A solution for the tension and torsion problems for the curvilinearly anisotropic nano/ microtubes made of orthorhombic crystals in the framework of the Saint-Venant's approach is given. We find that the number of partial auxetics among the tubes is twice asfrequent among the rectilinearly anisotropic crystals, at the same time about one third of 136 orthorhombic crystals are auxetics. It is shown that the torsion causes extension of the nano/microtubes even in the absence of a longitudinal tensile force. This Poynting's effect substantially depends on the chiral angle, and in particular, it disappears when the chiral angle vanishes. We also investigate an inverse Poynting's effect when the extension of the nano/microtubes is accompanied by their twisting. It is shown that the signs of Poynting's effect and Poisson's ratio are changed several times with the change of the chiral angle.
Analytical and numerical features of the elastic properties of curvilinearly anisotropic six-constant tetragonal nano/microtubes are considered. The analytical formulas for Young's modulus and Poisson's ratio are obtained in the case of axial extension. Numerical calculations are performed using these formulas and data on the elastic constants from the Landolt-B€ ornstein Handbook. The parametric dependences of Young's modulus and Poisson's ratios for nano/microtubes are analyzed in detail. The basic parameters are elastic compliances, chiral angles, and ratios of the radii of hollow cylindrical tubes.
Effective Young's modulus and Poisson's ratios of two‐layered cylindrical hollow tubes made of cubic crystals (auxetics and nonauxetics) are considered. An analysis of longitudinal tension of stretching tubes is performed within the framework of curvilinear‐anisotropic elasticity and Saint‐Venant's approximation. Analytical dependences of effective Young's modulus on the compliance coefficients of the initial crystals and layer thickness as ratio of composites auxetics–nonauxetics are obtained. Deviations from the “rule of mixtures” predictions which increase with increasing Young's modulus of initial nonauxetics are demonstrated. It is found that effective Poisson's ratios of two‐layered tubes depend on the ratio of their thicknesses, the dimensionless combinations of compliance coefficients and a dimensionless radial distance. An effect of tube components on negativeness of effective Poisson's ratio of the composite auxetics–nonauxetics proved to be strongly dependent on the value of Young's modulus for nonauxetic component. It is shown that effective Poisson's ratios for some characteristics of the initial crystals and ratios of layer thicknesses may fall outside the limits on Poisson's ratios of isotropic materials. It is shown that many two‐layered tubes composed of pairs of nonauxetics can have large negative effective Poisson's ratios.
Analytical and numerical features of the elastic properties of the stretched rectilinearly anisotropic 6-constant tetragonal crystals are considered. Analytical formulas for Young's modulus and Poisson's ratio are obtained. They are expressed in terms of the elastic compliance coefficients in Voight notation and the parameters of crystal orientation. Numerical calculations are performed using these formulas and data on the elastic constants from the Landolt-Börnstein Handbook. Possible types of Young's modulus and Poisson's ratio are analyzed. More than eighty tetragonal crystals were studied. About 60% of them are characterized by negative Poisson's ratio for certain particular orientations of the crystals. Such auxetics are listed in the Tables. Ten crystals can have Poisson's ratio greater than unity, and Poisson's ratio for six crystals is less than -0.5. The same six crystals are characterized by high variability of Young's modulus. Young's modulus for more than ten crystals exceeds 300 GPa.
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