So in a world where ‘chain mail’ doesn’t meaningfully exist, and ‘full plate’ probably means a healthy meal, 5e doesn’t have a useful way to deal with armor. 
How about this instead- You get an armor class bonus based on how much armor you’re wearing. If you have hard armor (metal, bone, wood), then it counts for the full value. If you have soft armor (cloth, leather, furs) then it counts for half this value.
It goes like this:
- Helmet: +2 AC
- Breastplate: +4 AC
- Greaves/Vambraces: +1 AC
- Shield: +2 AC
So the dude in the top left? He’s got a sick hat but not much else. It looks like it’s mostly cloth, but it’s got bones on it. Let’s call it +2 armor. Without any Dex bonuses, he’s got 12 AC. Bottom right? Metal helmet, cool chestplate, nice shield. That’s +7 AC.
As a general rule of thumb, if you have more than +2 AC from armor, you can only add up to +2 of your Dexterity bonus to your AC. If you have more than +4, you can’t add any, and you have disadvantage on stealth rolls.
One idea I’m still kicking around is giving +1AC to somebody who’s ‘fully covered,’ to put this about on parity with stock 5e. This lets somebody who’s wearing a thick cloth gambeson (counts as breastplate and greaves, since it covers the arm) get a slightly better AC bonus than otherwise. 5AC, plus one bonus, for a total of +3 AC. Gambeson plus cloth helmet puts you at +4 AC, which is pretty solid. With a shield, you’re able to be a historically accurate medieval infantryman and have a very good AC of 16.
Not too shabby, eh?
 And even in worlds where it does, I think it’s more interesting to have players think of their armor as bits and pieces that they cover themselves with, rather than one big suit that’s assembled once and then done.