[01] Belov Petr A., Bauman Moscow State Technical University, Engineering Research and Education Center «New Materials, Composites and Nanotechnologies», Moscow, Russia.

The model of two-dimensional defectless medium is formulated as a special case of the general theory of three-dimensional medium with fields of conserved dislocations with adhesive properties of a surface limiting it. Potential energy in the general theory is the sum of volume and superficial integral from the corresponding densities of energy. In a limit case, when thickness of shell is equal to zero, volume part of potential energy become equal to zero. As a result the potential energy of such an object is defined only by the surface potential energy. A Single Wall Nano Tube (SWNT) is examined as an example of such two-dimensional medium. The problem statement of a SWNT axial deforming, and the torsion one, are examined. The general statement of an axisymmetric problem within the gradient theory of adhesion is formulated. Special cases are studied: a case of ideal and purely gradient adhesion, quasiclassical case, cases at big and small sizes of radius of SWNT. It is shown that the case of ideal adhesion corresponds to correct statement of the membrane theory of cylindrical shell. The case of purely gradient adhesion corresponds to correct statement of the theory of edge effect of cylindrical shell. It is shown, that particular case of the quasiclassical theory of cylindrical shell is not consecutive approach of the general theory when moduli of ideal adhesion are partially considered, and partially - moduli of purely gradient adhesion. The characteristic feature of all statements is the fact that the mechanical properties of SWNT are not defined by “volumetric” moduli but by adhesive ones which have different physical dimension which coincides with the dimension of the corresponding stiffness of classical and nonclassical shells.

Gradient Theories of Elasticity, Ideal Adhesion, Gradient Adhesion, Mechanical Properties of SWNT, Nonclassical Moduli

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