Equilibrium of inverted shell of varying thickness 2

[fabster1]

Hi,
I am doing FEM (Marc) of soft contact lenses simulating the inside out flipping of such lenses. While my FE results compare very well to measurements, I am having trouble to find literature about why the lens settles in a particular state.

The geometry of the soft contact lenses is not spherical, indeed the lens has a centre thickness of around 0.1 mm and the thickness varies along its diameter between 0.1 and 0.25 mm. Lens diameter is ~14mm and the lenses are made of silicone hydrogel materials, for my analysis I am assuming linear elasticity with M =~1 MPa. See attached for a sequence of the lens inversion.

Is there someone who can shine some light on why the lens assumes a specific shape when its flipped?
thanks loads in advance!

 

[unclesyd]

Way out of my league but while reading an article on the return of extended care contact lens there was mention that on of the things that help make this possible was that the surface of the lens was plasma treated, oxidized. To what extent wasn't mentioned. Could this be influencing your analysis?

 

[fabster1]

possibly yes, so far I've compared traditional materials and coated silicone hyrdrogels and the inverted lens shape seems to be relatively insensitive to the coating. That would be another interesting to model.

 

[JStephen]

Generally, the energy required for bending a surface is much less than that required to stretch or compress the material. So, for example, rolling a steel plate into a cylinder is fairly easy, and pressing it into a spherical shape is quite a different proposal.

As applied to the contact lens, I would say that the flipped version has almost no stretching/compressing of the middle surface, which would imply the middle surface is the mirror image of the unflipped one.

 

[btrueblood]

What JStephen said. As far as predicting the shapes (i.e. "why this shape?"), you are finding (the FEA code is solving for) the minimums of strain energy for the two configurations (flipped/unflipped).

 

[fabster1]

Thanks guys for the explanation, is there a reference you know of that I can quote? thanks loads for your help!

 

[Compositepro]

The effect is sometimes called "oil canning". Thin sheets have little flexural stiffness. The tensile stiffness of the material is much greater. In both stable forms the hoop and radial dimensions of your part will be almost identical (measured at the neutral axis in flex).During the transition from one configuration to the other, the hoops are stretched and the radii are compressed.

 

[btrueblood]

is there a reference you know of that I can quote?"

How about Timoshenko, Theory of Elastic Stability

or

http://en.wikipedia.org/wiki/Buckling

see the section headed "Energy Method"

 

[Compositepro]

On second thought, the hoops and radii toward the center of the disc are compressed and they are stretched at the O.D. (during the transition). Tin cans, for example, have corregations in the top and bottom to reduce the radial stiffness and reduce the snap action.

 

[williedawg]

Although I can't suggest anything as to the mathematics or physics behind why the lens takes on that particular shape...

perhaps there's something relative in how a small kids' toy that you purposely turned "inside out", then set it on a flat surface. It pops back into the original shape in a few (maybe 5 or 10) seconds.

Its initial shape was a hollow hemishere. The shape when inverted was quite different than its normal or relaxed state, but still a "constant profile" which looked like a miniature cooking kettle; the difference due to inner/outer surface areas being forced to change; which neither liked, and it popped back. The material was some tough rubbery substance akin to urethane. (maybe it was)

The toy was about 2 or 2 1/2" diameter, and of constant thickness (maybe 3/16 or 1/4") in the normal state as near as the eye could tell.
This may provide a little insight into why a lens of variable thickness takes on a non-constant shape