Are there any helicopter blades that fold in the middle? Let's assume that, for some arbitrary reason, helicopter blades are too long for transport or storage. Folding them at the rotor hub, as is done with conventional folding helicopter blades, would still be too long and there is a need to fold them further. So, they are folded somewhere in the middle of the blade instead (or as well).

Do such folding helicopter blades exist? If not, has there been theoretical studies on how it could be done? What would be the impact on blade performance?

This is a question about the theoretical feasibility and difficulty of using such folding blades, and whether there have been existing studies or designs for it. As such, the practical applications and whether it would be worth it, or whether there would actually be a real-life scenario where this would be useful, should mostly be ignored.

(Bonus point if it is possible to deploy the folded blades simply by starting the engine, but this is probably too outrageously complicated to pull off anyway.)
Bending a helicopter blade in the middle is of course possible, but poses many serious problems and risks. The designers would look for different solutions first, like they did for the UH-60.

The blade loads are lift, centrifugal force, and twist. Manufacture the blade with modern composite technology, mount it with the fully articulated hinges that are usually a requirement anyway, and trust the blades with your life because a breakage would be catastrophic.

Any repeated action poses additional risk. Mounting a hinge and lock that operates every time, is not open to human error, and never fails - that is would be the quest for the folding blade designer. 

Of course a folding blade can be designed, like the folding wings on navy fighter aircraft. But not for some arbitrary reason. Only for a vital reason that cannot be solved in any other way.