  Through molecular mechanics we find that non-covalent interactions modify the
fractality of crumpled damaged graphene. Pristine graphene membranes are
damaged by adding random vacancies and carbon-hydrogen bonds. Crumpled
membranes exhibit a fractal dimension of $ 2.71 \pm 0.02$ when all interactions
between carbon atoms are considered, and $2.30 \pm 0.05$ when non-covalent
interactions are suppressed. The transition between these two values, obtained
by switching on/off the non-covalent interactions of equilibrium
configurations, is shown to be reversible and independent on thermalisation. In
order to explain this transition, we propose a theoretical model that is
compatible with our numerical findings. Finally, we also compare damaged
graphene membranes with other crumpled structures, as for instance, polymerised
membranes and paper sheets, that share similar scaling properties.
