There is jeweler in my town that makes what he referrers to as an "Eternity" bracelet. The bracelet is most often made by reusing gold ( many are made from old high school class rings), which is melted down and formed into wire that is 1mm to 1.5mm square. This wire is then formed into an oval that is slightly larger than the wrist. It is then fitted to the individual wrist. It is sized so that the bracelet is not able to fit over the wide part of the hand even when the thumb is turned in, but so that it can slide up and down the arm for about 3 inches. The wrist is then wrapped with a 2 inch wide piece of cloth. Next while the jewelry squeezes the ends together the two ends of the wire are SOLDERED together forming the bracelet. This makes the bracelet permanent, it can not be removed in any manner, except to destroy the bracelet, hence the name "Eternity Bracelet".
There are several variations to the basic design but the most common is shown below. This Jeweler who started out to make one, just to see if he could, has been surprised by wide interest. I believe this interest is because it does not represent one symbol, but instead has a different meaning to each wearer. Husbands give them to wives, Mothers to daughters, Wives to husbands, or people have them had from old family jewelry.
A simpler design is to take a gold or silver chain that
is the proper size for the wrist and instead of a clasp use a "Jump Ring"
to close the chain around the wrist. There are many different types of
chain that would work for this.
My wife always had a problem breaking out from rings since
they lay so close to the skin on her finger. I designed a bracelet for
her to take the place of a wedding band. Also like yours, it had to be
permanent if it was to be a wedding band. It is an oval shape about 1/8
of an inch thick and just under a 1/4 inch wide. She has worn it for 29
years and the marrage has lasted, so something must be right. This bracelet/wedding
band has been secured to her left wrist with a pin, which was tapped into
place with a small metal hammer (tack hammer). This caused the pin to spread
out on each end, causing it to become permanent. I know of the Cartier
bracelet. I purchased her one on our twentieth aniversary, at a jewelry
store on the French side of St. Maarten Island. It is gold and is held
by a screw, which is kept in place with a drop of "superglue" to prevent
loss by the normal movement and vibration of a persons hand and arm. She
has worn it on her right wrist ever since.