modelling a hysteresis/viscoelasticity

[robobobo]

Hello everybody,
i have a problem. I make uniaxial tests (compression) with cylindrical elastomers without friction (I use Teflon). The strain is 8% and the frequency is 40Hz for example. I make 10000 load-cycles. Another test is with a strain of 4% and 10Hz. From the tests I get the loss modulus and the storage modulus for every strain and every frequency. I also get a hysteresis when I plot stress vs strain from the test data. Now I want to use abaqus to get a similar hysteresis like I get from the test data. I want to use a hyperelastic model (neo hook) with viscoelastic. My step I defined as sinusoidal boundery condition (displacement with amplitude-I hope it is right). Now I want to define the viscoelastic behaviour. I want to use the “domain: frequency” with “frequency: tabular” and “preload: uniaxial”. I put the frequency the strain and the loss modulus and storage modulus which I get from the tests which are depending on the strain and the frequency. when I start the analysis I don´t get a hysteresis. Only a linear response. But when I use time domain with prony I get a hysteresis. But I want to use the frequency domain. Can someone tell me where my mistake is? Or does such analysis only work with time domain with prony?
Thank you.
I hope you can help me.
And sorry for my bad English!

[Jorgen]

I think your approach should have worked just fine. From one of the output files you should be able to see what Prony series parameters that ABAQUS extracted. I recommend that you take a look at and compare the Prony series values for the two cases (time domain, and frequency domain).

Note that even with a linear viscoelastic model you will only get hysteresis and in a certain frequency range. Is your testing frequency in the same range as your experimental data?

- Jorgen

[robobobo]

Hello Dr. Bergstrom,
Thank you for your help.
My test are for example: 10000 load-cycles at one frequency (for example 10Hz) and at the same strain (8%).
I get a hysteresis from test data and with matlab (a program file) I can calculate the loss and storage modulus.
The problem is that I don´t have any prony series. (The prony parameter in the time domain I have choosen before were arbitrary).
To Abaqus:
The Material I defined like I wrote before: hyperelasticity with viscoelasticity => “domain: frequency” with “frequency: tabular” and “preload: uniaxial”. I put the frequency, the strain and the loss modulus and storage modulus which I get from the test.
With this procedure I always get a linear response.
Could I use the viscoelasticity only with the time domain under this conditions?
But how do I get “g_i Prony, k_i Prony and tau_i Prony” for the time domain?
Or could you tell me how else I can modelize a hysteresis, which is similar to the hysteresis from the test?.
I´m deeply grateful for your help!