Chiral elasticity of nano/microtubes from hexagonal crystals

The elastic properties of chiral cylindrically anisotropic nano/microtubes from hexagonal crystals are analyzed. The problems of longitudinal tension and torsion of such tubes demonstrate that there is a linear direct Poynting effect with an elongation (shortening) of a twisted tube and a linear inverse Poynting effect with the twisting of the stretch tube. It is shown that both effects disappear at zero chiral angle and at some other chiral angles. Many chiral tubes with negative Poisson ratios are revealed. It is shown that Poisson ratios do not depend on the sign of the chiral angle. It is found that the dependence of the torsional stiffness of the tubes on the chiral angle is stronger than the dependence on the thickness of the tube walls. At the same time, chiral tubes made of graphite are separated from other tubes from hexagonal crystals. Their Young's modulus varies rapidly from large to small with a change in the chiral angle. The value of the torsional stiffness is large and it varies rapidly with the change in the chiral angle and the thickness of the tube walls.