Improved GWO algorithm for the determination of the critical wrinkle length of graphene

Abstract

Graphene, one of the most important discoveries in the field of materials, is an interesting two-dimensional flexible membrane which has been highly studied by physicians in the last decade as it has shown tremendous utility in fundamental studies, industrial and electronic applications, ranging from nanoelectronics to biology, thanks to its notable electronic, mechanical and chemical properties. Graphene in its natural state is non-flat and tends to crumple. The wrinkles are usually considered to be a result of stretching and bending forces, and are viewed as local minimizers of a suitable elastic energy.

In this paper we focus on the study of the wrinkling shape of graphene. A detailed geometric model provided by Yamamoto et al.  describing the shape of the wrinkles in terms of a deflection profile, is numerically analysed. The Euler Lagrange equation associated to this problem is formulated in the context of a constrained optimization problem and numerical simulations are carried out to compute the optimal profile using the Grey Wolf Optimizer (GWO), leading to good results in comparison with the ones found in the litterature.