As a general rule, it's better to use the material you want to look at vs.trying to modify the pig's ear.
Given the latter, what metal are you hoping to patinate?

I have not purchased the metal yet. I want the look in this photo. Any suggestions?

Here is a link that might be useful: Chimney Cover

The best material would be Cor-Ten steel, which develops a coating of rust which becomes passive. Originally developed as a structural steel that would not require sandblasting/painting. May be difficult to obtain in small amounts.
Patina on virtually any other metal will require coating of some sort to maintain a steady state, and the coating is subject to breakdown.
What about plaster, concrete or ceramic molds/applique?

That is just the product I was hoping to find. With the right words "Cor-Ten steel" I was able to find chat rooms and suppliers.

Thank you so much Alphonse!

You're welcome. Maybe post a pic when you're done.