I have been finally writing the follow up to my 5e Manual of Arms: Weapons; the name is 5e Manual of Arms: Armor and shields.
It's been a bit of a headache. Armor is a lot more complex (and maybe less interesting) than melee weapons. The weight varies immensely, and the types of armor 5e uses have only a vague resemblance to reality (I've heard many people say that "leather armor" is not a thing, and that padded armor should be a lot better, "chain mail" is redundant, etc.).
Real armor can vary in weight, size, etc. It is also used in many combinations – a breastplate with chain armor, with padding underneath, and so on. There are also cultural differences; think of samurai, gladiators (with asymmetric armor), armor made of exotic materials, etc.
The issue is further complicated because, even in the original rules, some types or armor are just smaller parts of others, while some include greaves, gauntlets, protection for the legs, layers, etc.
Helmets? Not mentioned in 5e. I guess it is not an important piece of armor...
To make things a lot simpler, you could just ignore the names of the armor and judge them by price, weight and AC. Let the players choose how they present their armor, as long as it makes sense. Chain mail with breast plate and no helmet? Cool! Shoulder pads to protect you in your right arm, big scary helmet, and bare chest? Nice!
So, I'm adding this is an alternate system. Build your own armor, never mind the name. Also, an encumbrance system that is both easier and more sensible.
(I already wrote about this here)
But I feel I should at least fill the gaps that 5e leaves for people who don't want a new system. For now, I've got a few shields, but only two types of armor (I don't think we need more than that):
A long, padded jacket with a skirt. In this context, a heavier (maybe thicker or longer) type of padded armor.
AC 12 + Dex modifier Str — Disadvantage to stealth 15 lb. 20 gp
Small steel plates riveted inside a jacket of cloth. The arms and legs are covered with similar protection, or chain. Overall, lighter than chain mail but heavier and more expensive than ring mail.
AC 15 Str 11 (?) Disadvantage 45 lb. 60 gp
Not great. I think brigandine should be lighter (i.e., medium armor) and more expensive, but there is no niche there to fill. And brigandine sounds simialr to the way splint mail is described, so...
I'd like to add a Jack of plates as medium armor... but again, no niche (unless I give it stealth disadvantage, which sounds bad).
Any ideas? I'd be happy to hear them.
Anyway, if you want a detailed treatment on weapons, you can also check the Dragon Heresy Introductory Set. I wrote a very small section of it (about half a page, similar to that link, above), and although I haven't talked much to Douglas since the demise of Google+, I know he only creates good stuff AFAICT. Here is another example.
Dragon Heresy has new types of armor, shields, weapons, and a completely novel combat system. Douglas know his stuff - he makes actual shields! If you like to add more detail to your D&D combat, it is worth checking out.