MIMF

The cap for my new electric guitar build is 1/2" and is cupped upward with a 1/8 inch bow in the center,
What can I do to straighten this flat?
I can just clamp it flat, but this is using a carvin thru neck and so will be glueing the sides and the top cap at the same time, likely will glue wings first and then the cap. I am concerned about cracking the top.
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I doubt the top will crack with only an 1/8" deflection over the width of the wood.
I would just clamp it with big thick flat cauls on both sides and let it be.

I agree you can clamp it out but it raises an interesting question. Which side do you glue? The wood is cupped because there is more moisture on the convex side. If you use a water based glue, it will add more moisture to the wood. So, should you apply the glue to the convex side or do you think it doesn't matter?

Is it one piece? Figured? Expensive and prized piece? Gluing, as Chuck says, is probably going to be okay. You might test clamp it before gluing. If it cracks, it's an opportunity for another day. I wouldn't think it would crack after it was glued if it doesn't before. Another way to get some of the cupping out is to rip it up the middle and rejoin the pieces. If done well you would barely see the joint. You could also plane it flat but you sould then have a 1/4" cap that might still cup, twist or warp on you when you thin it.

You could also clamp the convex side down to a surface so that the concave side only is exposed to the air, leave it for a few weeks and see if it equalizes.

Of course that will depend on whether the RH is going up or down in your area. If its going down then you may want to do the opposite. Most wood will equalize over time, it's just a matter of how much time.

If you use a water based glue, it will add more moisture to the wood. So, should you apply the glue to the convex side or do you think it doesn't matter?

To use that trick, Al, you would add glue on the concave side so that it expands that and flattens the piece.
There is no guarantee the glue will make much change, so I would just pick the side you want to show and clamp the crap out of it.

You can also Dry the other side, by using a hair blower, or a clothes iron.

I was told by an old violin maker once to lay it out in the sun for a few hours and it will straighten up. I had moderate success trying that, but it was in the summer. It's getting too cold around here to try it now I think.

I had moderate success trying that, ...

Yea, that is why I said there are no guarantees with the "wetting" method.
If the wood was "case hardened", causing it to cup, then you would have to soak one side to get it to flatten. That is not good for anybody!
Or it could be residual stress from how the tree grew ... can't fix that. In that case, thinning the plate may actually make it worse. I have some African mahogany that I was hoping to use for necks, but after resawing a stabilized piece (been in the shop well over a year) it went crazy-twist on me. It's looking like firewood to me now.

The thing is, there are many possible reasons why the wood is cupped.
The right way to make a stable instrument is to use wood that -when cut- remains flat. However, If it is a thin cap on a thick solid body ...

Okay, this might be a nutty idea but I was thinking about it when gluing up wedge shaped wood for top and back for a mandolin. If you are doing a carved top of some kind, it might work. If you are worried about it too much (and not sure that you should or shouldn't), would it be possible to make the body of the guitar match the curvature of the top piece? In other words, arching the body so it matches the 1/8" contour of your top piece and gluing the top down with a strong glue, maybe something gap filling just in case you don't get it perfect. Binding would hide the edge on a carved top. Just a thought to add to add to the pot.

Usually the cupped side is the most recently cut surface of the piece, which shows thew wood had not really dried out. If it is not case hardened you should be able to flatten it by wetting both sides and after a while clamping it flat until totally dry, which might be a week or two. It will be flat if not case hardened.

Once dried, scrape or plane both surfaces to be glued and glue them together. Clamp well until dry.

The first question is why did it cup in the first place? How has the OP storing it? How long has he had it? Where did it come from? What is the current RH in his shop?
All of this could matter in the long run. Just gluing it to a back and clamping the hell out of it could result in a body with a permanent cup or cracks in the body if the top and back are wildly different in moisture content.