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Prony series with temperature dependent stiffness

Hello,

I have implemented a viscoelastic model (Simo/Hughes approach: Prony series for small strain)

in Abaqus using Umat and it works fine for dynamic isothermal simulations (I validated with the Prony series implemented in Abaqus).

Now, I want to consider thermal loads (I have temperature dependent stiffnesses from a DMA experiment).

How should I use these temperature dependent stiffnesses in the model?

In my code I only have a $G_infty$ = constant and the $g_k$ and $\tau_k$. Should I consider the $G_infty$ as funtion of the temperature using a table?

 

Many thanks

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