It would seem you're not familiar with Garen then...
I would be split pushing either top or bot as Garen, to the point of the enemy team having to send people my way. This often attracts a Yi if one is on the enemy team. A late game Yi will have to get through at least 300 armor after last whisper when fighting a late game Garen, which is no small amount.
In team fights my goal would be to silence the Yi before he can Q to a squishy target, and once everyone has gotten a few shots at him I ult. If I don't get my silence off I just spin to win and ult instead. A teamfight will always require proper focus.
Now, I would like to point out that I was only mentioning a 1v1 situation, you brought the team fights into this. In a 1v1 situation the only reason a full build Garen will not kill a full build Yi every time is because Yi can escape. If you are unwilling to take my word for it please try it instead of ignoring my points like most people on these forums seem to do when faced with contrary points of view.