Question

Why does a rubber band not go back to its original length after it has been stretched?

Answer 1

Say the original length of the rubber piece is L0. Then twice this length is 2L0. There are two ways to calculate the ensuing strain. One is engineering strain e, which is defined as the change in length relative to the initial length:

e=L−L0L0

The other way is true strain ϵ, where the displacement is referenced to the instantaneous gauge length rather than the original gauge length as with engineering strain:

ϵ=lnLL0

The question asks what the true strain is for a displacement twice the original length. Therefore, in the equation above for ϵ take L=2L0. This gives ϵ=ln(2), or 0.69.

Therefore, the answer to the question is 0.69.

Incidentally, one advantage of using true strain over engineering strain is that true strain accurately characterizes strains in compression whereas engineering strain does not. Another is that for pulling a part in increments, the total true strain is the sum of the incremental true strains, but this isn’t the case for engineering strain.

Answer 2

 rubber band that has a 5 cm diameter (Assume a perfect circle). The rubber band is then stretched. The rubber band returns to it's original shape. The rubber band now has a 6 cm diameter. What is this effect called?

Is there a material that returns to it's original shape exactly and always or is that imp