An approximate mathematical treatise is proposed to improve the accuracy of multiscale models for nonlinear mechanics of two-dimensional (2D) nanomaterials by taking into account the contribution of dihedral energy term in the nonlinear constitutive model for the generalized deformation (three nonzero components of each strain and curvature tensors) of the corresponding continuum. Twelve dihedral angles per unit cell of graphene sheet are expressed as functions of strain and curvature tensor components. The proposed model is employed to study the bending modulus of graphene sheets under finite curvature. The atomic interactions are modeled using first- and second-generation reactive empirical bond order (REBO) potentials with the modifications in the former to include dihedral energy term for accurate prediction of bending stiffness coefficients. The constitutive law is obtained by coupling the atomistic and continuum deformations through Cauchy–Born rule. The present model will facilitate the investigations on the nonlinear mechanics of graphene sheets and carbon nanotubes (CNTs) with greater accuracy as compared to those reported in the literature without considering dihedral energy term in multiscale modeling.
Mathematical Treatise to Model Dihedral Energy in the Multiscale Modeling of Two-Dimensional Nanomaterials
Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received December 7, 2017; final manuscript received February 21, 2018; published online March 23, 2018. Assoc. Editor: N. R. Aluru.
- Views Icon Views
- Share Icon Share
- Cite Icon Cite
- Search Site
Singh, S., and Patel, B. P. (March 23, 2018). "Mathematical Treatise to Model Dihedral Energy in the Multiscale Modeling of Two-Dimensional Nanomaterials." ASME. J. Appl. Mech. June 2018; 85(6): 061003. https://doi.org/10.1115/1.4039437
Download citation file:
- Ris (Zotero)
- Reference Manager