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!

  • 1
    $\begingroup$ 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. $\endgroup$ Commented Sep 30, 2021 at 19:55

2 Answers 2


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

enter image description herehttp://qpeng.org/publication/pdf/Peng_2014_nanoscale_silicane.pdf


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.


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