This short tutorial will show you how you can (almost) instantaneously calibrate an Abaqus linear viscoelastic material model storage (E’) and loss (E”) modulus data from a DMA test using a direct solver available in MCalibration version 6.2 (and later).

The first step is to read in the experimental data into MCalibration. The experimental file should contain 5 columns: mean strain, strain amplitude, frequency, storage modulus, loss modulus.

The next step is to specify the fitness weight factors for the storage and loss modulus. Note that linear viscoelasticity may not be able to accurately match both the storage and loss modulus, and the weight factors can be use to specify if the storage or loss modulus should be emphasized. You should also verify that that loading mode is selected properly. MCalibration can use any of the predefined loading modes (e.g. uniaxial, biaxial, shear, etc). Finally, make sure that you check “Use a direct frequency domain solver)”. This will enable the new DMA solver for linear viscoelasticity which is crazy fast.

The next step is to specify the material model. In this example I will use an Abaqus hyperelastic material model with linear viscoelasticity. In this case we are only calibrating a material model to small strain DMA data, so the type of hyperelasticity does not matter much. The number of Prony series terms will be discussed in the next step.

MCalibration will now look at the experimental data and ask if it should set the number of Prony series terms based on the data. This is the recommended option. Press OK. In this case MCalibration will select 30 Prony series terms to cover the whole range of frequencies.

Setup the graph and then click Run Once. The results will then look like in the following figure. We see that the model predictions for the storage modulus as a function frequency are almost perfect. This is because MCalibration has already selected the hyperelastic and Prony parameters based on the experimental data.

If you would like to include also the loss modulus in he calibration, then you can simply click the Run Calibration button. The results is ready after a few seconds and shown below. In this case the average error is reduced further.

That’s it. That is all you need to do to (almost) instantaneously calibrate an Abaqus linear viscoelastic material model to experimental Dynamic Mechanical Analysis (DMA) data.

## 3 thoughts on “Instantaneous Calibration of Abaqus Linear Viscoelasticity using DMA Data”

sobeckiA very informative tutorial, Jörgen.

How did you collect the DMA data that span over 20 decades in frequency? Are these frequency-sweep storage modulus and loss modulus spectra master curves at a certain reference temperature?

/Pawel

jbRektorHello Pawel, I used time-temp superposition (TTS) from tests performed at frequencies between about 0.01 and 100 Hz. The material was a polyurethane. I plan to write another article about TTS in the near future.

/Jorgen

sobeckiJorgen,

I look forward to your article about TTS then. Does MCalibration offer the TTS curve shifting features to construct master curves?

/Pawel