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Viscoelastic material modeling


I have a question regarding viscoelastic materials and property definitions through prony series.

If i am not wrong ,the values wi and τi of the series can be expressed either in terms of time domain or frequency domain.

Having the prony series expressed at time domain, how can the relaxation tensor be expressed? Do i still need to perform

Laplace-Carson transformation, of the time dependent relaxation and creep functions or their prony series expression is enough,

so i can get the full relaxation tensor (isotropic case) as:


 G(t) = G0(1-Σν1 (wi*(1-exp(-t/τi))) (similarly for K(t))

and the full tensor: Gijkl(t) = 2G(t)Idev +K(t)1⊗1

Idev = deviatoric of fourth order unit tensor

1 = second order unit tensor

⊗ = tensor product


Thank you in advance.

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