Apple pie box model and animation

Question

What is the best way to animate apple pie box folding from die form to folded view?

I need rather technic then solution. In my case I should be able to fold abstract apple pie box from die form, not vice versa.

These type of box seems to be pretty easy, but on close view no so... I spent whole day and still have no idea how to start folding...

Does blender has any tools to fold and bend faces keeping it's UV geometry constant?

UPD: moonboots thank you for the answer, but... I think it's a bit dirty and tricky way... I would like (if it's possible) to make it more realistic way... First of all, applie pie box is not trivial geometry. It's a cross section of bunch of cilinders, you can see them on the gif:

Actually I created that cross section, and applied bones. Going try to unfold it (at least):

For now I have problem to pose bone in parralel to XY-plane (the goal is to unfold box). I think I tested all kinds of snapping, but has no luck ( I would be very grateful if someone would explain to me how to rotate a bone parallel to the XY plane?

UPD2: here is my version, pure bones, as much real as possible, but not strict real... It can be used for cartoon-like animation, but not for packaging production visualization and preview...

Finaly it seems there are should be more dedicated software for package modeling. Paper and folding cardboard physics should be considered much more precisely...

note that box flaps has arc form when box is folded:

Answer 1

So 2 solutions:

I've tried with B-Bones, it works fine. Don't forget to put the Subdivision Surface under the Armature modifier, otherwise you'll have bad shading:

You could also use both bones + shapekeys:

• Create your flat object. Give it 3 bones, one main, one for each face hinge:

• Give your object a basis shapekey and a second shapekey, modify the object:

• Mix both shapekeys and bones animations, use the bones to move and close the object: