It is the

basic unit to build other dimensional carbonaceous materials, such as zero-dimensional fullerenes, one-dimensional carbon nanotubes, and three-dimensional graphite [1, 2]. Graphene sheets/ribbons/films have attracted the interest of the scientific community because of recent exciting experimental results [3–6]. Their growth, atomic makeup, electronics, doping, and intercalation have attracted many investigations [7–10]. A suspended graphene sheet [1, 11] can be used in a variety of ways, such as for pressure sensors or gas detectors [12] or mechanical selleck compound resonators [13]. It is still debatable whether a graphene sheet is truly a two-dimensional structure or if it see more should be regarded as a three-dimensional structure since it exhibits a natural tendency to ripple, as observed in recent experiments [2, 14–16]. Carlsson addressed that an understanding of the coupling behaviors between bending and stretching of graphene sheets is necessary to fully explain the intrinsic ripples in a graphene sheet [15]. In addition to theoretical investigations, recent research has been carried out to measure the mechanical properties of suspended graphene sheets by utilizing an atomic force microscope (AFM) [17]. Through weak van der Waals

forces, graphene sheets Combretastatin A4 were suspended over silicon dioxide cavities where an AFM tip was probed to test its mechanical properties. Their Young’s modulus differs from that of bulk graphite. Poot and van der Zan [18] measured the nanomechanical properties of graphene sheets suspended over circular holes by using an AFM and suggested that graphene sheets can sustain very large bending and stretching prior to the occurrence of fracture, which indicates that the classical Kirchhoff plate theory used in Mirabegron the bending and vibration analysis of graphene sheets may not be suitable since deflection and stretching are considerable [19]. Some researchers thought that the large deflection plate theory of von Kármán may be a better candidate to model

the graphene sheet, and they have characterized its bending and stretching through that theory [20, 21]. Lee et al. measured Young’s modulus and the maximum stress of graphene by using an AFM in the nanoindentation experiment [22] and reported the effect of grain boundaries on the measurement of chemical vapor-deposited graphene [23]. Fang et al. [24] has studied the mechanical behavior of a rectangular graphene film under various indentation depths, velocities, and temperatures using molecular dynamics (MD) simulations. The physical models of the rectangular graphene film established by Fang et al. are doubly clamped using a bridge-type support and are loaded by a flat-bottomed diamond tip.