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# Prony series determination in ABAQUS

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(@malcheda)
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Joined: 15 years ago

I have uniaxial stress relaxation data at several temperatures for a mold compound material (epoxy-based thermosetting polymer). A master curve was constructed by shifting these relaxation data. Now what I am trying to do is expressing the relaxation modulus as a Prony series.

Since ABAQUS/CAE (I believe ANSYS as well) requires shear and bulk relaxation modulus, I needed to convert uniaxial relaxation modulus to shear and bulk modulus. Simply I used the relationship G=E/2(1+nu) and K=E/3(1-2*nu) with assuming nu=0.3 (I dont have data for Poissons ratio). My questions at this point are:

1. Is it still valid to use those formula to convert E(t) to G(t) and K(t) in case of viscoelastic materials?

2. Is it safe to use a fixed Poissons ratio? If so, is the assumption of nu=0.3 appropriate for thermosetting materials? I know that nu=0.5 is typical for elastomers.

In order to input relaxation test data in ABAQUS, viscoelastic material input requires normalized shear/bulk modulus (i.e. G(t)/G0 and K(t)/K0). However, since they are normalized values, G(t)/G0 and K(t)/K0 become identical and essentially the same as E(t)/E0 when the above relationship about E, G, and K is used. So I was wondering whether I followed correct steps.:confused: Is it necessary to have both shear and bulk relaxation modulus for FEA? (maybe a silly question)

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Posts: 37
(@lamvuong84)
Eminent Member
Joined: 16 years ago

yes, the formulae are valide also in case of viscoelasticity.

no, namely the Poisson ratio itself is a viscoelastic relation in such a way

that it has low values for small times and a larger value, probably 0.5, for

long times and/or elevated temperatures. For calculation purposes it migth be

suitable to furnish nue(t) as function of time t and, thus as function of temperature T, in a similar and appropriate manner than seen from the relaxation Youngs modulus E(t).

Is it necessary to have both shear and bulk relaxation modulus for FEA?

No/Yes, to my oppinion is should not be necessary in any case - at least for most of the practical cases it is sufficiant to fix the bulk modulus as a constant. It may be reasonable to consider the bulk modulus as a constant over a broad range oft temperature and times, respectively, while at the same time the shear modulus may be considers as a viscoelastic property.

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Topic starter
(@malcheda)
Active Member
Joined: 15 years ago

Follow-up questions:

How do you determine the Poissons ratio as a function of time and temperature? And, how do you deduce G(t) from E(t) if you dont have data for nu(t,T)?

When you fix the bulk modulus what value do you choose? I guess K=E0/3(1-2*nu), where E0 is the instantaneous Youngs modulus?

Posts: 80
(@FrankMonkey)
Trusted Member
Joined: 15 years ago

You can take a look at the ABAQUS example Viscoelastic rod

Posts: 37
(@lamvuong84)
Eminent Member
Joined: 16 years ago

One solution to the posted problem may be as follows:

One solution to the posted problem may be as follows:

Let E(t) be

and let us assume that this is the only viscoelastic function which is known

and let n(t) be

with the following properties

so that we arrive at

so we may set for example n0=0.3 and n=0.498!

Then we are able to perform:

..

unfortunately all my formulae are gone!

Now I have tried to attach a word document with all my explanations

but Im not sure whether it is really attached!?

Posts: 80
(@FrankMonkey)
Trusted Member
Joined: 15 years ago

If you want to go the real hard way search for publications from

Professor Harry Hilton

Department of Aeronautical and Astronautical Engineering

National Center for Supercomputing Applications

University of Illinois at Urbana-Champaign

Urbana, Illinois 61801

Youll find a discussion of time-dependent Poissons ratio in his publications, including anisotropy.

I failed to specify in my previous posting that the example mentioned is listed in the Benchmarks Manual.

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