Small size effect on the wrinkling hierarchy in constrained monolayer graphene

The present paper investigates the small size effect on a localized transition zone in the merging of two wrinkles in constrained suspended graphene under in-plane shear. It is found the classical elasticity theory overestimates the wrinkle amplitude and wavelength in contrast with the results of atomistic simulation. The analytic formulations for the wrinkling hierarchy are obtained by using nonlocal plate theory. Here, this small size effect can be estimated by correct value of nonlocal parameter e0a = 1.9 nm. Besides, the orientation of graphene slightly influences the wrinkling hierarchy of graphene. The temperature effect is significant under small shear strain, while this effect is significant in the constrained edges and insignificant in the middle region under large strain. The occurrence of cracking is always in constrained edges, where the stress concentration releases in the wrinkling hierarchy. This work is expected to provide a better understanding of the mechanism of nanometer scale wrinkles.