You can use Prony Series, but as far as I remember, you are limited to 12 characteristic times...

Thank you Vincent. the problem is how to convert the Maxwell parameters to Prony series. we have G-i and K-i and tau in ABAQUS, and I would like to know how I can get them from the table attached in the question.

Thank you.

OK. I never did that, but as a first trial, I would have set the K_i values to zero, assuming the viscoelasticty as deviatoric. Then I compute the shear modulus from the young modulus assuming the poisson coefficient as a constant. And you already have the characteristic times...

Nothing is detailed in the documentation of Abaqus? There is no example?

Dear Yassine,

as you mentioned, in ABAQUS 3 sets of parameters need to be defined for the viscoelastic material in terms of Prony Series i.e., ratios of shear and bulk relaxation moduli (g_i and k_i) and relaxation time (tau_i). However, you do not clarify your experimental setup to obtain the relaxation data as attached, i.e., pure shear test or combined test. If you conducted shear test (here in your data E_i=G_i), all k_i Prony are defined as 0. Seeing your attached data, I assume G_inf=0; therefore, shear relaxation moduli g_i=G_i/G0; where G0=sum(G_i) satisfying the relation:sum(g_i)=1. For sure, all tau_i in your data are remained for the Prony relaxation time.

If bulk modulus (or bulk relaxation modulus) contributes in your experiments, then you need to define k_i Prony in ABAQUS. To my best knowledge, many users consider constant bulk modulus for the sake of simplicity. In stead, if you want to improve your simulation, bulk relaxation ratios should be defined in ABAQUS, e.g for creep displacement. In this case, you can define instantaneous modulus E0=sum(E_i) and then compute G0 and K0 from Poisson's ratio (nu). The ratios (weighting) of g_i and k_i are defined similarly as above.

Dear Anh Tuan vu and Vincent Le Saux.

Iwould like to kbank you about your time and your help.It's work now.

Thank you

This help me

http://www.brown.edu/Departments/Engineering/Courses/En2340/Projects/Projects_2015/Final%20Project%20AS.pdf

this is even better

Article A Viscoelastic Constitutive Model Can Accurately Represent E...