What about some variation on the following simple rule?
AC - "Armor Class", what an attack must roll to damagingly (to the wearer) hit armor.
RC - "Resist Class", what an attack must roll to ignore armor resistance.
Hits below RC do half damage.
Example: Joe the Fighter has AC 15 and RC 18. Attacks 14 and below miss completely, as usual. Attacks from 15-17 do half damage. Attacks 18 and above do full damage.
In general, armor could modify both AC and RC, although not necessarily in the same way. I'm not sure how the interaction with dexterity should work, but I think the desirable result (in terms of gameplay that supports fantasy archetypes) would be such that characters in light armor will have good AC and mediocre RC, while characters in heavy armor have mediocre AC but fantastic RC. (Note that I'm rating AC and RC on different scales, RC is always no less than AC.)
With this rule armor can obviate relatively weaker attacks (this and dodge are joined in a single abstraction as is traditional) but also support the idea of armor that takes the blunt of a blow. Unlike DR it does not make low-damage attacks pointless, and in terms of final damage done scales, on average, the same for a few strong attacks as for many weaker ones. Moreover, DR requires extra calculation for every hit, and this does not. Abstracting the absorbing ability of armor to half also keeps the damage calculation simple for any given attack and, importantly, identical for every character. Modifiers to RC can carry the burden of letting some armor absorb damage better or worse in an average sense.
Another possible benefit is that it introduces just a little more mechanical room for other game elements. Hits against AC but not RC represent armor getting in the way of an otherwise solid hit. This might be important for various maneuvers, handling whether someone is actually poisoned by the arrow, item sundering, or interaction with spells. Likewise, effects that are best represented by cushioning blows but not necessarily avoiding them might be handled well by modifiers to RC. Certain crushing weapons might partially ignore RC because the force to the armor is transferred efficiently to the wearer, and this could be done without causing the more significant balance changes associated with changing the attack roll or partially ignoring AC. It might also be a good jumping-off point for more detailed armor modules.
I also like that the impact of armor is spikier than DR. If I have DR 5 armor, then I know that no matter what happens I take 5 less damage. Not knowing if armor will be effective on any given hit heightens the tension in a way I enjoy (although, of course, others may not). Against high-damage attacks it could also be very memorable in a way 5 DR is not.
Anyway, that's a lot of potential benefits for adding a single number that is largely static and works in play in a familiar way. The obvious downside is that every hit >= AC requires a second comparison to resolve. Comparison is faster than calculation, but it is still a slow down. Worth it? Maybe.
(I'd also like to add that this avoids one property I dislike about CrazyJerome's idea of DR that activates when a damage threshold is reached. Namely, that sometimes rolling 10 damage is paradoxically worse than rolling 9 damage. With the AC/RC rule, a larger damage roll is always better for the attacker, all other things being equal.)