I shred up all our junk mail and put it in the rummage basket for the birds. They don't eat the shred, just pull it out and make an uber-mess all over the floor. But that's OK: they get
so much fun out of it, that I really don't mind a paper uber-mess. For chomping, they prefer egg cartons and cardboard of a particular stiffness and texture. Some cereal boxes are OK, others they won't touch. All corrugated cardboard is great as is anything made of wood or plastic.
Sadly, Dominic has recently discovered the rubber gasket on the fridge (he spends much of his day on top of the fridge, remodelling cardboard boxes and turning them into confetti for me). In an effort to deter him from degassing my fridge, I put an old wooden chopping board over the door so Dom couldn't nom. Of course, the first result of this was that everyone got brained by the (rather heavy) chopping board falling on top of them when opening the fridge. This was good for our collective waistlines; not so good for our collective heads. The second result was that Dominic began turning the chopping board into matchwood which settled onto the top of the fridge gasket. Again, whenever anyone opened the door, a shower of splinters would fall in their hair. Sigh. The third thing was that Dommie learned to hop onto the fridge door as you open it and get a couple mouthfuls of rubber before you scoot him off. Wicked old bird!
Watch your bird and take note of what he likes to chomp on. Then, find ways of giving it to him in different places: a basket or box, stuck in his cage bars, tied to a string etc etc. Chewing is the most important Work our parrots do and they really can't get enough of it.
PS. Note to self: ring fridge-gasket-man in the morning...