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Viscoelasticity FEA at high frequency (250+ kHz) and small strain across short time

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My first post here. My apologies if Im asking an exceedingly foolish question. My apologies also, in advance, for the length of this post.

I have been reading a great deal about FEA of viscoelastic materials over the past week or so. This (PolymerFEM website and forum) is clearly a great resource! However, I have not really come across any threads (yet) that address several aspects of the situation Im looking at.

Specifically, material-wise, Im looking for a viscoelastic material that displays good damping characteristics for our application BUT also has relatively high stiffness for good transduction from the viscoelastic material to a (much stiffer, non-viscoelastic) material in contact with it. (Im seeking a high-|E*| tan(delta) material, in some terminology appearing in the literature.) Added complications are that the transduction will occur at relatively high frequency (250-500+ kHz) and across a very small time interval - 10s to 100s of micro-seconds, i.e. 1e-5 to 1e-4 seconds, a good thing is that the strains are very (very) small also - as small as 1e-10 and certainly no larger than 1e-8. Basic (potentially naive) general question: Can materials exhibit viscoelastic behavior - in particular, damping - at such high frequencies with such small strains across such small time intervals?

As a candidate material, Ive been looking at data for PMMA. (A number of posts here address this material explicitly.) Ive found a few references that had some Prony series data, some of which covers quite a few decades of time constants. However - and here comes, potentially, my first exceedingly foolish question (if the one in the preceding paragraph was not the first such question) - given the short time period of interest to me, wouldnt I need Prony series terms with relatively small time constants? I.e., ones close-ish to my time interval of interest? Im certainly not interested in what might be happening at 1e2 (or even 10 or 1) seconds, let alone, 1e6+ seconds.

I did a run last night with a 3-term Prony series that had time constants of ~0.5, ~25, ~250 s. I didnt have shear relaxation moduli so (in Ansys) I selected Prony Volumetric Relaxation. The results appeared a bit odd to me. Not only did the ringing that I want to see disappear (or at least be mitigated) NOT decrease, the amplitude of the ringing increased (I cant tell about duration since the simulation cut-off time is early in the ringing) in comparison to the identical model with the Prony specification removed, i.e. just density, Youngs modulus, and Poisson ratio for PMMA carried over.

I did not specify hyperelasticity etc. Thats another question: Do I definitely need to? At these frequencies with these strains and this time interval, it didnt seem necessary.

Also, I noticed the execution (cpu) time was nearly 11X greater with the 3-term Prony series. Yikes! Does anyone know a rough rule-of-thumb for how much additional FEA cpu time is required per additional term in the Prony series? Given my short time interval etc., should I be able to get away with using only a single term perhaps?

I believe I have now well-exceeded common-courtesy in terms of post-length. Sorry about that.

Thank you all (or anyone) for your time and assistance and good day,


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Posts: 3998
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Hello David,

Welcome to PolymerFEM. Here are a few comments in response to your questions:

There are certainly materials that dissipate energy at high frequencies, but the energy dissipation typically goes down with increasing stiffness.
The specifics of what you are looking for are not commonly discussed in the literature.

Yes, you need the Prony series constants to be in the right domain of time. Otherwise they would not do anything.

I dont quite understand what you mean by ringing.

Yes, you need either elasticity or hyperelasticity AND (linear?) viscoelasticity.

The 11X run time seems odd! I would expect more 1.5 to 2X.


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Posts: 124
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Joined: 17 years ago

Hello David,

I do hope I am not being rude or generally inappropriate, may I suggest a very useful reference, Viscoelastic solids by Prof. R. Lakes.

In my view there are very few people with the kind of detailed knowledge to answer your questions with reference to material selection and characterisation at fast frequencies, and Prof. Lakes is certainly one.

PS. I am not in any way related to Prof. Lakes, but Give to Caesar what is Caesars..