How graphene flexes and stretches under concomitant bending couples and tractions

TL;DR

This paper develops a nonlinear discrete mechanical model of graphene to analyze how it deforms under combined bending and stretching forces, revealing how its mechanical response varies with load and potential type.

Contribution

It introduces a nonlinear model incorporating bond, angle, and dihedral energies, and applies it to analyze graphene's bending and stretching behavior under various forces.

Findings

Graphene is easier to bend when subjected to combined forces.

Stretching resistance varies with load magnitude.

Model validated with Brenner potential calculations.

Abstract

We propose a geometrically and physically nonlinear discrete mechanical model of graphene that assigns an energetic cost to changes in bond lengths, bond angles, and dihedral angles. We formulate a variational equilibrium problem for a rectangular graphene sheet with assigned balanced forces and couples uniformly distributed over opposite side pairs. We show that the resulting combination of stretching and bending makes achiral graphene easier to bend and harder (easier) to stretch for small (large) traction loads. Our general developments hold for a wide class of REBO potentials; we illustrate them in detail by numerical calculations performed in the case of a widely used 2nd-generation Brenner potential.