About definition of the elasticity module of single-walled carbon nanotubes by methods of structural mechanics

Anton Karvatskii, Ihor Mikulionok, Taras Lazarev, Kateryna Korolenko


The purpose of article is working off and check of numerical techniques of definition of the elasticity module of single-walled carbon nanotubes with use of a method of final elements, and also ties between parameters of molecular and structural mechanics. Researches were conducted for nanotubes of various types of spatial and frame models, namely the armchaіr type, the zigzag type and the chіral type. Program codes with use of freely open software of Gmsh are developed for design of models of nanotubes of these types. Formulations of linear and nonlinear ratios for determination of parameters of structural mechanics on the basis of energy potentials and power coefficients of molecular mechanics are considered. The formulation of a nonlinear problem received a certain specification regarding definition of ratios "the generalized deformation – the generalized tension". The numerical models for research of the elasticity module of nanotubes of various dimension-types (chіrality and diameter) representing macroes in the APDL ANSYS Mechanical APDL programming language are developed. Results of comparison of the received results showed satisfactory coordination with theoretical and experimental data: the divergence with the known theoretical estimates makes 0.08–5.1 %. The offered verified numerical techniques for definition of the elasticity module of nanotubes are planned to be used further for development of new polymeric nanocomposites.


elasticity module; single-walled carbon nanotubes; molecular mechanics; structural mechanics; numerical modeling


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