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# How to calculate the dynamic modulus from cyclic compressive indentation test?

## How to calculate the dynamic modulus from cyclic compressive indentation test?

(OP)
Hi Everyone,

I am working with cartilage and I have performed a dynamic test by simply applying 20 sinusoidal cycles of compressive strain with constant amplitude which results in a same sinusoidal form of stress response with a phase lag. The software gives me the Time, Displacement of the top indenter, and the load cell force output. I want to calculate the dynamic viscoelastic parameters, e.g. Elastic modulus, Loss modulus, Dynamic Complex modulus. I start by calculating the phase lag which is the time difference between the strain and stress peak values of each cycle.

As we know the cartilage shows viscoelastic properties like rubber. So, if you plot stress Vs. Time you will see the stress peak values is decaying by the increase of cycles until it reaches to a steady state after almost 10-15 cycles in my case.

Now my question is that should I calculate the viscoelastic parameters of each cycle separately and then take an average of all 20 cycles? Or should I consider only the steady state cycles? In other words, what is "σ0" in σ (t) = σ0 sin (ωt + δ) ? Is it the peak stress of each cycle, meaning that for instance, I have to calculate 20 Elastic modulus values and take the average? Or is it just the peak stress values for the steady state cycles (in my case after 10 cycles I get the stead state condition) and I only need to take an average of the steady state cycles?

I hope I've explained it clear enough.

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