Scaling up ultrathin boat-graphane with the non-classical stiffness relation to macroscopic metamaterials

Scaling up ultrathin nanosheets with unusual mechanical properties to macroscopic metamaterials is an intriguing topic considering the significant gap of their characteristic scales. In this regard, we investigate the relation between the in- and out-of-plane stiffness of monolayer boat-graphane in two principal axis directions by quantum mechanical calculations. A non-classical relation between the two types of stiffness is found, in opposition to the classical one for orthotropic thin plates. Analytical lattice dynamics models are proposed and suggest that the two kinds of stiffness stem from different covalent interaction sources, giving rise to the discrepancy. Guided by the geometry of boat-graphane and the model predictions, the non-classical relation successfully scales to macroscopic metamaterial plates, as justified by finite element simulations. The key structural parameters for successful scaling are also explored. The present work not only enriches our understanding of the nanomechanics of ultrathin nanosheets but also suggests a novel approach to construct mechanical metamaterials.