Bendable, rigid and flexible tubing?

I know the title is very oxymoronish, but I’m at an impasse with this prototyping project, so please bear with me.
For obvious reasons, I can’t reveal much about the project, but I’ll try to get my message across…

I’m trying to make a flexible frame that have an elastic fabric stretched over it. Basically the idea is to manipulate the frame into different shapes and study the geometry changes of the fabric.
So I need a tube-like material that will be bent into an oval-like shape. This shape will be the default, non-sprung state of the material. Basically this could be done with aluminium tubing, but the material has to have a high modulus (?) and significant springiness to it (think of a 3’ rod that needs to be bent to a perfect U-shape with significant force). I could make the frame from aluminium sections and use rubber joints to simulate, but I was wondering if there’s some material with the right properties for this?
Basically Nylon or fiberglass tubing have the right properties, but they are challenging to manipulate into the unsprung oval shape. Maybe I could CNC the oval from a thick nylon sheet?

Any suggestons and help welcome!

EDIT: Should mention that in this case cutting this piece from a sheet has one disadvantage: it’s a planar process, where the final shape I’m looking for should preferably have a doubly curved profile to it… A real nut cracker.

Carbon rods are great for these types of applications.
You can also devise a platform allowing for different configurations using two boards - wood or plastic sandwich board - for the stiff sections that on the ends have a series of connections you can mount flexible rubber profiles onto.
For automotive frames we sometimes create rough prototypes from PVC tubing, these are quite flexible.

If you are more specific in terms of the desired properties I can give you better advice.

Hint: look into gooseneck mounts and lamps. Normally there’s a solid state metal tube in there which you can just pull out. I’m not sure what metal is in there. FYI: Lead has the properties, but I doubt they use that (any longer).

Much appreciated!
Composite rods are definitely an option, unfortunately they’re readily available only in straight sections, which complicates things a little.
The gooseneck is halfway there, but lacks the necessary spring properties. If only you could combine the two…
ralphzoontjens, I’m basically trying to build a springy hoop. I can obviously use the platform to manipulate the shape a little but can you elaborate a little on your description of the platform?

Thank you Robin! Getting close!
I actually found a reference that’s pretty close to what I’m looking for:

Basically looking to make that frame part bend and flex in different ways…