# [Solved] Predicting Dynamic Moduli and Damping from B-B model

Hello Dr. Bergstrom,

For linear viscoelastic materials, we can measure their dynamic moduli and tan delta from forced oscillation tests and they should be strain-independent. Meanwhile, for nonlinear viscoelastic materials/composites, such as filled elastomers, we can still obtain the equivalent dynamic moduli and tan delta (I think rigorously speaking these terms are valid only in linear viscoelasticity) from forced oscillation tests, however they are strain-dependent (or stress-dependent). Since B-B model can well capture the large-strain and time-dependent stiffness and hysteresis of elastomers/filled elastomers, suppose we have all necessary material parameters for B-B model, how do we predict the dynamic moduli and tan delta of such a material? Or are there any references related with this topic? Thank you!

Rui

Good question. The BB-model can nicely capture the dynamic response of various elastomer-like materials. In your case, if you have the material parameters, then I can think of 2 ways to determine the dynamic behavior:

(1) Run a set of Abaqus/ANSYS simulations with a sinusoidal input strain, and the extract the dynamic response

(2) Use a designated material model software such as [URL= https://polymerfem.com/content.php?9-MCalibration ]MCalibration[/URL].

-Jorgen

Thanks a lot for your suggestions, Jorgen! I will try Abaqus/Ansys to simulate the strain-driven dynamic test. By the way, how you evaluate this approach for determining the dynamic properties (dynamic moduli and tan delta)? For example, if given an isotropic linear viscoelastic material (maybe fitted prony series) and very small strain amplitude, are we going to have a reasonable prediction compared with theoretical values? I would go through the documents of these FEA packages on this issue, and do you have any other references? Thanks! ðŸ™‚

Yes, the BB-model can rather accurately predict also the small strain viscoelastic behavior, including the amplitude dependence of the storage and loss modulus. I gave a few presentations on this topic, and they may actually be available here on this website.

-Jorgen

Hi Jorgen,

I recently bought your book Mechanics of Solid Polymers (it is a really nice book!) and have the same question as Rui:

How do you get the complex modulus when using the Power Flow Model (see Figure 8.14 on page 391)?

I assume that you have developed a closed-form formulation of these dynamic moduli, as used in the MClibration software.

I am really interested in learning how to derive these kind of formulations. Have you published any paper about this so far? Or, is there any paper that could give me some guide?

Thanks a lot.

Dear Dr. Jorgen,

I see that your nice model can be calibrated from uniaxial tests, however, it works well for my shear tests too. It gave me very close results to the experimental simple shear data. I want to make sure of this. Thanks alot.

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