Apple filed the 10,104,787 patent in September 20, 2016, and was posted on the US Patent and Trademark Office website a couple of days ago.
Below is the abstract of the "Flexible display devices" patent:
Electronic devices may be provided that contain multiple housing portions. The housing portions may be 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. Flexible displays may be mounted to the housing portions overlapping the hinges. When the housing portions in a device are rotated relative to each other, the flexible display may bend. The hinge may be configured to allow the flexible display to be placed in a front-to-front configuration in which an active side of the display faces itself or a back-to-back configuration. Engagement structures may be used to help the housing grip external objects and to hold the housing portions together. The hinges may be provided with rotational detents to help hold the flexible display in desired positions.
Some key patent figures are illustrated below:
In patent FIG. 10, the device with a flexible display has a hinge that is based on a four-bar linkage configuration. FIG. 11 illustrates a side view of a device where the housing has been manipulated to place the display in a back-to-back configuration.
In FIG. 22 which is another back-to-back configuration, but instead of using a hinge mechanism, Apple notes that the engagement could use magnetic structures, hook-and-loop fasteners, hook and notch structures and/or other mating structures.
In the FIG. 23 and FIG. 24 you can see a device in a tri-fold configuration with a two hinge construction.
Apple's patent also touches on the use of fabric for the device's housing:
An electronic device comprising: a foldable housing having a flexible portion, wherein the flexible portion flexes to allow the foldable housing to move between open and closed positions; and a foldable display mounted to the foldable housing, wherein the foldable display has first and second display portions separated by a third display portion, wherein the third display portion overlaps the flexible portion of the housing, wherein the first and second display portions face toward each other when the foldable housing is in the closed position, wherein the first and second display portions face away from each other when the foldable housing is in the open position, and wherein the flexible portion of the housing comprises fabric.