I wrote a bit of script for Image Magick and generated some images:

Test_Cut1_800.png Test_Cut2_800.png

Then laser cut these in thin card. The cuts went well...

Tes_Cut_Real1.jpg

... but they both absolutely do not stretch in the Z direction. Not even a bit - which I found quite surprising. They are both like card as though it were not cut at all. On the one with the radial lines you can press into the cut areas a bit but the center circle does not move.

So there is no stretch at all in these with cuts in.

The next step is to make finer spaced cuts and get the cuts closer to the edges. It should be obvious that if I cut a pure spiral to the center circle then it would move but would have no structure. So there must be a point in between the two extremes where it moves the right amount.

So back to the scripting...