Noob question, sorry but there's no clear answer that I could find. 
I'm seeking a rod that is flexible enough to be wound up but which would prefer to be a straight line.
Imagine one of those auto-erecting tents that fold up into a round bag, but in this case would fold up to around 15cm diameter. Something like that would serve that purpose when piped into the outline of fabric.

I think 1, 2, or 3mm carbon rod may do for what I need but I'm not sure.

Thanks.