Building closed loops with springy wire Background: I am a mathematician who is attempting to build some simple visual aids to assist in the presentation of my research. 

To build the desired models, I need two things:


Exceptionally springy wire.  By springy, I mean that it should quite difficult to put a permanent bend in it.  Guitar wire seems like it could be a possible candidate here, but I'm not sure.
A way to fuse this wire together.  It could be soldering, crimping, etcetera—I simply need to be able connect two loose ends together in a permanent way.  (Note: Any sort of connection that allows the wire to twist will not suit my purposes.  I need to maintain torsional pressure on the wire.)


I've already managed to build models of what I want using the wire manufactured for high tensile cattle fence (you can get crimps that go with that wire), but the wire is so stiff that my models are too big to travel with.  Does anyone know of any potential material and/or methods I could use in place of the fence wire and crimps?  I'm at somewhat of a loss, so any advice here is much appreciated.

Not the most professional pictures, but this is what I have right now (banana for context):
What you are looking for is called spring steel or spring-tempered wire. Tempering is a process where the wire is hardened by heating which allows the resulting spring steel to return to its original shape, despite significant deflection or twisting. When you bend a spring wire, it will maintain a strong, circular loop without kinking anywhere along its circumference.



Product Search: Spring Tempered Wire

To close the the loop, you can use a wire crimp sleeve. They come in many many lengths and diameters, so it shouldn't be too difficult to find one that fits your needs.

 

Product Search Wire Crimp Sleeve