Universal deformation pathways and flexural hardening of nanoscale 2D-material standing folds

In the present work, we use atomic force microscopy nanomanipulation of 2D-material standing folds to investigate their mechanical deformation. Using graphene, h-BN and talc nanoscale wrinkles as testbeds, universal force-strain pathways are clearly uncovered and well-accounted for by an analytical model. Such universality further enables the investigation of each fold bending stiffness κ as a function of its characteristic height h ₀. We observe a more than tenfold increase of κ as h ₀ increases in the 10-100 nm range, with power-law behaviors of κ versus h ₀ with exponents larger than unity for the three materials. This implies anomalous scaling of the mechanical responses of nano-objects made from these materials.