Bending at the nanometre scale can substantially modify the mechanical, chemical and electronic properties of graphene membranes. The subsequent response of chemical bonds leads to deviations from plate idealisation in continuum mechanics. However, those phenomena have thus far been investigated exclusively by measuring the electronic properties of graphene deformed by compressing and stretching with local-probe techniques. Here, we report that the interatomic-attractive forces applied on the convexly-curved graphene by the probe tip give rise to a pin-point breaking of the plate idealisation in the continuum mechanics, facilitating atomically-localised enhancements in its chemical reactivity and mechanical strength. Thorough characterisations were conducted by atomic force microscopy and force field spectroscopy on hollow nanotubes, rolled-up graphene, with different diameters. Their topmost parts supplied well-defined curvatures of the convex graphene. We found that a significant enhancement in the out-of-plane Young’s modulus from 13 to 163 GPa, “superhardening”, was realised with the nonlinear transition of bond configurations. Our findings provide a fundamental understanding of the relationships between the structure of atomistic membranes and the dynamic behaviour of approaching exterior atoms or molecules and their subsequent interplay with chemical and mechanical properties. Thus, these results encourage the application of such membranes in functionally-controllable materials or devices.