My (admittedly possibly flawed and definitely incomplete) understanding is that Superman's invulnerability has limits. If you can keep up enough pressure on him, or catch him when he's exhausted, he'll eventually go down. That's just going to be a lot harder for someone to do who isn't on the same power level as he is.
Even after Supes' powers got rewritten to "de-God" him a bit, he's still almost in a class by himself in terms of invulnerability and overall power.* AFAIK, no mundane material short of a kryptonite variant has ever injured him. So mere adamantium- or whatever super-hard material you'd care to name- won't cut it. (Sorry, had to.)
* Supes' main concerns would be: kryptonite, magic and its wielders, quardian energies and its wielders, and beings of like power. A list of these would include (but would not be limited to) Green Lanterns, Daxamites, Capt. Marvel (and the other Shazam-powered bunch), Ultra-Boy (occasionally), Martian Manhunter (occasionally), Wonder Woman (occasionally), Super Girl (occasionally), Power Girl (occasionally) Ultraa, Doomsday, certain Eternals and any being or tech of Kryptonian (or presumably Daxamite) origins.