Parallel network model for non-linear viscoelasticity

Dear Sir,

 

I am a user of Abaqus, specifically on biomaterials. I am very happy to see that the software has now incooperated the generalized Maxwell-Wiechert model (parallel network model, as the manual noted it) in the algorithm. 

 

However, I ran into a problem in using it and I sincerely need help.

 

In the past literature I found, almost all talked about the Maxwell-Wiechert model with a linear spring:

σ = k ε

 

However, in the parallel network, the spring is hyper-elastic, where

σ = f(ε)

 

And due to this non-linearity, the Boltzman convolutional integration cannot be applied.

 

So it is different. In order to get the material viscoelastic parameters, I would need to know how the derivation of the Maxwell-Wiechert model with hyper-elastic spring is done.  I went through the documentation, and see that this derivation has not been documented. I also went through our school library and tried to google around, but still with no luck.

 

Would you please help me in referring me to some publication or textbooks where I can get this derivation correct? 

 

Thank you very much!

 

-Shawn