How to impose internal pressure in a 2D hyperelastic cylinder

Hello,
i’m new to fenics and i’m trying to solve a hyperelastic 2D problem. My problem looks exactly like this, however it’s hyperelastic and the pressure is internal. I tried to formulate my problem like this, using a mixed formulation

Pi = psi*dx - dot(Pressure,u)*ds(4)
F1 = derivative(Pi, (u,p),(du,dp))
J = derivative(F1, (u,p),(v,pp))
solve(F1 == 0, w, bcs, J=J)

with

P = Constant((10.0))
n = FacetNormal(mesh)
Pressure = -P*n

and psi the correspondent form of the hyperelastic law (Neo hook in my case).

However when visualizing the results I don’t get the expected results.

  1. does the variational formulation of hyperleastic problems differ from 2D to 3D?
  2. How can i impose an internal pressure on the inside of the cylinder?