# Potential Energy Stored by Elastic

1. Apr 27, 2004

### Mikoden

Hi.

I'm trying to calculate the amount of P.E. stored by a piece of elastic. I've been looking for formulas but all i can find is how to calculate gravitational potential energy and spring potential energy. The piece of elastic is to be streched by about 1-2cm (from an original 30cm length) along the horizontal, and then twisted alot.

Any links to sites talking about this sort of problem would be handy, as well as any help that can be posted here. I'm after a formula of some sort to theoretically calculate the energy that is going to be stored, so that i have theory to back up my assumptions.

Thanks,

2. Apr 27, 2004

### HallsofIvy

Basically, an elastic is just a spring. The force necessary to stretch a spring (or elastic) a distance x is kx (k is a constant depending on the particular spring (or elastic)) and the work done (therefore potential energy stored) is (1/2)kx2.

3. Apr 27, 2004

### arildno

If you are interested in learning some of the basics of general elasticity theory,
"Continuum Mechanics" in the Schaum's Outline's series might be a good start.

4. Apr 28, 2004

### turin

The structural moduli will allow you to translate the strains (Young's for stretch and shear? for twist) into required forces. If you integrate these from some relaxed state up to the deformation you specify, then they should give you the work required to cause the deformation. If the order of the deformations has no influence on the work calculated (for which I am suspicious of the twisting), then you can interpret this as an increase in the potential energy.

I think the spring potential energy will only give you a first order approximation. If your strains are a significant fraction of original length, then I suspect that you will incur significant (at least) second order corrections.

5. Apr 29, 2004

### arildno

For the type of deformations you're talking about, I suspect that the
"small deformations theory" used widely would be invalid, and that stress-strain relationships should utilize the fully nonlinear tensor of relative displacements