I would also like to ask you whether there is any material that is flexible enough to form in your palm under small pressure, but tense when formed under strong pressure

Look into:

  1. non-Newtonian fluids, D3O material has been used in product design
  2. plastic mechanophores, most interesting for smartphone cases. Research is being done currently, I haven’t seen a commercial mechanophore plastic yet.
  3. nanomaterials that are activated electrically

The friction of your handle to the skin is also important - the handle will need to curl up smoothly rather than the edges sticking into the skin so I recommend using a plastic like 3mm polypropylene with live hinges or overmolded silicone for the hinges.

By the way, you can also take pictures while using the smartphone horizontally and clicking the volume ‘up’ button :wink:
People will generally don’t use this much because they have a less steady hand on the smartphone. So if you design proper indentations with grip areas in the side of the cover you may also have a marketable solution.

Thanks for all the valuable informations, I really appreciate it. And would 1mm polypropylene be enough? If not, maybe some alternatives to it as my goal is to preserve normal case thickness.
I don’t want to be so persistent but, assuming it works properly, how do you like the idea? Thanks!

Polypropylene living hinges.

Any material with some clever kerf patterns

Laminate process. Plastic or metal on the inside sandwiched between fabric or thin plastic on the outside. Similar to Surface and iPad covers.

The key will be how you keep it flat when not in use. How about a simple rotating & telescoping handle? I like your idea but have you explored others?

Thank you for those helpful informations!
Yes, I have explored other solutions, including rotating handle. I finally chose this one as it allows to keep the whole case thinner that in other options, makes it very easy to use, serves an additional feature which is a regulated stand and in my opinion it is the most visually appealing one.(like I said, I didn’t want the handle to be seen when not used) The only drawback of this solution is that it uses magnets, those magnets of course are not harming phone in any way, are relatively cheap but can destroy credit cards when moved closely and might repel some potential buyers.

Check this old post. Similar to what you are trying to achieve.

Maybe use elastic straps or tabs on the upper corners to hold the handle in place when not in use?