A new shell formulation for graphene structures based on existing ab-initio data

TL;DR

This paper introduces a new rotation-free shell formulation for graphene structures based on ab-initio data, enabling accurate and straightforward finite element simulations without molecular interaction complexities.

Contribution

It extends an existing membrane model to a shell formulation with bending capabilities, calibrated from ab-initio data, and verified through numerical examples.

Findings

Formulation agrees with analytical solutions

Successfully models indentation and peeling of graphene

Performs well in torsion, bending, and axial stretch tests

Abstract

An existing hyperelastic membrane model for graphene calibrated from ab-initio data (Kumar and Parks, 2014) is adapted to curvilinear coordinates and extended to a rotation-free shell formulation based on isogeometric finite elements. Therefore, the membrane model is extended by a hyperelastic bending model that reflects the ab-inito data of Kudin et al. (2001). The proposed formulation can be implemented straight-forwardly into an existing finite element package, since it does not require the description of molecular interactions. It thus circumvents the use of interatomic potentials that tend to be less accurate than ab-initio data. The proposed shell formulation is verified and analyzed by a set of simple test cases. The results are in agreement to analytical solutions and satisfy the FE patch test. The performance of the shell formulation for graphene structures is illustrated by several numerical examples. The considered examples are indentation and peeling of graphene and torsion, bending and axial stretch of carbon nanotubes. Adhesive substrates are modeled by the Lennard-Jones potential and a coarse grained contact model. In principle, the proposed formulation can be extended to other 2D materials.