cabinetshinges
I need to replace some bent (30 year old) hinges on our kitchen cabinets, but I don’t know what to search for. I have looked in the big box stores and haven’t seen any that resemble the kind I need. I’m hoping that I can order some online, I just don’t know what search terms to use.
To be clear, I'm not asking for a particular brand recommendation, I'm asking for the type or style of hinge. 
Your main concern is the wood warping. I've used plywood for cabinet doors in the past and they have all warped to one degree or another.
Your best bet might be getting marine ply which is designed to withstand moisture and hence less liable to warping.
If you can get a thicker ply (7 or 9 ply perhaps) then this will also minimise the amount it will bend.
Barrel Hinge:
But note that there's nothing intrinsically wrong with fitting a completely different type of hinge.
You obviously need hinges explicitly intended for outdoor use. Not like these
Best Answer
I think that's a partial wrap overlay hinge. Overlay means the door sits on the front of the faceframe when closed. Partial wrap means the cabinet side of the hinge wraps along the edge of the faceframe where it is attached. There are more components in the hinge though - maybe it's self-closing?