Gaussian curvature energy of graphene sheets

The energy density of an elastic sheet is the sum of a mean curvature H   term, 2kcH22kcH2, and a Gaussian curvature K   term, k¯K, where kckc, k¯ are constants. The sign of kckc is commonly understood to be positive, but the sign of k¯ and even the role of K   are subject to debate. We give reasons for the Gaussian contribution to be k¯|K| instead, with k¯ positive. This is used to obtain the mean amplitude of thermal fluctuations of a graphene sheet.

► A modified Gaussian curvature energy of an elastic sheet is proposed.
► The curvature expression is applied in four general cases, including graphene.
► An accurate prediction of ripple size in graphene monolayer sheet is obtained.