This is interesting. Most games use the armor stat to absorb a percentage of physical damage, though some use it as an extra health bar. If it's the latter, armor can usually not be restored once broken. Both kinds of games can have an armor penetration stat, though it works differently. In the first case, it reduces the percentage absorbed, and to be worthwhile it has to reduce the percentage enough that it's not swapped for a Damage stat. In the second case, it increases the amount of damage done to armor. Here, too, it needs to be balanced so that it's not prioritized away.
There are also other interesting concepts such as avoidance (dodging or parrying an attack, or an attack missing outright). The hardest part is to balance all these things against each other so that fights take a reasonable amount of time, otherwise the player might get bored due to fights being too long, or fights being too short.
A third way to do it, that'd be somewhat harder to balance and that I personally haven't seen much in the wild, would be to subtract the armor value from the attack value and deal the difference in damage to the entity. This would strike against casters (assuming you have magic in the game), and other characters with weak damage stats, such as tanks (assuming you have tanks in the game), and might leave them unable to do damage against some foes - not fun for the player.
Based off of what I have now, I was thinking I could divide the attack by 2 and and deal damage towards the armor and the health. When the victim runs out of armor, the full attack damage is dealt on their health.