Mullins effect in the elastic material I was thinking on a experimental question, but I couldn't get the answer:
How can we measure how the Mullins effect influences in the pressure inside a balloon? (I mean that, if there is a formula, tell me!) 
 A: A good way to measure pressure inside a balloon is to create a setup with a balloon, a manometer (long thin liquid filled U shaped tube), and a three way valve. You increase the pressure in the balloon by pumping it up, then measure the pressure with the manometer. Keep increasing the pressure and measure the diameter of the balloon as you go. Let the pressure out, and repeat. You will find that the pressure-diameter curve keeps shifting, just as it does in the curves in the article you linked.
Key to doing this experiment properly is having a good technique for measuring the volume. I would recommend placing the balloon in a darkened room with a small bright source of light, casting a shadow onto a piece of graph paper. Or cast the shadow onto a piece of tracing paper and take a digital picture of the shadow. Or just take a picture of the balloon against a differently-colored background. The volume will scale approximately with the area to the power $\frac32$, but if you plot area itself as a measure of "strain", it would show the effect. In fact, since the area of the balloon surface scales with the area of the projected volume (for an object with reasonable symmetry), just measuring the projected area and not converting to volume will actually be better... 
There is one other thing to keep in mind - and that is the analysis given in this earlier answer to this question which relates to the fact that a balloon becomes thinner during inflation, and that this will affect the pressure as a function of diameter. But by repeated cycling and seeing that the curves shift you should be able to differentiate between Mullins effect and this other phenomenon.
