I'd like to do sledgehammer workout at home. Unfortunately, my apartment is not large enough for the tire, and the noise is a problem between neighborhoods. Therefore, I am looking for a smaller and quieter alternative for a tire. For example, maybe a 12" cube of foam or rubber?
You can imitate the movement using a TRX Rip or a similar rip / training bar of any brand.
Attach the end of the rubberband to the top of a closed door. Stand 1-2m from the door with your back facing the door. Now, you can hit an imaginary tire in front of you. Using the rip/rubberband makes virtually no noise. Change the load by using a stronger/weaker band or two parallel bands (not possible on a TRX rip).
Of course, the feeling and the load will be different from using a real sledgehammer.
Some people have suggested the shovelglove workout (I'm not affiliated with the guy, but his webpage looks to be the best description I've found). It's basically the sledgehammer workout without actually hitting anything. Alternately, if you do want to be hitting something (and have room in your apartment to do so despite not having room for a tire), people have suggested a roll of old carpet, which they also say is quieter. If you have a Habitat for Humanity ReStore in your area, they usually sell rolls of carpet very cheaply.