Mathematical treatise to model the dihedral interaction energy in the multiscale modelling of 2D nanomaterials

[+] Author and Article Information
Sandeep Singh

Department of Mechanical Engineering, Birla Institute of Technology and Science Pilani, K. K. Birla Goa Campus, Goa, 403726, India

B. P. Patel

Department of Applied Mechanics, Indian Institute of Technology Delhi, New Delhi, 110016, India

1Corresponding author.

ASME doi:10.1115/1.4039437 History: Received December 07, 2017; Revised February 21, 2018


An approximate mathematical treatise is proposed to improve the accuracy of multiscale models for nonlinear mechanics of the 2D nanomaterials by taking into count the contribution of dihedral energy term in the nonlinear constitutive model for any generalized continuum deformation. The proposed model is employed to study the bending modulus of the graphene sheet at finite curvatures under generalized continuum deformation. Under any generalized continuum deformation, three strain and three curvature components are nonzero and the twelve dihedral angles, corresponding to the unitcell, for the case of graphene sheet are expressed as a function of these strain and curvature components. The first and second generation reactive empirical bond order (REBO) potentials are considered to model the atomic interactions. The constitutive law is obtained by coupling the atomistic and continuum deformations through Cauchy-Born rule. First generation REBO potential is also improved to predict the bending modulus accurately by including the dihedral energy term of second generation REBO potential into it. The present model will facilitate the further investigations on nonlinear mechanics of the graphene sheets and carbon nanotubes subjected different kinds of loads viz. transverse bending of graphene sheets, postbuckling of carbon nanotubes under bending/axial compression and boundary conditions with greater accuracy as compared to those reported in the literature without considering dihedral energy term constitutive model.

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