Abstract
The paper systemizes numerous cubic crystals which can have both positive and negative Poisson’s ratios (the so-called partial auxetics) depending on the specimen orientation in tension. Several complete cubic auxetics whose Poisson’s ratio is always negative are indicated. The partial cubic auxetics are classified with the use of two dimensionless elastic parameters. For one of the parameters, a critical value is found at which the orientation behavior of the crystals changes qualitatively. The behavior of mesotubes obtained by rolling up plates of cubic crystals (crystals with rectilinear anisotropy) is considered in detail. Such mesotubes with curvilinear cubic anisotropy can have micron and nanometer lateral dimensions. It is shown that uniform tension of nano/microtubes of cubic crystals is possible only in the particular case of zero chirality angle (the angle between the crystallographic axis and the axis of a stretched tube). It is demonstrated by the semi-inverse Saint-Venant method that solution of the axial tension problem for cylindrically anisotropic nano/microtubes of cubic crystals with a non-zero chirality angle is possible with radially inhomogeneous fields of three normal stresses and one shear stress. In the examples considered, the cylindrically anisotropic nano/microtubes of cubic crystals are auxetics even if they are initially non-auxetics with rectilinear anisotropy.
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Original Russian Text © R. V. Goldstein, V.A. Gorodtsov, D.S. Lisovenko, M.A. Volkov, 2013, published in Fizicheskaya Mezomekhanika, 2013, Vol. 16, No. 6, pp. 13–31.
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Goldstein, R.V., Gorodtsov, V.A., Lisovenko, D.S. et al. Negative Poisson’s ratio for cubic crystals and nano/microtubes. Phys Mesomech 17, 97–115 (2014). https://doi.org/10.1134/S1029959914020027
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DOI: https://doi.org/10.1134/S1029959914020027