Helio Chacham1 Ana Paula Barboza2 Alan de Oliveira2 Camilla Oliveira3 Ronaldo Batista2 Bernardo Neves1

1, University Federal-Minas Gerais, Belo Horizonte, , Brazil
2, UFOP, Ouro Preto, , Brazil
3, UFPR, Curitiba, , Brazil

Two-dimensional (2D) materials, such as graphene, have mechanical properties that are both new and unique to their class. At the same time, upon exfoliation and/or transfer to a substrate, they are prone to ordinary processes, like folding and wrinkle formation. With the ever-increasing interest on 2D-material based stretchable devices and nano-electromechanical systems, a natural question that arises is how the above mentioned unique properties and ordinary processes couple. In other words, do the exquisite 2D-material properties lend any uniqueness, or universality, to mundane features such as wrinkles? For example, when a wrinkle is compressed vertically, what are the deformation pathways and do they portray any general pattern? Do any unforeseen mechanical properties emerge? The present work brings some answers to these questions. Therefore, we investigate the mechanical deformation of few-layer suspended structures (wrinkles) made of graphene, h-BN and talc. Through their atomic force microscopy-based nanomanipulation, we find that their experimental restoring forces fall into universal functions of their strain. Two distinct, and universal, pathways are revealed: with and without lateral displacement of the wrinkle topmost part. Such universality further enables the investigation of each fold bending stiffness κ as a function of its characteristic height h0. We observe a more than tenfold increase of κ as h0 increases in the 10-100 nm range, with power-law behaviors of κ versus h0 with exponents larger than unity for the three materials. This implies in anomalous scaling of the mechanical responses of nano-objects made of these materials. These reported properties may play a major role in nano(electro)mechanical devices and stretchable electronics.