Well, in a perfect system any object that inflicted X amount of damage would have X-Y-Z amount of damage inflicted back on it where Y depends on the deformation of the object in question and Z depends on the deformation of the object being struck. This is simply Newton's laws.
However, our system is far from perfect because 'damage' X is an abstract concept that assumes as its basic assumption that the thing being damaged is human flesh (or something very similar)
and that damage is proportional to some ability of the damage to disrupt the biological function of that flesh. These are conveinent assumptions for what weapons are primarily used for, but are not particularly conveinent when weapons are turned on things that are not very like human flesh and are not biological objects at all.
In a perfect system, a weapon is generally has a hardness much higher than the amount of damage it normally inflicts. This hardness protects it from damage from regular use. Alternately, the object could generally be used only on soft objects that deformed easily (those with high Z) so that the force of the impact was absorbed by the mechanical deformation of the thing being struck. Alternately, the striking object is itself pliant and deforms in responce to striking a harder object.
In the case of a sword chopping down a metal door, I wouldn't want to write a system out for handling every case with weapon, but I can make several observations:
In the case of a sword, a large part of the damage it inflicts is dependent upon the ability to cut the object easily, and by extension, that biological tissue doesn't take well to being severed. The door is not alive so being scratched doesn't effect its function all that much. If the object being struck has a hardness higher than the hardness of the sword, it will not be cut easily (if at all) and so the damage actually inflicted should be reduced by some ammount (probably only 1/4 normal damage for a sword). Secondly, the admantium door is probably not very pliant at all and does not easily deform. The sword is normally intended to strike things that are fairly yeilding so we might assume that the damage done to the sword by the door is higher than what the swords hardness normally overcomes. Thirdly, the sword itself (if it is a quality sword) is designed to be somewhat pliant (because it must strike other swords and armor) but not excessively so (otherwise it wouldn't cut), and that deformation to the sword ruins the swords function. So, over time, damage will be done to the sword. I would rule that with each blow the sword took essentially the ammount of damage inflicted minus the sword's hardness. A strong man would probably shatter, dent, or bend his sword against an adamantium door without doing significant damage to the door at all.