The ironic thing about DR, what didn't really work well for me in 3e, would probably work better with 5e's bounded accuracy.

In the armor revamps I've played around with in my head, the first half of your health is your 'stamina', with any damage received after you reach half health (when you're 'bloodied' as it were) being more serious damage. Stamina you can get back more easily, but damage received after that would need active healing to regain. Critical hits bypass your stamina, and sneak attack bypass your armors damage reduction, and possibly your stamina too.
What I've never figured out is how to decide what AC is after armor becomes just a source of damage reduction. In my head being a Dex fighter should become less and less effective during a fight, as your acrobatics and fencing take a toll, but this is possibly no longer heroic fantasy, but without a dedicated defense skill it does seem like Dexterity and possibly Strength are what we have left.