# A new efficient hyperelastic finite element model for graphene and its application to carbon nanotubes and nanocones

## TL;DR

This paper introduces a new hyperelastic finite element model for graphene-based nanostructures, offering improved computational efficiency and accurate simulation of complex behaviors like buckling, validated through various numerical examples.

## Contribution

A novel hyperelastic model for graphene structures that is fully nonlinear, faster, and capable of simulating buckling and postbuckling behaviors with validation against existing data.

## Key findings

- Model is 1.5 times faster than previous models.
- Accurately captures buckling and post-buckling behavior.
- Validated with numerical examples showing good agreement.

## Abstract

A new hyperelastic material model is proposed for graphene-based structures, such as graphene, carbon nanotubes (CNTs) and carbon nanocones (CNC). The proposed model is based on a set of invariants obtained from the right surface Cauchy-Green strain tensor and a structural tensor. The model is fully nonlinear and can simulate buckling and postbuckling behavior. It is calibrated from existing quantum data. It is implemented within a rotation-free isogeometric shell formulation. The speedup of the model is 1.5 relative to the finite element model of Ghaffari et al. [1], which is based on the logarithmic strain formulation of Kumar and Parks [2]. The material behavior is verified by testing uniaxial tension and pure shear. The performance of the material model is illustrated by several numerical examples. The examples include bending, twisting, and wall contact of CNTs and CNCs. The wall contact is modeled with a coarse grained contact model based on the Lennard-Jones potential. The buckling and post-buckling behavior is captured in the examples. The results are compared with reference results from the literature and there is good agreement.