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In this paper we focus on the studies of graphene wrinkling, from its formation to collapse, and its dependence on aspect ratio and temperature using molecule dynamics simulation. Based on our results, the first wrinkle is not formed on the edge but in the interior of graphene. The fluctuations of edge slack warps drive the wrinkling evolution in graphene which is distinguished from the bifurcation in continuum film. There are several obvious stages in wrinkling progress, including incubation, infancy, youth, maturity and gerontism periods which are identified by the atomic displacement difference due to the occurrences of new wrinkles. The wrinkling progress is over when the C-C bonds in highly stretched corners are broken which contributes to the wrinkling collapse. The critical wrinkling strain, the wrinkling pattern and extent depend on the aspect ratio of graphene, the wrinkling level and collapsed strains do not. Only the collapsed strain is sensitive to the temperature, the other wrinkling parameters are independent of the temperature. Our results would benefit the understanding of the physics of graphene wrinkling and the design of nanomechanical devices by tuning the wrinkles.

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a b s t r a c tA new Modified Displacement Component (MDC) method is proposed to accurately predict wrinkling characteristics in the membrane by eliminating the singularity of the displacement solution. In MDC method, a singular displacement component is primarily obtained at the wrinkling point by introducing the first-order characteristic vector multiplied by a positive intermediate parameter in the singular stiffness matrix. The non-singularity displacement solution is then obtained by modifying the singular displacement component based on three equality relationships at the wrinkling point. Where, the accurate introduction and the timely removal of the critical wrinkling mode are two key steps. In our simulation, we use a direct perturbed method to accurately consider these two key steps. In the direct perturbed method, some small, quantitative, out-of-plane forces are applied onto the membrane surface directly based on the first wrinkling mode, and then removed immediately after wrinkling starts. Several effective strategies are then used to advance the convergence. A wrinkling test using photogrammetry is used to verify the validity of our method. In addition, we also studied the secondary wrinkling characteristics occurred in the post-wrinkling phase in the end. The secondary wrinkling characteristics are the basic explanations of the wrinkling expansion and evolution in the post-wrinkling phase.

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The wrinkling characteristics of a rectangular graphene membrane under local tension are studied in this paper based on the continuum theory. The characteristics of the primary bifurcation and secondary wrinkling are studied to discover the physics of graphene wrinkling. The wrinkling geometry is predicted by a continuum theory model. The results reveal that the first wrinkle is formed at the primary bifurcation point. The non-uniform stretch-induced compressed effects, that originate from both the loaded portion and the clamped edges, buckle the graphene to form the first wrinkle. Secondary wrinkling is generated on the boundary of the wrinkled regions and the slack regions near the loaded portion in the post-wrinkling stage is the intrinsic nature of the wrinkling rupture and evolution of graphene. In addition, the length of the loaded portion and the aspect ratio of graphene have great effects on the wrinkling characteristics. These results are tremendously useful in understanding the intrinsic nature of the structural instability of graphene.