Inducing and controlling three-dimensional deformations in monolayer two-dimensional materials is important for applications from stretchable electronics to origami nanoelectromechanical systems. For these applications, it is critical to understand how the properties of different materials influence the morphologies of two-dimensional atomic membranes under mechanical loading. Here, we systematically investigate the evolution of mechanical folding instabilities in uniaxially compressed monolayer graphene and MoS
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