Extremely thin geometries

I created a cylinder with radius 1e-6 m and thickness 9e-10 m in 3D to make a continuum simulation of graphene. I have initial radial stress, an uniform body load along the thickness of the cylinder and use fully clamped boundary conditions on the radial edge. When I try to mesh it the process never finishes, and earlier when I had a mesh on a similar geometry the simulation didn't converge.

Question: What do I need to consider while trying to simulate extremely thin geometries?