rabbits?..the experts here will comment..see what they say..I have an oak leaf with similar damage and concluded that I have rabbits..

I would almost guess some kind of caterpillar. We have climbing cutworms here that will cause damage similar looking. Go out after dark with a flash light and look. Start at dusk, you may have to make more than one trip.

reading from a tablet now..not my phone..a better look at your pics and your damage is much worse than mine..probably not the same problem..

I would check for a bigger type of pest that can reach to the center. But still, check at night and at dusk like morz8 if you want to catch something/anything in the act. That is when small pests like larvae and worms and snails come outside to "play". Bunnies and deer and squirrels can cause damage probably at any time... You could also spread some flour on the ground (several feet away, >3 feet maybe) and then see if you detect new damage; if so, see if the flour was disturbed and based on the footprint left, guess what animal it could have been. If you see new damage and no footprints then it must be something small or something that flies.