Apple has been granted a patent (number 9,684,196) for a “display having a flexures element” that hints at flexible iPhones — and perhaps iPads,
The invention is for a display device may incorporate a cover glass with one or more flexure bearing sections. The flexure bearing may permit the cover glass to flex and/or bend in response to stresses or strains while still maintaining contact with an attachment point. If the attachment points have different heights, for example, the cover glass may flex at the flexure bearing, thereby permitting the portion of the cover glass between the attachment points to maintain a relatively planar alignment.
Of course, Apple files for — and is granted — lots of patents by the U.S. Patent & Trademark Office. Many are for inventions that never see the light of day. However, you never can tell which ones will materialize in a real product.