O-ring force modeling - FEA

You may just have to close the solution loop yourself - make a guess as to the load the o-ring will apply, use that load and see if the parts deflect as much as the o-ring does for that same load. If it deflects too much, lower the load. If it deflects too little, then increase the load.

It may be an approximation anyway unless the deflection curve also includes the precise area the o-ring acts on. Also consider that the force will not be uniform across the contact patch with the o-ring.

Keep in mind that springs add when in a parallel arrangement.  The stiffness of the o-ring that skunks simulates is the sum of the 8 springs used.  If more springs were desired to make a smoother result, the stiffness of the individual springs would still need to add up to the stiffness of the o-ring being simulated.

A similar use would be a door seal on a vehicle door in contact with the vehicle.  A seal stiffness per unit length is how this is thought of.  (N/mm  / mm)  It is implemented with discrete springs along the length where the stiffness and spacing resolves to the desired stiffness per unit length.  A non-linear stiffness - deflection curve can follow the same principals of summing and per unit length.

There can be some difficulty with the singularities at the discrete points.  Some choices to get past this might be one or more of the following(they all likely involve some trade-offs.)

1. exclude the singular geometry.
2. add small rigid surface regions at the singularity to spread the force over an area
3. limit the order of the elements and/or use generally large elements.
4. last resort is to use a actual seal in a contact model.  Prove in a separate test that the o-ring matches the force vs. deflection curve