I was animating a book page - quick and dirty - with a few Shapekeys. However, as I would bend the subdivided Plane, it would inevitably stretch out and actually become a larger Object than it was initially.

Most of us don't think about it much, but this happens with virtually everything in Blender, and yet it NEVER happens in the real world. In the real world, Objects don't magically gain mass spontaneously and become larger.

So, a solution in Blender would be very simple: Have a Constraint for Mesh's which maintains a constant Area. So if the plane was originally 4.000 Blender units, even if you stretch out one of the Edges, then other Edges automatically shrink to maintain the consistency of its area.

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