I created a Disk with a Mooney-Rivlin material to test FEBio against the analytical solution of a bulge test as given by this paper [1].

The parameters are:

- Radius = 4mm
- Thickness = 0.05mm
- mu = 4MPa -> c1=2MPa
- Pressure = 28 kPa

Max displacement from analytical solution: 1.5302715

In this figure is the displacement that I obtain as a function of the bulk modulus. I varied the bulk modulus between the most extreme values that still converged:

EffectOfBulkModulus.png

As you can see I can get a result that is close to the analytical solution for k/c1 in [10,10000]. However, the result seems to be consistently 6% above the analytical solution (i.e. more compliant than expected). This didn't change with mesh refinement.

I then tried to see if I could get the augmented Lagrangian enforcement of incompressibility by adding "<laugon>1</laugon>" and "<atol>0.01</atol>" but unfortunately that seemed to have no effect. Am I doing something wrong? Attached is my .feb file.

AugLagTest.feb

PS: If I switch the BCs to FixedDisplacement instead of FixedShellDisplacement the error reduces to 3% instead of 6%.

[1] Sheng, J.-Y., Zhang, L.-Y., Li, B., Wang, G.-F., & Feng, X.-Q. (2017). Bulge test method for measuring the hyperelastic parameters of soft membranes. Acta Mechanica. https://doi.org/10.1007/s00707-017-1945-x