Modelling Metallic Diaphragm

I am a novice COMSOL user using the software for a student project so apologies if my problem below seems simple.

I have a 2D axisymetric model of a thin metallic diaphragm (approx 25mm di and 0.025mm in thickness).
The diaphragm is deformed by a uniform pressure load and fixed around its perimeter.

To begin I have used a simple flat diaphragm and the model produces deflection results that agree well with theory for small deflections (up to approx 2xthickness)

When a greater pressure differential is applied the model appears to become over "stiff" and the predicted deflection is significantly below that given by theoretical results.

Currently I have tried varying the mesh size and shape (quad/tri) with no significant change in the result. I have also trialled both linear and quadratic elements with no significant improvement (the element quality is always extremely high due to the simple geometry).

I am using a linear elastic model with non-linear geometry enabled. Is this Ok to use when there is considerable strain in the model?

I would be great full if anybody has any feedback on how to improve the model / experience with a similar model or ideas on why it may be differing from theory?

Thanks in advance!

Matt