How do I glue broken headphones?

We have 2 pair of the wireless Sony headphones for TV watching and one pair has snapped right above the earpiece on the 'plastic' framework. What is this stuff made of and what works as an adhesive? Neither superglue or JB weld seems to work.

sounds like you have three options 1. use sugru to fix it. 2. take apart the old pair and make it work with any pair headphones. 3. buy a new headset.