PIXXO 3D shows how to make a dead-simple paint-peeling effect using Blender.
Check out this tutorial from Pixxo 3D Juandre (Jay) Labuschagne, which shows a simple way to make a dynamic effect. The tutorial shows how to work with particles, cloth simulations, and other tips for creating a paint-peeling effect that you can use anywhere.
Others have created paint-peeling effects with Cinema 4D, Substance 3D, Houdini Vellum, and more. Have a look at some of the other paint-peeling effect tutorials here.