Fluctuations in Stress - Young's Modulus

Dear Users,

I am interested in determining the elastic modulus of polymers. I am following the below link to conduct simulations.

I am using a fix deform to apply a lateral strain in X-direction. However, stress (Pxx) shows large fluctuations.
After searching a few posts in the mailing lists, I have added fix ave/time based on Steve’s advice in one of the threads.
But that does not seem to help, still, there are large fluctuations in the stress. However, a lot of published papers show smooth stress vs strain profiles.

Could anyone help with this issue to obtain smooth stress vs strain profiles? I am pasting a few lines of input script.

Hi! Those published papers likely used moving averages in post-processing to smooth out the curves even more.

I also use ave/time to obtain smoother curves, but they’re still not “smooth”. I attached one of my input scripts I use to obtain Young’s modulus (called “N0228IFFRPlyYM1125.in”) and I attached the resulting stress-strain curve (same filename, but with “_Stress_Strain…pdf” after it). As you can see in my stress-strain curve, it’s definitely not smooth, but you can still determine the trend. I like to average data points however often my thermo dumps, which is usually every 1000 steps at 1 fs time steps.

Hope this helps,

N0228IFFRPlyYM1125_Stress_Strain_Data_sxx_etruex_Plot.pdf (43.1 KB)

N0228IFFRPlyYM1125.in (4.22 KB)

Dear Will,

Thanks for your reply and special thanks for sharing your scripts and an example profile with me.

I guess you have used ‘v_etruex’ and ‘f_sxx_ave’ for plotting the True strain vs True stress profiles.
Is it possible to get eng. strain vs eng. stress as well. I know there is a variable for eng strain (v_eengx) but can we determine eng. stress?

Also, your figure shows Young’s modulus of 1.6 GPa. Could you tell me which part of the data was used to determine the slope? Was it below the blue circle?

I am still wondering how could we smoothen the stress vs strain profiles to systematically study the effects of strain rates, chain lengths, etc. I am worried if it makes any differences with such large fluctuations.


Yes, the figure is true stress vs true strain (both in the x-direction). You can get engineering stress via the equation: sigma_eng = sigma_true / (1 + epsilon_eng) or via words: engineering stress is equal to true stress divided by the quantity of 1 plus the engineering strain.

The Young’s modulus in that figure is the slope of the first fitted line (below the blue circle).

You can reduce the amount of fluctuation by making your system larger, but you’ll still see fluctuations. If you’re trying to compare stress-strain curves at different strain rates, it would be easier to do another moving average (on top of the ave/time moving average) in post-processing. From the paper that your link’s information is from (this paper: https://doi.org/10.1016/j.polymer.2010.10.009), they were able to study the effect of strain rate on the stress-strain curves just fine (their systems were 20,000 to 200,000 united atoms).

Best Regards,

Hi again,

Thanks for your suggestions and these posts are really helpful.
I appreciate your help again.


Hello Will and LAMMPS users,

With support from Will, I am able to get much better stress vs. strain profiles.

Now, I am wondering is there any way to determine “% elongation at break” using the same profiles or even perform a different simulation.

Thank you very much in advance.

You may be able to use the same profiles if you actually see failure occur. If you don’t see failure, you’ll need to deform the simulation box to a higher strain. Percent elongation at break is change in box length divided by the initial length or you can just take the strain at which the stress drops to zero. Depending on the polymer, it may take a long time (high strain) for the polymer chains to actually break or slide free of each other. I recommend using a reactive force field like ReaxFF or a force field which uses the Morse potential if you want to study failure. Traditional harmonic bond potentials will give you issues if individual bonds are stretched too far because the energy will go to infinity (which is unrealistic).

Best Regards,

Thanks Will,

I am interested in modeling the biopolymers using the COMPASS force field. Doesn’t it give qualitative comparisons for % elongation at break with experiments at least?


I am not sure. You’ll have to check the literature. I’m not familiar with biopolymers (my expertise is polymer nanocomposites for aerospace and defense applications), but if the specific biopolymer you’re interested in behaves more like a thermoplastic, then compass may be fine. If it’s more thermoset-like, I recommend a reactive force field.