# A new material property of graphene: the bending Poisson coefficient

## TL;DR

This paper introduces a new bending Poisson coefficient for graphene, distinct from the in-plane Poisson ratio, which influences its bending response and is derived from atomic interactions.

## Contribution

It identifies and defines a new material property, the bending Poisson coefficient, that affects graphene's bending behavior and differs from the classical in-plane Poisson ratio.

## Key findings

- The bending Poisson coefficient is conceptually different from the in-plane Poisson ratio.
- A physical interpretation of the bending Poisson coefficient is provided.
- Quantitative evaluation of the bending Poisson coefficient is performed.

## Abstract

The in-plane infinitesimal deformations of graphene are well understood: they can be computed by solving the equilibrium problem for a sheet of isotropic elastic material with suitable stretching stiffness and Poisson coefficient $\nu^{(m)}$. Here, we pose the following question: does the Poisson coefficient $\nu^{(m)}$ affect the response to bending of graphene? Despite what happens if one adopts classical structural models, it does not. In this letter we show that a new material property, conceptually and quantitatively different from $\nu^{(m)}$, has to be introduced. We term this new parameter bending Poisson coefficient; we propose for it a physical interpretation in terms of the atomic interactions and produce a quantitative evaluation.