Numerical algorithms for prediction of mechanical properties of single-walled carbon nanotubes based on molecular mechanics model

The objective of this paper is to develop the numerical algorithms for the prediction of mechanical properties of single-walled carbon nanotubes (SWCNTs). By using the energy method, the analytical expressions are obtained and the five independent variables algorithm is developed for the prediction of the elastic properties of SWCNTs via a molecular mechanics model in which the geometrical relationship of carbon nanotube is introduced. It can be found that due to the introduction of the geometrical approximate conditions some errors may exist in the calculation of mechanical properties of SWCNTs in terms of the five independent variables algorithm. Therefore, two improved algorithms, i.e., eigenvalues modified method (EMM) and eigenvalues and eigenvectors modified method (EEMM) are proposed to analyze the possible errors in the numerical results. It is found that the results obtained by the three kinds of algorithms are almost consistent with one another, but EMM and EEMM are preferred to be used because they have properties similar to those of the finite element method, where the consistent equation works just as the constraint condition to void the singularity of the element stiffness matrix. The computational results also reveal that both the surface Young’s modulus and Poisson’s ratio depend on the diameter of carbon nanotubes, and finally converge to the values of the graphite sheet with an increase in the tube diameter in the inverse trends. For SWCNTs with approximately the same diameters, the surface Young’s modulus is in direct and Poisson’s ratio is in inverse proportion to chiral angles, respectively.