Man, that's a NEAT pair of sunglasses! 
Hmm, I'd probably model that as a datum curve to simulate the flat pattern, then wrap that curve on an extruded surface with the short side arc. Then I'd use the curve as a cut. Then I'd thicken the surface so that the original surface was retained, and the thickened surface was the one where the metal has stretched. Then I'd do a spinal bend on the whole thing, making sure my spine was the exact length, and in the right direction.