Typically, if you had a suit of plate (which was terribly, terribly expensive) you would wear it with chain maile and padding underneath. It was heavy, and it was hot. And at the very least I would imagine you wouldn't wear plate without padded gambeson underneath, anyways.
Having done some Heavy Armored Combat in the
SCA in the past, in my experience pretty all armor (In my experience, typically
half-plate or
brigandine are used. Occasionally
chain maile,
scale maile, or
lamellar) is made to be used with a padded
gambeson underneath. Kneepads and elbowpads were typically used at the joints for extra protection (unless you had well-made gambeson sleeves). Otherwise you're going to get pretty beat up just from the metal getting smashed into your body by the blows coming at you. It's painful and your own armor can hurt you if not padded against. Metal will absorb some of the impact, but it doesn't cushion it very well. The impact will transfer right through, especially if used by a blunt weapon.
Plate typically was designed and shaped in such a manner as to deflect blows. However, a good solid hit is still a good solid hit and is going to do a heck of a lot of damage. Generally a warhammer, as pointed out by Vester, had a small, concentrated head and a pick on the back to maximize damage and create holes in the armor. There were weapons designed to counter plate armour specifically.
Blunt weapons should not ignore armour. In fact, I daresay that realistically, nothing should
ignore armour. They should have an advantage against plate. No. I disagree with that previous statement. Blunt weapons should have less of a
disadvantage against plate
in comparison to bladed weaponry. The same goes for puncturing weapons. Picks especially, spears, and even longswords were used with great force to try to puncture plate, though you still needed a rather powerful, solid hit with a spear or a longsword to puncture plate.
Plate armour was designed to give maximum protection, especially against bladed weaponry. Weapons were then designed to counter plate armour. Concussive and penetrating forces were ideal, since you aren't cutting through that metal with a blade of similar metal. Even normal swords slowly grew to be fairly heavy around the time of plate armour. A good hit from an arming sword or a longsword could still, due to its size and weight, do damage against plate armour. You aren't cutting through anything, but the force of impact from that size blade could still cause bruises and dent armour. A good hit to the helmet with a sword of that size and weight, could concuss you or disorient you at the very least. Albeit, not as effectively as hammers and maces.