  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.
