This is probably a very broad question. What I mean by it is, were war mauls ever used? I mean long sticks with a great hammerheads attached, or just a blunt object. Usually very heavy, I can't see how these weapons could have any practical value in a fight except for someone very, very strong - so were such weapons used, or are they just a fictional fantasy weapon that has made its way into the mainstream?
In terms of a two handed maul specifically, perhaps one of the more knowledgeable historians can help you here, however I would place it that as armour became more and more advanced, from ringlets of mail to plate for example, swords became more and more ineffective, and blunter weapons were used, however longer swords such as a Zweihander may have been useful against spears perhaps, but as soon as they joined the Melee, a shorter sword would have been used.
The reddit user 'TheJucheisLoose' responded to a question similar to this here, which is quite an extensive analysis and indeed a wider depth of how something like a war hammer became used "as a response to advanced armor technology"(TheJucheisLoose, 2013).
At the end of his/her thread it is remarked: "war hammers like Thor's Mjölnir, or like those you see in a Dungeons and Dragons illustration, were probably not much used", so my guessing is that two-handed war mauls may not have been used extensively, so that a shield and war hammer could be used for both speed, protection and versatility.
Considering TheJucheisLoose came up with that cracking answer, so perhaps he/she or the other historians can help you better!
Hope this helps!