After effects is a still mostly a 2D ‘Layer’ application, as far as ‘thickness of a layer’ goes.
You can rotate layers in 3D, but in most cases can’ t add thickness or ‘bend them’. Although, more advanced artists can often fake it (with time and patience).
There are a few plugins that can help you recreate ‘thickness’ (if you a willing to spend a minimal amount of money)
3d invigorator, 3D layer, etc., but again, these are all basic as far as 3D goes, and creating a warp that looks good in a 3D world will likely require the use of an actual 3D app. Maybe somone alse can throw some ideas…
Good luck,
Vince