Here are some pictures of two of these truss rod assemblies, and how they go together. These are in a guitar length, for 25 1/2" scale necks. These are double-acting single-rod truss rods, which are made into a "cartridge" assembly, with adjustment at the heel end via a spoke wheel. The whole assembly is cast solid in epoxy in a special mold. These are installed by routing a tapered trough in the neck and gluing in the whole assembly, while gluing the fingerboard on.
Anyway, you can see the two vertical aluminum plates on either side of the rod. These are an option for my clients who want additional stiffness in the their necks. The standard models have maple strips where the aluminum is on these. As I mentioned above, the plates are made from 6061 aluminum, 0.070" thick. They stand vertically and are wedge-shaped, the same as the whole cartridge, starting at 3/8" deep at the anchor end (which ends up between the nut and the 1st fret) and tapering to 5/8" deep at the heel.
The plates are simple stiffening beams. Making them thin and tall gives them more stiffness per weight added, as compared to putting a wider shallower bar up against the underside of the fingerboard. The plates could even be thinner than 0.070" and be nearly as stiff. Even 0.030" thick plates of this same depth would provide plenty of stiffness for the job, as long as they are fully supported on either side to prevent them from buckling. I used 0.070" plate for these because it worked right for the stack up of these parts.
The tapered depth and the additional saw slots along the top of the plates vary the stiffness along the length of the neck, which is what I want. As the string tension is applied, I want the neck to curl up into a particular shape, with most of the curvature in the 0 to 5th fret zone and very little curvature from the 5th to the heel. The tapering stiffness of the plates, combined with the geometry of the truss rod, cause that to happen. The truss rod, of course, allows you to adjust the amount of curvature.
Now, if I were installing this style of aluminum stiffening plates directly into a neck, rather than in this cartridge assembly, I would rout or saw a 1/4" wide slot x the 3/8" to 5/8" tapering depth. The aluminum plate would go into the slot, with a slice of maple tightly beside it to fill up the 1/4" width. All set in with hard epoxy. Putting in a 1/4" thick aluminum plate would be a waste of weight, even in aluminum. From an engineering standpoint, what makes it stiff in this case is the depth of the plate, not the width (thickness).
And yes, this same idea can be used with other materials than aluminum. If I wanted to use carbon fiber, I would make up plates similar to these aluminum plates, like 1/16" wide x 3/8" to 5/8" deep, installed about the same way. Carbon fiber TOW stranding, set into epoxy resin. That's how I make the "back straps" on most of my other truss rod installations. But, aluminum is simple and very light weight for its strength.