I came up with a very similar system one time. Armor points absorbed damage, except that poison and psychic damage would bypass it (since those types can't affect objects). You got all your points back on a short rest, when you had time to patch up your armor and re-adjust the straps, etc.
The armor points were based on your level and the type of armor you had:
padded: 1 at 1st level, +1/level
leather: 1 at 1st level, +1/level
studded leather: 2 at 1st level, +1/level
hide: 2 at 1st level, +2/level
chain shirt: 3 at 1st level, +2/level
scale: 4 at 1st level, +2/level
breast: 4 at 1st level, +2/level
half plate: 5 at 1st level, +2/level
ring: 4 at 1st level, +3/level
chain: 6 at 1st level, +3/level
splint: 7 at 1st level, +3/level
plate: 8 at 1st level, +3/level
Meanwhile your AC was 10 + Dex for light armor, 10 + Dex (max 12) for medium armor, and just plain 10 for heavy armor.
The armor point values were based on how much more you would get hit with the lower AC numbers. For example, full plate is normally AC 18, so at AC 10 that's about a 40% change in hit rate, so to compensate it gives you roughly +40% hit points per level. Obviously this is back-of-the-envelope math and not super accurate.
EDIT: It comes back on a short rest because healing magic doesn't work on it. I thought about allowing hit dice to work on it, but that throws off the hit dice math, and creating spells to repair armor in the middle of a fight just seems weird to me (well, weirder than ablative armor, anyway).