I suppose it would be possible to have armor half the damage. Hit or miss could be determined by 10 plus DEX modifier, then anything that hits the armor only does half damage, and anything that hits above what the armor provides does full damage. Double the range of numbers the armor provides protection for to make up for it not stopping damage completely.
If a character had DEX 20 and leather armor, AC would be 15 no damage/ 17 half damage.
same character in chain shirt would be AC 12 no damage/ 18 half damage
Half Plate would be AC 12 no damage/ 22 half damage
Chain would be AC 10 no damage/ 22 half damage
Plate would be AC 10 no damage/ 26 half damage