What is the foam board coated with (paper? plastic?) and how thick is it?

What kind of adhesive did you use?

Is the frame bent, too, or is it not yet in the frame?

Sue

Okay, I'll tell you what I know and see if it helps.

Wood and paper-based sheets tend to behave the same way:  if one side is wet or dampened, it curls upwards when it dries.  It just does, as you have discovered.  I think the paper surface of the foam board is the culprit and it is pulling the foam core with it.  And, since the decorative materials are on the front, there may be more shrinkage and pulling from that, too.

Woodworkers often have to treat the back of their flat pieces as well as the front, with shellac, paint, or whatever, so moisture is absorbed into both surfaces and when they dry, they are pulling against each other, so there is less chance of warpage.

If you don't have water-soluble paint on the surface, you might try misting water over the entire surface, letting it absorb, then weighting down the piece, either at all the corners or across it.

HOWEVER, since you have used some materials that don't absorb water very well, namely the white pva glue, this might not work.

If you can temporarily flatten the whole piece by hand just by holding it down, you might consider mounting the project on a thicker, stronger full-sized board, a piece that is thick enough to fight the pull of the artwork and not warp itself.  And I would weight it down at the corners as it was drying, also.

Another possible solution might be to put a couple of papers of papier mache strips over the entire back of the project, and see if it straightens itself out.  One thing that I would do if you take this approach is to monitor the dryness of the back.  As soon as the surface has dried, but the whole back has not finished drying, I would weight it down until it is dry, probably for several days, depending on the humidity.

I don't think bracing the frame with corner plates would help very much, as  corners are the weakest point of the whole piece, and they alone wouldn't have the strength to counteract the pull of the rest of the piece.

Sue