Samsung is developing unbreakable bending AMOLED units, which are supposed to enter the mass-production cycle in two year. You should definitely check their awesome video demonstration.
The video below shows a standard AMOLED screen with glass and the new AMOLED display. It can handle bending and heavy hammers. See for yourself.
The new screens use plastic AMOLED panels with polyamide protective film. It seems this works well enough.
Samsung expects to push the new AMOLED into mass-production within the next two years.