When the countertop was installed, it should've been screwed to the island from underneath. Was it? Has the cupping pulled the screws loose, or has the cupping all occurred in the overhang area (the latter seems improbable)?

Wood changes shape, or "moves," because its moisture content changes. When it absorbs moisture, it expands. When it loses moisture, it shrinks. When the moisture content changes more on one side than on the other, it cups. The most likely scenario here is that the wood was not as dry at the time of fabrication as it should've been for installation in your house. Perhaps the fabricator's shop and/or wood storage area is very humid? Perhaps you've got the A.C. going so that the humidity in your house is quite low? Maybe the countertop gets a lot of direct sun? Regardless of the details, it happened because the fabricator didn't properly deal with MC (moisture content) issues.

3/8" - 1/2" is a lot of cupping for a countertop. It wouldn't be acceptable to me. Brackets under the overhang are a good idea, but I doubt they'll be able to remove the sort of cupping you're seeing.

The house is under construction and the AC is not on. It is very hot and humid in the house. The countertop is screwed into the cabinets on two sides and the screws have not pulled loose at all. The cupping appears on the 50" span toward the center.

I visited the fabricators shop before he cut the radius. It was cupping right from the start - he showed it to me and said it was normal.

Was he stretching the truth?

Jon 1270 thanks for quick response.

Just to clarify, is it cupping such that the top surface is concave or convex? Is that the same direction in which it cupped in the fabricator's shop?

A disclaimer: There's very little I can say for certain, because I can't see or measure the problem to confirm my suspicions. I can say what's likely. That and a buck will buy you a Coke.

What is certain is that the countertop is cupping because it's either losing or gaining moisture. Since it was already cupping in the fabricator's shop, that means it was gaining or losing moisture even then. It's possible that the wood he used was extremely dry, and reacting to humid conditions in his shop and then in your house. It's more likely that he used wood that was either not fully dried, or had been stored in too-humid conditions after drying, and it cupped as it lost moisture. Countertops tend to be thick. Thick lumber is time consuming and expensive to dry properly. A lot of thick wood gets sold that isn't appropriately dried for an application like this.

"Normal" is subjective. He obviously considers it normal. That doesn't make it true in any objective sense, because there is no objective sense. You can probably believe that it's normal for his countertops, but that doesn't mean it's unavoidable.

There are lots of things that can be done to ensure that a wide countertop stays reasonably flat. In a perfect world, your fabricator would have:

1) Purchased properly dried wood from a reputable supplier.
2) Stored the wood in climate-controlled conditions similar to the conditions inside your finished house.
3) Checked the MC of the lumber using an electronic meter before fabrication
4) Alternated the orientation of the boards' annual rings so that alternate boards would tend to cup in opposite directions, thereby helping to keep the slab flat despite MC changes.
5) Kept the newly made top out of direct sunlight and ensured that both sides were always exposed to the air (i.e. not left lying flat on a workbench for any significant length of time).
6) Installed it only after the house was closed up, with climate control systems working.

In reality, though, it may be hard to get thick, properly dried wood in the species a customer desires at a price the customer is willing to pay. Climate control for shops and storage areas is expensive, and often goes by the wayside. The barriers to entry into the woodworking business are rather low, and many professionals don't have moisture meters or understand how to use them. They may also lack understanding of how wood responds to moisture changes. General contractors also frequently lack understanding of wood movement issues, and demand installation of interior woodwork in times / environments that are inappropriate.

Many small shops get away with shortcuts because the nature of the products they make allow them to get away with it. Wide, thick, solid wood slabs (e.g. island countertops) are among the least forgiving of bad practices with regard to moisture.

"When the moisture content changes more on one side than on the other, it cups."

Not necessarily.

Wood changes shape even if the mosture content change is uniform throughoutthe pieces of wood.

See Chapter 3, Figure 3-3, p. 8 in the 'Wood Engineering Handbook' linked below.

There is not a lot you can do to stop the movement of the wood.
If you manage to fasten it down well enough to stop the movement the result is likely to be cracking, splitting, and checking of the wood as it dries and builds up internal stress.

The best method is to have the wood very close to its final moisture level before using it, and then make sure it is not exposed to wide changes in relative humidity.

No finish can stop the movement.
The wood has 24/7/365 to come to equilibrium.

