Fit of initial_modulus vs log(strain_rate) master curve using prony series
I am working on generating a strain rate based master curve from short-time tensile stress-strain data at different temperatures and strain rates.
After the initial fitting of tensile stress-strain data using 2 parameter equation, I got parameter initial youngs modulus vs strain rate for different temperatures. Afterwards, shifting along the horizontal axis (i.e, strain rate) was done to generate a Master curve for the initial youngs modulus. It was a success up till this point.
Moving ahead, I am required to fit this master curve (initial youngs modulus vs strain rate) using prony equation for the GMM model. Here is my fit for your kind reference:
Legends highlight 20 Maxwell elements for the GMM model each fitted considering each element per decade. In the end, 20 elements are fitted over the entire range of strain rate.
I did everything using Python. Ideally, the relaxation times for 20 maxwell elements should be in increasing order but this is not the case with my results.
If you see the graph below, which is relaxation times vs no. of maxwell elements, I experience certain waviness for elements ~11-16. I guess this is an abnormality and I did something wrong in my python algorithm written.
Could you please suggest something in this direction?
I am not convinced that you did something wrong with your Python code. When I look at your master curve it seems that the curve seems to my eyes that they cannot be horizontally shifted to create a smooth continuous curve. That may be why you see he waviness. Another way to say it, there is now guarantee that you always create a smooth master curve. The results you see may be an indication that the material is not a linear viscoelastic thermo-rheologically simple material.
I would not trim the curve/points unless you have experimental reasons for it. I have seen many DMA results that look really bad at higher frequencies, so perhaps there is a reason for doing that here too, but I always try to avoid removing data that I don't like.
I would be interested in exploring a non-linear viscoelastic material here. That may fit your raw data better.