# Determining elastic limit for a nonlinearly elastic material, to be used for calculating chord modulus (i.e. Young's modulus) in tensile testing

I have a protein material that is nonlinearly elastic; from the get-go, the stress-strain curve shows quite an immediate curvature.

I have to use chord modulus (reference to ASTM E11-04).

The problem! How should I choose the 2nd point to get the chord modulus, by plotting from origin to this 2nd point? The 2nd point should be the point of elastic limit; how do I find it?

My solution:

1. I calculate the chord modulus at increment of 1% strain;
2. I compare the mod calculated using 1% strain as elastic limit, and the mod calculated using 2% strain as elastic limit;
3. if the difference is <5%, then I continue my increament to 3%, get the mod, and compare this new mod to the mod calculated using 1% strain;
4. I keep doing this until the difference is >5%; then that strain will be my elastic limit.

I ran this for quite a few samples and most of them have elastic limit (determined by my method) to be either 4 - 6 %.

Is this the right way to go about it? Does anyone has reference, papers, standards etc that show how to determine the elastic limit of nonlinearly elastic materials? Or how should I explain it?

Appreciate your help!

• You cannot estimate the elastic limit without running loading-unloading experiments. Those tests have been run extensively for common metals/alloys and standards developed (so you can get estimates for a loading curve). But that's not the case for new materials. Commented Sep 30, 2021 at 19:55

## 2 Answers

This is not an answer to your question, but to show the content of the linked article, which may provide the help you need.

The 2nd point should be the point of elastic limit; how do I find it?

By running load-unload tests.

i.e. load to 0.1% strain then unload. load to 0.2% strain then unload. load to 0.3% strain then unload. If you come back to 0% strain (or very nearly 0%) after the unloading, then you are still in the elastic region. If you come back to a high positive value, then you are in the plastic region.

For a linear elastic material with a clear proportional limit (i.e. starts with a straight line and then starts to yield), you can determine the yield strength purely from the loading curve (e.g. using the 0.2% offset method). But if your material is non-linear elastic, there is no way to tell the elastic region other than by load-unload and looking for plastic deformation.