Though this question is over a year old, I'll add that something in the cage, like a chewable tunnel or a cardboard tube or box seems to help. I have single male that does the same thing. Though I think he does it for attention, I know he's probably bored as well. He chews right through the twig tunnels in a week or so but during that time he chews less on his bars. Toilet paper or paper towel rolls work good. Only good for a few days but it's not costing you anything.