Q. What can I do to prevent warping of some of my relief carvings? I add kerfs to the back, make certain I am carving on the proper side, and still some of the carvings warp. I use basswood almost exclusively, and most of my carvings are 8 X 10 X 1 inch.
Ivan sez:
Two important points here: Wood is a “living material.” It expands and contracts in response to the temperature and the humidity of its environment. Secondly, we’re dealing with a rectangular plaque cut from a circular tree with a variable ratio of sapwood to heartwood, depending on the size of the tree and the part of the tree the wood is cut from. Different boards from the same tree will cup at differing rates in different places. The main cause is “differential shrinkage” based on the position in the log each board is sawn from. In the hardwoods, tangential shrinkage is greater than radial shrinkage causing plain-sawn boards to cup towards the outside of the tree.

Of course you can use only boards with the rings 90 degrees to the surface of the board (quarter sawn) as A. However, quarter sawn wood is expensive. The generally available wood is plain sawn, or flat sawn, a good portion of it prone to cupping.
That said, there were several precautions that traditional carvers took to limit the checking and the cupping of their reliefs:
1.Leave more wood than you take away. Rule of thumb, the deepest point of the carving should be less than half the thickness of the wood. That may reduce some cupping but primarily keeps the thin parts from checking as the wood expands and contracts through the seasons. We know the thin parts shrink/expand faster than the thick parts, so avoiding extremes lessens the stresses which lead to checking.
2.On single boards (plaques that are not glued up), carve from the heartwood into the sapwood. (Put the cupped side against the bench, the convex side up.) A board cups towards the sapwood, and since a board may also cup towards the carving, the two forces may cancel each other out. I use “may” here a lot because, as above, the position of the board in the log dictates most of what happens to it.
3.On larger plaques, laminate the wood, flip-flopping the grain. A wide board can cup substantially, so to minimize the effects, it is cut in half or in thirds, depending on its width, the sapwood/heartwood directions are alternated so that the tendency of one segment to cup is counteracted by the opposite cupping of the next segment.

4.Carve away wood in the back of the carving to balance the stresses. This can work for some of the thicker carvings, but can be counterproductive if removing wood from the back gives you very thin areas that dry much faster than surrounding wood.
ILLUSTRATIONS:(Click to enlarge)
Here is a basswood board showing the tendency to cup towards the sapwood.

This carving was from a single board 9 1/2 inches wide. Even though it was carved sap side down, following rules 1 and 2, it still cupped. The growth rings show that the board is from the B position of the log above, prone to cupping. 
This carving, on the other hand, shows no cupping because it was laminated, alternating the sapwood/heartwood.

MY PERSONAL EXPERIENCE:
If the plaque is under eight inches wide and I don’t mind a little cupping, I’ll carve it sap side down, “leaving more wood than I take away.” This generally keeps the plaque fairly flat. However, if the plaque is wider than eight inches, and especially if the board is from a less stable section of the log, as shown by the pattern of the growth rings, I’ll laminate it, flip-flopping the grain. I’ll also leave more wood than I take away. That has proven the best precaution against cupping. I’ve done many reliefs using these two techniques through the years. Laminated reliefs that I carved 40 years ago still show no signs of cupping or checking.
OTHER SUGGESTIONS:
Make sure the wood is dry and acclimate it to the shop environment before you work with it. Wood that has more moisture than the environment will lose it faster in freshly cut areas and therefore will cup even more into the carving than it would if dry.
Keep in mind that Wood shrinks and expands side to side more than it does the length of the grain. A large plaque can shrink or expand several inches throughout the alternating wet summers/dry winters. If put in a frame, the carving should “float”–that is set in a way that gives it space to expand and contract. (I once got a call from a church about an altar screen that would crack in the winter. They would fill the cracks, only to have them reappear the next winter. The solution to the problem was easier than they realized. After I explained that wood is a “living material” and needed space to expand and contract, they realized that the screen had been mounted wrong—someone had anchored all four corners against the wall. In the winter the carving shrunk but the wall it was mounted on didn’t. By slotting the mountings to let the screen float, the opening and closing of the cracks was eliminated.)
I’ve talked to carvers who said they’ve straightened boards by putting them concave side down on the grass. The sun dries out the top side and the grass adds moisture to the bottom. I’ve not tried that, though my concern would be that the cupping might eventually return. I’d prefer glue the plaque up for long term stability.