I would build it out of PVC plumbing pipe.
It will tolerate an arch or arc shape, with a hair dryer to help it.
It should be spray painted when you’re finished, as PVC pipe will break down in UV exposure.
We did this exact project! here is how - https://www.charlestoncrafted.com/diy-raised-cucumber-garden-trellis/
Here are a couple of tutorials for you from right here on Hometalk: https://www.hometalk.com/34793817/diy-vertical-raised-bed-with-trellis
Here is one: https://www.hometalk.com/28014881/raised-bed-and-trellis
I did this exact project - here is how https://www.charlestoncrafted.com/diy-raised-cucumber-garden-trellis/