Can Invisalign Fix an Underbite?

Your picture definitely shows what appears to be a more complex case with a possible upper to lower jaw size discrepancy.  There can be multiple ways of treating this case which might still include Invisalign.  The key is a thorough exam by a dentist who is certified in Invisalign therapy but also has a good relationship with an orthodontist who can treat a more advanced case if a referral is needed.  Actually, my biggest concern is for the potential TMJ (jaw joint problem) that may be developing as indicated by the cracking and tooth/jaw movements you are now seeing.  Most of the time the TMJ problem may need to be treated first to determine its correct position and then to see where the teeth need to be moved to make that position stable and comfortable.  There are various plastic splints that can be used temporarily to stabilize the TMJ.  Make sure the dentist feels comfortable treating TMJ as not all do.

From your picture it appears that you have not only an "underbite" but also a significant difference in upper and lower jaw size and asymmetric jaw development. In many situations of this type some form of jaw surgery is required for correction. The fact that you are having progressive jaw "cracking" is a sign that treatment is best done sooner rather than later ("An ounce of prevention -------- etc.").

Having said that, if you do need surgery, you will probably also need to have some tooth alignment done in preparation for surgery - and Invisalign may be an option for that alignment. I suggest you schedule a consultation with an orthodontist so you can learn more about the nature of your bite imbalance and the approaches to its correction.