"Structural" rubber band--no creep/stress relaxation?

[solobo]

I'm looking for an off-the-shelf "rubber band" to use for sealing the casing of a prosthetic component. The band would sit in a shallow groove on the exterior of a part to basically hold two halves of a cylinder together. The outer circumference is about 11 inches and I'd like the band's cross section to be about .375x0.05. The band needs to have some tension on it (not much, just enough to hold the fitted pieces together).

Any suggestions on material/type of band? I'm visualizing something in the proportions of one of those silicone "Livestrong" type wristbands, but I'm worried that silicone will get looser with time due to stress relaxation. The material will be exposed to sunlight and water.

Thanks in advance.