Buckling of a non-Euclidean annular plate

The effect of free edges of a monoatomic graphene sheet leads to excess edge energy due to the reconstruction of dangling bonds. Molecular static calculations show, that individual carbon atoms near the edge are displaced out of plane for relaxed nanoribbons [1]. In this work we are considering the effect of excess edge energy for almost circular graphene patches. To tackle this problem in the framework of continuum mechanics we are modelling the edge effect with a non-Euclidean plate model. A linear stability analysis of the flat configuration leads to the stability boundary in the parameter plane. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)