsion of cylindrically anisotropic nano/microtubes of the cubic crystals obtained by rolling the crystal planes (011)

R. Goldstein1, V. Gorodtsov1, D. Lisovenko1
1Institute for Problems in Mechanics RAS, prospect Vernadskogo 101, b1, Moscow, 119526
Abstract
Elastic torsion of cylindrically anisotropic nano/microtubes is examined by Saint-Venant approach. It is assumed that the tubes were obtained by rolling the plates of the cubic crystals with plane orientation (011). The analytical expression for the torsional stiffness for such nano/microtubes is obtained. Torsional stiffness is dependent on three compliance coefficients of cubic crystal, thickness parameter, chirality angle and radius of the tube. Numerical analysis of the torsional stiffness of nano/microtubes is made. This analysis showed that for most crystals the dimensionless ratio of torsional stiffness to torsional stiffness at zero chiral angle of nano/microtubes slightly varies with thickness parameter of tubes. Materials for which there is a substantial change in the dimensionless ratio of torsional stiffnesses, are revealed. Torsion of chiral nano/microtubes from cubic materials in the absence of tensile forces is accompanied by a linear Poynting’s effect. Сomparative analysis of the dimensionless ratios of torsional stiffness to torsional stiffness at zero chirality angle for nano/microtubes obtained by rolling the crystal planes (001) and (011) is given. It is shown that the variability of torsional stiffness for nano/microtubes obtained by rolling the crystal planes (011), is much higher than for nano/microtubes produced by rolling the crystal planes (001). Comparative analysis of linear Poynting’s effect for nano/microtubes obtained by rolling the crystal planes (001) and (011) is also given.
Received: 08 October 2016   Accepted: 18 October 2016
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