I'm just going to do away with the spoilers box here, because it would literally contain everything after this sentence throughout the entire thread.
This is a question of theory validity. I have evidence to back it up, but I want to see whether or not it's at all realistic. There are also a few things that I'm not quite sure how they would line up.
I'll just dive straight into it: Shardblades and Shardplate are made of aluminum. I know it might sound ridiculous, or maybe just random, but there is some evidence to back it up.
In mistborn era two, it becomes very obvious that aluminum is an investiture block. People wearing aluminum can't be manipulated emotionally, and, more importantly to this theory, aluminum can't be pushed or pulled on. This is so important because the surge of gravitation is so similar to the external physical metals. Now, if aluminum can't be pushed or pulled, and is similar to gravitation, it would stand to reason that gravitation would not affect aluminum either. Now, in Oathbringer, we have evidence of Szeth's claim, very early on in the series, that shardplate can't be lashed. When the Fused are carrying of Moash's plate, they have to carry it by two ropes instead of lashing it directly. This suggests, separate to what happens in Words of Radiance, which is an entirely separate matter, albeit which also supports this theory, that lashings simply don't work on shardplate. There must be a connection of some sort.
Then there are two pieces of evidence to be found in Words of Radiance, as well.
The first is to be found when Kaladin and the other bridgemen are training with and against shardblades under Zahel, they comment that it is heavier than they expected, and Zahel explains that while it is much heavier than what others may have implied, it is still much lighter than a sword of it's size should be. He says that a sword that looks like it has two or three times as much steel in it would be heavier, not lighter. Therein lies the reason. Shardblades are so light because they are not made of steel at all, but rather out of a tempered form of aluminum.
The second is during Adolin's disadvantage duel, when Kaladin, after making use of the shardplate helm as a glove for blocking blades, it 'eats' his stormlight. Kaladin lurches to a halt when he suddenly finds it gone. This is extremely similar to the occurrence in Mistborn: The Final Empire, when Vin is forced to burn a nugget of aluminum. She finds her investiture has vanished, similar to the realization that Kaladin comes to in this scene. In both cases, the evidence shows that aluminum drains investiture into itself. If shardplate can also accomplish it, there is a possibility that it is due to it's nature as aluminum, not because it needs it to perform self-repair.
What I still don't understand, however, is how plate and blades can have effects using investiture, despite blocking it. It might have something to do with the fact that Aluminum can be used for feruchemy, which is another bit that I don't understand. If anyone has any ideas about this, please let me know. I'd love to have a full theory with solid evidence on all sides to get a WoB on this one.