Here is a link that might be useful: Chapter 3, Wood Engineering Handbook, USDA

It's safe to say it's got less moisture on the concave side, or more moisture on the convex side.
Is there any steel brace under it? I think 1" thick wall square section steel tubing laid under it would be needed to pull the cupping out. The bolt holes in the steel need to be elongated so the top can shrink and expand without splitting. The steel needs to be set into notches in the cabinet top and secured to something substantial, preferably the cabinet sides, or additional framing/reinforcement inside the cabinets. Or knee wall if any.
All that aside, was the top finished the same top & bottom before install? A good finish on both sides is the first preventative measure against the differential uptake of moisture.
I'm not encouraged by the fact that it was apparently already cupped in the shop; it indicates that he really did not know what he was doing. If it doesn't start out table-flat how does he expect it to become flat?

Casey

"When the moisture content changes more on one side than on the other, it cups."

Not necessarily.

Yes, yes. I thought it best not to overcomplicate this.

jon1270 has done a good job explaining the situation. In the article linked, the two most important paragraphs and ones that explain all that's happening are,

Wood never stops moving
"Wood in service is exposed to both long-term (seasonal) and short-term (daily) changes in relative humidity and temperature of the surrounding air. Thus, wood is always undergoing at least slight changes in moisture content. These changes usually are gradual, and short-term fluctuations tend to influence only the wood surface. Moisture content changes can be retarded, but not prevented, by protective coatings, such as varnish, lacquer, or paint. The objective of wood drying is to bring the wood close to the moisture content a finished product will have in service (Chs. 12 and 15)."

Wood moves differently in each direction
"With respect to shrinkage characteristics, wood is an anisotropic material. It shrinks most in the direction of the annual growth rings (tangentially), about half as much across the rings (radially), and only slightly along the grain (longitudinally). The combined effects of radial and tangential shrinkage can distort the shape of wood pieces because of the difference in shrinkage and the curvature of annual rings. The major types of distortion as a result of these effects are illustrated in Figure 3-3."

One option would be to have used quartersawn wood instead of plainsawn. Quartersawn tends to have most distortion in thickness and less tendency to cup or twist. But q/s wood is expensive because of additional handling and waste during sawing process. It would have changed the figure of the wood. It even may not be available in all areas at all or in all thicknesses.

"It's safe to say it's got less moisture on the concave side, or more moisture on the convex side. "

No, it is NOT safe to say that.

The wood could be uniformly dry throughout and still be cupped.

Brick,
That could be so, but indicative of very shoddy fabrication procedure. The cupping was either
a) built in via inadequate preparation of the lumber (not jointed straight, flat, without twist and lacking square edges)
-or-
b) cupped after the assembly, which I'd say 85% of the time would have to be attributable to differential moisture, the rest of the time to reactive grain structure.
Mostly these warpage issues can be controlled for. But if a customer requested a top made from slash grain hackberry wood, I'd refuse the job because I know it's an un-winnable battle.
Casey

"cupped after the assembly"

It may have cupped after assembly as the moisture content became MORE uniform.

You need to read and understand the Wood Handbook.

Brick, you're being pedantic. Casey understands this stuff quite well, as do I. I'm not saying that the points you're making are wrong, because they're not, but you're making this harder than it needs to be for the purpose of addressing the OP's question. The "You need to read and understand" stuff is uncalled for.

So there.

See where I said "differential moisture"? Yeah, I get it.
Casey

I'm the OP and I've been following, or trying to follow, the responses. Let's pretend I'm in 3rd grade and a slow learner that doesn't understand technical terms.

The countertop was installed exactly one week ago. Since then it appears that the cupping has diminished. With your trained eyes you might pick it up, but the average person would never see it. The countertop is attached to the base cabinets of the island on two sides. The third side is a rounded radius which is where the stools will go. This is where the fabricator would like a few brackets installed (3). When you press down with all of your weight there is slight give, very little - there was more last week. We opted for a mineral oil finish; it has only been oiled on one side. If I oil the bottom will this help? There seems to be differing opinions on this so I'm confused.

In any case, the top looks absolutely beautiful, but I'm concerned that in a year or two I will have problems. I paid $2700 for the countertop, including template and installation. There are no cut outs. The fabricators shop is located in an old mill with a dam in the back; it is very damp. In fact, it smells a little moldy. Could this have been a factor?

I don't want to go to war with the guy, but if he delivered less than what I should have received, I will. I'm not looking for perfection, but I am looking for something that is going to endure for the long haul.

What is my prognosis? Is my countertop terminal or will it live for the next 10 years.

Thanks again to all of you. You know your stuff.

Since you're using mineral oil, finishing the bottom won't make much difference. Mineral oil doesn't do much to inhibit moisture transfer. If you were using a varnish or other film finish, it would be a different story.

The fabricators shop is located in an old mill with a dam in the back; it is very damp. In fact, it smells a little moldy. Could this have been a factor?

Yes, absolutely. It sounds very much like he's storing wood and working in an environment that, while picturesque, is pretty far from ideal in a technical sense.

