The new phones simply swap plastic for glass in the screen. The OLEDs you find in plenty of other displays can be put on flexible materials—like metal foil—which then makes it possible to create a device which is both unbreakable and bendable.
Samsung hasn't told the Journal how much it's invested in the new bendy phones. However, it points out that it has been spurred along by growing innovation in the display market, from the likes of LG and Sharp. Seems that's enough to rush out a bendy phone as soon as possible.
Which is just what it plans to do. The Journal reports that a "person familiar with the situation" told it that devices will be released in the first half of 2013. Bendy phones for all!