Can I get a refund if invisalign didn't work for me?

Usually you can get some partial refund of the treatment that failed. Since you already paid for the treatment, you can find a good experienced orthodontist (not a general dentist) to redo your treatment. You can safe money this way, since the lab fee is paid for already and orthodontist can transfer the case to his or her account. In the future, be aware of limitations when being treated by a general dentist for this complex issue. It is like asking your primary physician to perform a cosmetic surgery. It is the same when asking a general dentist to treat your orthodontic problem. Good luck to you.  

because most dentists do not have the orthodontic education or experience as an orthodontist who has taken an additional 2 years of post graduate specialized training, he is solely guided by his own conscience. therefore, in this case some sort of refund is definitely indicated.

This is a question that most won't want to answer.I am certified to do invisalign, but rarely do it because it just can't accomplish 90% of the cases and results I want to achieve.The public and many doctors are led to believe by invisalign can accomplish more than it really can.  I have been surprised what invisalign can accomplish in some instances.  Did you and the treating dentist have conversations about limitations about what invisalign can achieve and what it can't.Definitely get more opinions before you do anything.You can look for referrals from the International Asssociation of Orthodontics.