Bending mesh physics

I am trying to figure out of there is some form of physics system in place that allows me to “bend” an object, while having it being fixed to a point…

An example would be… Wheel of Fortune. When they spin the wheel, theres a rubber? thing that hits the pegs… It bends around the pegs… Or in the game of Life… when you spin the piece in the middle… Same concept.

Any ideas?

This post looks like it is very similar to what you want: "Bending" a model - Unity Answers