Viscoelastic properties of an alginate microsphere

[mysonsaysno]

I am trying to use Abaqus linear viscoelastic material model for modelling an alginate microsphere compressed up to a deformation under flat surfaces. The experimental data given are in the form of force vs time curve including compression and relaxation. I understand that in Abaqus there are two ways to use viscoelastic model (i.e. in time domain):
1. Input time relaxation data
2. Input Prony series data
and Abaqus asked for these above data as obtained from shear tests.

However, here I only have the force relaxation data (from compression tests only). Is there any way to obtain the shear relaxation or Prony series from the force relaxation data?

Many thanks,

[Jorgen]

If you have the force relaxation data, then I assume that you can convert that into (uniaxial) stress relaxation data.

You can then convert the uniaxial stress relaxation data into shear relaxation data if you know something about your material. For many materials the shear relaxation is much more significant than the volumetric relaxation. In those cases you can simply ignore the volumetric relaxation and convert the uniaxial relaxation to shear relaxation by dividing by a factor of 3.

- Jorgen

[mysonsaysno]

Thanks Jorgen,

Am I right to understand you meant that we can convert the force relaxation data into uniaxial stress relaxation data (and then relaxation modulus) if we also have the measured contact area? Unfortunately, we dont have these data. Would it be possible to convert without the contact data?

Many thanks,

[Jorgen]

If you don't have contact area information then you can perform a reverse finite element simulation to determine the Prony series.

That is:

(1) Assume a Prony series
(2) Perform a FE simulation of you material and geometry
(3) Extract the force relaxation response
(4) If the simulated relaxation response is not correct then adjust the Prony series parameters using some optimization method, and goto (2).

- Jorgen

[mysonsaysno]

By the procedure you advised, I am wondering if we can find a unique set of values of the Prony series? For example, even for a simplest model of viscoelasticity in Abaqus (1 Prony series) we need to find g1 and tau1, and a value for Young modulus as well. But they are mutually affect the simulated results.

Many thanks,

[Grant]

I would suggest using a closed-form elastic solution for compression of a ball between two flat plates to back out instantaneous values for your elastic constants, and then fitting a Prony series to those values. You'll need relaxation-type data to get the values you need for a Prony series. If your data are rate-dependent or in the form of creep (instead of relaxation), you're going to be in trouble because the values you have to work with are Prony coefficients, which is meant for a time series. Good luck!