Exploring the effect of dihedral energy on the nonlinear mechanics of the carbon nanotubes using a multiscale modelling

[+] Author and Article Information
Sandeep Singh

A313/12, Dept of Mech Engg K. K. Birla Goa Campus Zaurinagar, Goa, Delhi 403726 India mechmehal@gmail.com

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the Journal of Vibration and Acoustics. Manuscript received November 7, 2018; final manuscript received March 13, 2019; published online xx xx, xxxx. Assoc. Editor: Julian Rimoli.

ASME doi:10.1115/1.4043242 History: Received November 07, 2018; Accepted March 15, 2019


A hierarchical multiscale finite element model is employed to investigate the effect of dihedral energy term on the numerical simulation of two-dimensional materials. The numerical examples of the carbon nanotubes and graphene sheets are studied employing refined constitutive model in conjunction with multiscale finite element method. The constitutive law refined with the greater accuracy on the bending modulus using second generation reactive empirical bond order potential with dihedral energy term is employed to investigate the linear and nonlinear response of the carbon nanotubes incorporating material and Green–Lagrange geometric nonlinearities. The inclusion of the dihedral energy term predicts bending modulus close to those of through first principle calculations. The deformations at the nanoscale and macroscopic scales are related through the Cauchy–Born rule. The effect of the dihedral energy term on the response of the carbon nanotubes is studied in detail. The governing equation of motion for the carbon nanotubes are formulated through Hamilton's energy principle. The spatial approximation of the carbon nanotubes at the continuum scale is attained through the finite element method. The membrane locking in the circumferential strain is eliminated through the membrane consistent interpolation functions obtained through the least square method.

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