Besides the useful chemical properties of rubber, the physical properties of rubber make balloons such an interesting and fun hobby. A balloonist with a knowledge of rubber physics is able to exploit that knowledge to get the most out of balloons-- for example, the physical properties of rubber allow balloons to inflate successively larger on repeated inflations, allow the inflator to know when to stop blowing, and for a balloon whose inflated surface area can be 100 square feet to be stored uninflated in your pocket.
The most important physical measurement a balloonist should be familiar with is the stress-strain curve of rubber. I'll frame this discussion in terms of balloons; stress and strain are important in all other materials as well.
Strain is defined as the ratio of a balloon's size to its original, uninflated size. A balloon blown up to twice as big as its uninflated size would then have a strain of 2. In broad terms, think of strain as "how big the balloon is."
Stress is defined as the force with which the rubber molecules in the balloon pull on each other. In familiar balloon terminology, stress can be thought of as "how tight the balloon is." Alternately, stress can be represented as the pressure of the air inside the balloon, multiplied by the surface area of the balloon.
So consider the following illustrative examples before we move on:
By definition, we will say an uninflated balloon has a stress of zero.
As the strain of a balloon increases, so (generally) does the stress, and vice versa.
Rubber that is very elastic and soft will be such that high levels of strain are possible at low stresses.
Rubber that is less elastic and harder will be such that high levels of stress occur at low strains.
The stress-strain relationship in a balloon is sigmoidal (it has an S-shape), similar to the figure below.
The way to interpret this diagram is as follows (it should already be second nature to anyone who's blown up a balloon, especially blown one up to popping):
At first, the balloon must overcome its initial stiffness. When you first blow into a balloon, it springs "to attention" and a little pressure builds up before the balloon finally starts stretching and inflating. This represents an initial increase in stress with no increase in strain.
Once the balloon begins to inflate, the curve flattens out-- this is because as you continue to blow, the pressure inside the balloon remains nearly constant while the balloon gets bigger. At some point, the balloon begins to tighten-- you feel it getting harder to blow into the balloon. This is when the curve turns upward again.
The more you blow, the harder it gets to blow; also, the balloon will slow down and eventually stop growing. If inflation continues, the balloon will get tighter but not much bigger (stress increases faster than strain).
Ultimately, the rubber fractures at the fracture point. In other words, the balloon pops.
Balloon rubber is an elastic material (this should be obvious). In other words, after a balloon is stretched or inflated, it returns back to its original shape and size when the stress is removed... at least ideally. In reality, rubber doesn't always go back to its exact original shape and size when it is unstretched. In fact, if you've ever blown up a balloon, let it sit for a while and then deflated it, you've noticed that the deflated balloon is a bit bigger than it was before. This effect is called creep or hysteresis. Technically, it means that the current stress and strain of a balloon depend on its history: whether or not it was previously inflated, how big, how old the balloon is, and so on.
A Hysteresis Example. The first time a balloon is inflated (up the top half of the above hysteresis loop), allowed to remain at the upper-right point and the deflated (along the bottom half of the loop), the uninflated stage of the balloon (stress equals zero) happens at a higher strain-- the uninflated balloon is now larger than it was before.
Balloonists can exploit hysteretic effects in one fun way: using repeated inflations and deflations, a balloon can inflate larger and larger each time. Using this technique, an 11-inch balloon (for example) can be blown up to 14 inches or more. Consider the following example from my own experience.
An example of uninflated hysteresis-- these two balloons are both 12" Perfect Products brand from the same bag. The red one is fresh out of the bag, while the pink one has been tightly inflated more than a dozen times.