
Re: How do I input viscoelastic material data?
Peter Hanaway Nov 29, 2010 2:05 PM (in response to Peter Hanaway)I see that 27 people have viewed this, but no one has offered a response yet. I've been digging and am getting close to answering my own questions:
There are 2 ways to input viscoelastic data. One option is to do a relatively simple measurement of stress relaxation (i.e. measure the force when a sample is subjected to a constant displacement ) and input the data for this curve directly under "Tables and Curves" under "Materials". SWSimulation works with shear modulus and bulk modulus, so some translation is needed to get force and displacement into shear stress and shear strain. I didn't pursue this approach largely because the time constants of the material I am using are so short that it would be very difficult to accurately capture them with the equipment I have. Personally, I don't know how you would directly measure "Bulk or Volumetric Relaxation" so I think it would probably be more practical to measure in tension and (with the Poisson ratio) convert to Shear Relaxation and Bulk or Volumetric Relaxation, but that is mere conjecture on my part.
The other option is to use a DMA (Dynamic Mechanical Analyzer or Spectrometer) to measure behavior of a sample under load at different frequencies and temperatures to create a "Master Curve." This is the approach I am using. Therefore, I sought the coefficients to a mathematical model that attempt to map the actual material behavior. The answer to my first question is that SWSim does use the Generalized Maxwell Model, with the following equation: G(t)=G0*[1  sigma gi*(1e^(t/Tau_sub_i))], where sigma is the sum from 1 to the number of elements used in the model; G0 is the instantaneous shear modulus; and gi is the shear modulus corresponding to the time constant Tau_sub_i. A parallel equation exists for the bulk modulus.
In my case, my material data was derived in the frequency domain, so I had to transform the equation for the model and do my curve fitting in the frequency domain. I got some help on fourrier transform, then obtained the various constants by writing a program (in LabView) that creates the Master Curves and allows me to match up the curve fit to the actual data. My testing was in simple tension, so I had to translate to shear and bulk moduli. I also had to convert my equation somewhat to obtain the instaneous value for the shear modulus as my equation was set up with G0 as the modulus at time=infinity, not time=0. In the end, I'm pretty confident I derived the coefficients that go into the SWSimulation equation above. So far so good.
It took 3 elements to get this equation to nicely fit the master curve I created from the measured data. So under the "Properties" tab of "Material" I first selected "Viscoelastic" for the Model Type. On the right side I selected "3" for the number of elements. Sure enough, the number of Shear Relaxation moduli in the lower part of the screen increased to 3. I believe but still need to confirm the following points: The derived instantaneous shear modulus (G0) goes into the Shear Modulus line. The Shear Relaxation moduli are unitless because they are a fraction of the instantaneous shear modulus, and therefore have a value of less than 1.
I did all this and ran some analyses. The results are not yet what I expected as they do not yet replicate my measured data. I will continue working on this and try to report back.