**FEA Analysis of Butted Rings**

As any butted maille maker knows, there is a direct relationship
between how big a ring is (it's inner diameter) and how strong it is.
Likewise, there is a direct relationship between how thick the wire is and how
strong the ring is. So at first glance this might seem like a trivial
experiment. But I found it very enjoyable to do, because it puts concrete
values and comparisons on the table, and the fact that the simulation behaves as
we would expect gives us confidence in the results.

Finite Element Analysis (FEA) is a way to simulate the
deformation of bodies. With today's computing power, it is now easier than
ever to simulate the loading of virtual models to see how they will respond to
different forces.

For this simulation, I modeled a butted maille ring of different
inner diameters (IDs) and different wire thicknesses. I modeled
rings with IDs of 1/4", 5/16", 3/8", 7/16", and
1/2". Each of these rings was further modeled with the following wire
thicknesses: 12GA (.1040"), 14GA (.0800"), 16GA (.0625"), 18GA
(.0475"), 20GA (.0348") and 22GA (.0286")

To load the rings, I simulated a force directly on one of the
butted ring ends, vectored so as to open the ring. The other butted ring
end was used as a fixed surface, as shown here:

Using the FEA software, I changed the force exerted on the ring
end until the simulation determined that the ring had opened an amount equal to
1/2 of the ID. So for a 1/2" ID ring, the force was found that would
open the ring .25" for the various wire thicknesses.

Here is an example of the deformations for a 1/2" ID ring
through the range of wire gages.

Graphing the data provides expected, but nonetheless
interesting, results.

The first graph, "Ring Deformation Forces", shows how
rings of various IDs perform against each other. The graph clearly shows
that for a given ring diameter, the thicker the wire it is made of the more
force it takes to open it. Again "failure" is determined by the
ring opening to a distance equal to 1/2 of the ID.

The ring also allows us to compare rings of one ID against rings
of another ID of the same wire thickness. For example, we can see that a
1/2" ID ring made of 12GA wire requires less than 150 pounds of force to
fail, but a 1/4" ID ring of the same material requires over 300 pounds of
force to make it fail! So ID obviously makes a difference in the strength
of the ring.

But we can also see that wire thickness makes a big
difference. The graph below shows us, for example, that a 1/2" ID
ring made of 12GA wire requires nearly 150 pounds to fail, but making it out of
14GA wire requires only about 60 pounds. The 12GA ring is over
twice as strong as the 14GA ring.

The next series of graphs are also interesting. They
clearly show what happens to the strength of the ring as the ID changes but the
wire thickness is held constant.