I need to make an animation of peeling off the shells of an egg shaped object.
I need to do the animation in this sample video, but I couldn't find any solution.
Here's a perhaps too clean GN approach.. but in my experience, it's easier to mess up something that's too clean, than the other way round. There are lot of nodes and sub-groups in the final modifier, so this answer will just settle for a summary of the method; if you download the .blend, you can assign the subgroups independently, to see what they do.
Starting with a curve half-profile of the egg, such as you might Screw to the solid, the first step is a 'Curl Curve':
.. which sticks an aligned, fixed-length Curve Primitive > Spiral on to the end of the egg profile, as it's being trimmed. It then trims the combined curve from the other end, so the overall length is preserved. The original profile's XY radius is stored on the curled curve.
The next step is to rotate the points of duplicates of the curled curve in such a way as to fully span 1 segment of the solid egg, while preserving the stored original radius
And then the duplicates are lofted using the Loft Curves group from this answer to make one segment, The segments are duplicated and rotated to encompass the solid, and their UV's wrangled to unify them and make texturing possible.
Currently, the final group exposes U and V resolutions in the geometry, the number of segments, and the degree to which the wrapping is unfurled.
With this sort of result: