What type of metal can bend repeatedly without breaking?
If you're looking to bend the metal to fit a knee then straighten it then bend it again, it depends on how sharp the bend is and how many cycles you need. A wire coat hanger will if the bend is not sharp go through a surprising number of cycles before it fails, but eventually it will.
You might want to consider a friction-based approach. Google "joby gorillapod" for one example.
If you're willing to go with a process and not a product, get some 10-gage or 12-gage copper electrical wire from Home Depot or wherever and anneal it after every use--you can anneal it with a burner on a gas stove--just get it red hot and throw it in a bucket of water. Cut a bunch of extras and do a week's worth at a time.
If you want to get fancy there might be a way to do what you want to with nitinol.
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