Apple has revealed a patent that describes
a foldable iPhone with a flexible metal-backed OLED display capable of being
folded in half which is entitled as “Flexible display devices”.

Apple also notes that “it would be desirable to be able to use flexible
display
technology to provide improved electronic devices.” 

The described
device may contain multiple housing portions. For example, there could be two
housing portions that are coupled together using hinges. The hinges may include
hinges based on a three-bar linkage, hinges based on a four-bar linkage, hinges
with slotted members, hinges formed from flexible support structures, and
hinges based on flexible housing structures.
Apple has filed a patent that describes a foldable iPhone with a flexible metal-backed OLED display capable of being folded in half which is entitled as "Flexible display devices".
As granted by the U.S. Patent and
Trademark Office, Apple’s U.S. Patent No. 9,504,170 for “Flexible
display devices” describes an iPhone with a foldable full-screen display.
Like clamshell cellphones popularized by Motorola in the 1990s, Apple’s
proposed design also folds in two when not in use for easy storage.

To achieve a foldable format, Apple’s invention relies on a number of flexible
components, the most important being an OLED display and metal support structure.
For the latter, the document proposes nitinol, a nickel and titanium alloy
known for its elasticity and unique shape memory abilities. Alternative
embodiments involve flexible polymers.

Read more for full patent description.