softbody follow hardbody?

I did an animation of a technical process called blowmolding and I wonder if I could use softbody for this.
The white sheet is a hot plastic foil that gets extended and deformed by a plug that pushes onto it while the foil is clamped down.
The foil would be the softbody and all the other parts are normal objects. I already played around with the softbody feature, but I seem to lack some understanding of it. It seems the softbody feature always needs frames of animation to take place? But the only thing I want to animate is the plug! If I move down the plug I want the sheet of foil follow the plug and deform just as much as it necessary. Is this possible with softbody?
In the animation above I added a circular mesh to the foil coinciding with the center of the plug and then for every key I set the position of the circles by hand. This is tedious and not very precise. To make it a correct visualization, I need to do it more mathematically.
I also thought about writing a python script and calculate the needed tangent point (the last point where the foil “touches” the plug) for every frame. But then I would have to add a mesh circle in the foil at exactly the tangent point for every frame. Sounds difficult.
Any ideas or comments greatly appreciated!

well, is there no softbody specialist out there who can help me?

You could do it with softbody, but the collision detection is still really finicky.

I’d reccommend you take a look at the Hooks feature. You can make an empty deform the mesh as it moves, then parent the empty to the plug that’s pushing down.

The hooks feature is to my understanding only a help to organize the pulling of groups of vertices. But my problem is the geometry. At the spot where the plug hits the foil, the foil has to exactly follow the shape of the plug. And the size of the spot is changing over the animation.
Even with a hook, I have to manually adjust all the positions of the hook (actually several hooks, one for each circle) for every frame of the animation.
Is this not the same technique that one would use for clothing? One mesh follow the shape of another mesh? Is there a “clothing script” out there?

Have you tried the softbody tutorial from here;

several times now, but I never managed to download it without error.

just to make sure i understand what you are saying: you want the plug to push down on the foil and deform it like that, and the foil is/acts like soft heated plastic (like with a vacuum former)?

I would use a lattice for that

Worked just fine for me now. Send me a PM if it won’t work for you and I could send it to you somehow.