Mechanical characteristics for seven-constant rhombohedral crystals and their nano/microtubes

Stretching 7-constant rhombohedral crystals is described in the theory of elasticity. Numerical analysis, based on the obtained analytical expressions for Young's modulus and Poisson's ratio, is showed that three of the eight 7-constant rhombohedral crystals are partial auxetics, i.e. they have a negative Poisson's ratio in some directions of stretching crystals. Minimum and maximum values of Poisson's ratio and Young's modulus, values of the average Poisson's ratio and the minimum and maximum values of Poisson's ratio for particular orientations were obtained. Auxetic surfaces corresponding to zero Poisson's ratio were plotted. Solution of problems of tension and torsion curvilinear anisotropic nano/microtubes from 7-constant rhombohedral crystals was considered under Saint-Venant's approach. Analytical expressions of Young's modulus and Poisson's ratio for these nano/microtubes were obtained. Numerical analysis allowed to find six of the eight auxetics among nano/microtubes. Values of Poisson's ratio for thin-walled nano/microtubes from 7-constant rhombohedral crystals, as well as critical values of thickness parameter at which the change in the sign of Poisson's ratio were obtained. It is shown that Young's modulus slightly dependent on the thickness parameter of the tube. An analytical expression for the torsional stiffness of nano/microtubes from 7-constant rhombohedral crystals were obtained. The numerical values of the coefficient characterizing the torsional stiffness of nano/microtubes of 7-constant rhombohedral crystals were given. It is found that the influence of the chirality angle on the mechanical characteristics of nano/microtubes from 7-constant rhombohedral crystals in the case of the direct and inverse Poynting's effect unlike tubes from orthorhombic and tetragonal crystals are absent.