Doomsday made his first appearance in Superman: The Man of Steel # 18. In his first appearance itself, he was shown with his containment suit.
Superman: The Man of Steel #18 cover
Since then, the Containment Doomsday has made his appearance in several Superman and Justice League comics and also in the Injustice: Gods Among us game and most recently in the 2018's The Death of Superman movie.
In all the things I've encountered, I couldn't find details about the containment suit.
Is there any mention (in the comics, movies or otherwise etc.) about the material composition of Doomsday's containment suit? Like what is it made of, its durability etc.?