Schengen visa from Italy without visiting Italy

I presume you have a Schengen multiple entry visa of type C.

• You are allowed to enter the Schengen area multiple times.
• You can stay there 90 days out of 180 days.
• Your passport will be stamped by the first and last Schengen state of each trip. There may be random spot checks on the internal borders, or not, but they won't stamp your passport.

So the Schengen system will find it difficult to tell if you arrived at Frankfurt, took a in internal flight to Munich, then back to Frankfurt, then left, or if you took the train from Munich to Venice for most of your trip.

But the comments by pnuts raises a very important point. If the Schengen officials think that you deliberately lied to them, then any subsequent applications will be difficult and the visa will be revoked. You must have explained that you want to visit Italy, was that true at the time? Has it changed so much that you won't visit Italy at all during the validity of the visa?

Think about how your situation looks to a visa official. They have seen stories before. "My dog ate my homework," as the English proverb goes.