Abstract
A mathematical model is developed to study the folding behaviour of multi-layer graphene sheets supported on a substrate. The conformation of the fold is determined from variational considerations based on two energies, namely the graphene elastic energy and the van der Waals (vdW) interaction energy between graphene layers and the substrate. The model is nondimensionalized and variational calculus techniques are then employed to determine the conformation of the fold. The Lennard-Jones potential is used to determine the vdW interaction energy as well as the graphene-substrate and graphene-graphene spacing distances. The folding conformation is investigated under three different approximations of the total line curvature. Our findings show good agreement with experimental measurements of multi-layer graphene folds from the literature.