# Thread: *Elastic and *Viscoelastic for prony series in Abaqus

1. Junior Member
Join Date
2006-04
Posts
6

## *Elastic and *Viscoelastic for prony series in Abaqus

Hi,

I have prony series in terms of Relaxation tension modulus (E) . I also have prony series in terms of shear modulus (G). My bulk modulus is constant(K).

As far as I can understand the abaqus manual, I can use in this case , * Elastic option with * Viscoelastic option.

*Elastic, Moduli= Instantaneous
Youngs' modulus (E at time= 0 from expression for E), Poisson's ratio (nu, poisson's ratio as defined from instantaneous modulus and bulk modulus using elastic relations)

*Viscoelastic , TIME = PRONY
(line 1
g1(RATIO OF G1/G0 where G1 is the first term in Prony series for shear modulus and G0 is the long term shear modulus), k1=1( K1/ K0=1 since my bulk modulus is constant), tau1

(line 2
g2, 0 (since all other terms in bulk modulus series are zero ), tau2

etc etc

Am I thinking right ?

Peeyush

2. sq
Member
Join Date
2005-09
Location
New Jersey, US
Posts
70
Almost!

The sum of the terms of the Prony series in ABAQUS must be less than or equal to one. If this sum is equal to one, the material will relax completely at long time.

If k1=1, you will not have a constant bulk modulus. You need to set k1=0.

3. Junior Member
Join Date
2006-12
Posts
6
Hi Peeyush,

It seems that we work in same topic. The difference is the relaxation data I have is relaxation modulus but not in the form of Prony seiries. At this moment, I am struggling with viscoelastic modeling, I hope you may give me a big hand.
1. What software did you use to form Prony series? For my case, I just enter relaxation modulus data ( actually shear modulus data) and let Abaqus does it internally.
2. Here is how I define my viscoelastic parameter.
2.1. Define elastic modulus and poisson's ratio as you did.
2.2 Define Viscoelastic, TIME = relaxation modulus data ( actually it was tranformed to shear modulus data)
2.3 Define temperture dependency usinf TRS (WLF equation (reference temperature, C1, and C2))
3. run program.

However, one problem came to my mind after I run program. What temperature was used in this running analysis? Say, relaxation modulus data was obtained at -10C, 5C, 25C, 40C, 55C degrees to for master curve. If the analysis is need to be done at 50 degrees, where to define this temperature for model? Or if this temperature is not constant through the model, how to define again?

Abaqus help file seems not to make it clear where to define the temeprature it is to be analyzed.

Thanks.

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