If the counter is flattening out, that's a good sign. I'm presuming that the concave surface is the top surface -- yes? If so, what's going on is that the moisture content was high when the counter was installed, the top surface lost extra moisture faster than the bottom surface because the top is exposed to open air & perhaps sunlight, while the bottom surface is screwed to the cabinet. The differential in moisture loss caused temporary cupping, as Casey suggested, because the top surface shrank faster than the bottom. But, now the moisture content on the bottom surface is now slowly "catching up" to the top surface, flattening things out again.

At some point the moisture content throughout the slab will finally arrive at an equilibrium with the humidity levels in the house, and thereafter it should be pretty stable. Support brackets under the overhang sound like a good idea, but you might want to wait until the MC stabilizes first.

"If you were using a varnish or other film finish, it would be a different story."

While finishes may slow the movement of moisture in and out of the wood, they do not stop it very well.

Even if you finish every side.

Finishing only one side can exaggerate the wood movement when the humidity changes, but it will eventually come to equilibrium.

The wood has 24 hours a day to come to equilibrium.

This is easy.

Ask the nice man to come back and install the steel brackets he thinks are appropriate to support the countertop. $2700 should include that.

Because the cupping has diminished already, to the point you say the average person couldn't notice, i don't really think it is going to be a bad problem. Once you move in and keep the house climate controlled, the wood will reach equilibrium. An 1/8" of cupping over 4' is no big deal.

Glue and water re-introduce moisture to the wood.

It is possible the reason for the cupping in the fabrication shop was the guy washed the glue off with water and it soaked in the top side more than the bottom. If he starts out using properly dried wood, this issue is self-correcting. When I make a large glue-up, I'll flip it over a couple of times a day as it dries. I find this minimizes the cupping.

If you live in a desert climate and have woodworking, do not use an evaporative (swamp) cooler. Only use air conditioning. Swamp coolers will destroy fine woodworking in a few years. They put way too much humidity into the air, and during the monsoon season the wood swells, then quickly dries out in the fall as the dry desert air returns. That is why so many Southwestern homes have the "rustic" look with distressed wood finishes.

Wood is a very anisotropic material.

That means it does not have the same properties in all directions.

Wood barely changes dimension along the direction of the figure (what would be height in the tree).

It does change across the figure (parallel to the ground) and if you are on a line that goes towards the center of the tree (radial) the movement is less than on a line more parallel to the growth rings (tangential).

If you made a perect cube from solid wood, as soon as the moisture content changes it will no longer be a perfect cube.
If the mopisture content returns to the same level as when the shape was cut, the wood will revert back to a perfect cube.

These shape and size changes never stop in wood.
They will occur over and over as the moisture content varies.

If you look at Figure 3-3 in the Wood Engineering Handbook it shows how the shapes change, laid against a trees structure.

There is not a lot you can do to prevent the movement, so a lot of things are done to accomodate it.

By using large panlels ofg wood that have room to move, and smaller stronger pieces to make a frame to hold the panel the movement of the who;e structure is reduced greatly.

A 30 inch wide frame and panel door is only going to widen as the thick stiles on each vertical edge change size.
Since they are a fraction of the door width, the movement in this direction is greatly reduced.

The panel is free to change size in the grooves it is trapped in because it is not tight.
Extra room is left between the edges of the panel and the bottom of the grooves to allow for changes in size.

If the panel expands excessively, it can simply force the doors rails and stiles (the thicker framing) apart.

If you try to fasten wood to something that does not change the same way in the same direction (even cross grain construction) something is going to give.

Trim moldings are often fastened at one place to allow movement of the material they are fastened onto without splitting the molding or the panel of wood it is applied to.

Plenty of damage occurs as wood shrinks between fastened points.

Wood is much stronger in compression than tension.
When the wood dries out and shrinks between to fasteners that do not move it can split.

Hardwood floor strips are only fastened on one side.
The other side is held down by the tongue and groove of the boards.
This allows each board to change width as the moisture content varies.
Dry with open joints during heating season with low humidity, damper and tighter during a cooling season with higher humidity.

Wider board move more since the movement is a percentage of the board width.

The issue is being magnified by the very large size of the project, but all wood surfaces in your home will be adversely affected by an uncontrolled environment. You can't make any final judgments about any of the issues until the AC is on and has been for several weeks. You will need to make sure that you run a whole house humidifier in the winter, and use your AC in the summer. This will minimize the movement issues in all wood surfaces in your home, not just this counter. Your wood floors and cabinets need humidity control as well. Some cabinet manufacturers refuse to warranty their cabinetry unless a relatively steady state of humidity is being kept in the home.