Quote from the documentation:
If the user inserts zero compressibility coefficients, CalculiX uses a default value corresponding to an initial value of the Poisson coefficient of 0.475.
Strains are crucial in this case. Plus strain energy density.
Time step should correspond to the time of the simulated process. You may have to adjust incrementation but that depends on the convergence. Make sure that Nlgeom is included.
Check this thread: Hyperelastic Pipe
And some other threads that show up when you search for “hyperelastic” on this forum.