When the Washington State University researchers looked through the literature, they came across research that described the development of a bellows that took advantage of origami, the Japanese art of paper-folding. The research discussed applications relating to medical stents, or even deployable solar sails for spaceflight — but Westra and his colleagues adapted the design for rocket fuel bladders
The basic concept of a bladdered tank is that the bladder makes it so that only propellant leaves the tank and so that propellant can be used even under zero g conditions. Compare with a bladder-free tank that requires settling burns and/or propellant management devices. There are advantages and disadvantages to the two tank designs (bladdered vs bladder-free).
Except in the case of a bladder failure, there is no chance of pressurant gas leaving the tank. (Bladder failure is generally catastrophic.) Bladdered tanks can also result in pockets of trapped and hence unusable propellant. The bladder can also be a mass penalty.
Bladder-free tanks can result in pressurant gas leaving the tank, and that can be catastrophic. The settling burn requires yet another set of thrusters. This adds complexity and adds failure modes. Propellant management devices have their own multiple failure modes. It's a pick your poison type of situation.