CHAPTER 2: Nanoscale Buckling Mechanics of Ultrathin Sheets

In most 2D materials like graphene the calculated bending stiffness is found to be the same order of magnitude as that of the lipid bilayer. The non-planar configuration is easily generated, such as the nanoscale buckling morphology, which is widely observed, and is crucial to modulating the electronic and mechanical properties. In this chapter, recent theoretical efforts to reveal key factors causing the observed nanoscale buckling in a free-standing monolayer sheet, in a monolayer sheet on substrates and in a twist bilayer sheet are briefly reviewed. The buckling mechanisms due to thermal fluctuation, compressive stress and orientational bonding onto the substrate surface are discussed separately. Comprehensive mechanics models of nanoscale buckles for their formation and controllability hopefully offer a guide to the design of nanoscale buckles in these 2D materials for various applications.