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Two-dimensional crystals on adhesive substrates subjected to uniform transverse pressure

In this work we consider bubbles that can form spontaneously when a two-dimensional (2D) crystal is transferred to a substrate with gases or liquids trapped at the crystal-substrate interface. The underlying mechanics may be described by a thin sheet on an adhesive substrate with the trapped fluid applying uniform transverse pressure. What makes this apparently simple problem complex is the rich interplay among geometry, interface, elasticity and instability. Particularly, extensive small-scale experiments have shown that the 2D crystal surrounding a bubble can adhere to and, meanwhile, slide on the substrate. The radially inward sliding causes hoop compression to the 2D crystal which may exploit wrinkling instabilities to relax or partially relax the compression. We present a theoretical model to understand the complex behaviors of even a linearly elastic 2D crystal due to the combination of nonlinear geometry, adhesion, sliding, and wrinkling in bubble systems. We show that this understanding not only successfully predicts the geometry of a spontaneous bubble but also reveals the strain-coupled physics of 2D crystals, e.g., the pseudomagnetic fields in graphene bubbles.