If your material is simple like Maxwell or Kelvin type or ganeralized Maxwell, then Rayliegh damping is the simplest way to model. look into my paper on Local Absorbing Boundary Conditions to simulate beaver propagation in unbounded viscoelastic domain for some explanation.

Ravi shankar Badry

Is it possible to model rayleigh damping in ANSYS or ABAQUS ?

Yes, this is simplest feature and should be available with any software. Please search in the manual for how to define. I have no experience with these two software.

Thank you Ravi shankar Badry

But our problem is to define Storage modulus (E') and loss modulus (E") in ANSYS/ABAQUS.

E = E' + i*E" ;

Loss factor = tan(delta)= E"/E'

Hi Manish Kumar Dubey,

Modelling of viscoelastic behaviour is not possible with Rayliegh damping for E = E' + i*E". This requires constant loss factor for all frequencies. My previous posts are not useful in such case. Below is some explanation for some understanding of simple models.

For Kelvin-Voigt type of viscosity: It is similar to stiffness proportional damping where the loss factor is linearly varying.

sigma = (E + i*w*n)*epsilon

E* = E'+i*w*n

Storage modulus (E') and loss modulus (w*n). Where 'w' is the frequency 'n' is the viscosity. The loss factor is proportional to the frequency ('w'), and 'n' is proportional to stiffness proportional damping. If 'Beta' is stiffness proportional damping constant and 'K' stiffness then

i*w*n = Beta*K

Similarly for Maxwell type materials the loss factor is inversely proportional to frequency.

Hi Ravi shankar Badry ,

As per your explanations I came to some conclusion about modelling the complex viscoelastic modelling using Rayleigh damping. Please suggest some possible corrections.

The complex viscoelastic constitutive model

sigma = (E'+ i*E")*epsilon; or sigma = E'(1+ i*eta)*epsilon;

Implies

[K'+i*K" ] * u in the equation of motion. (where, K" = eta*K' )

Hence this complex viscoelastic model can be equivalently represented with Rayleigh damping as follows

i*K"*u = C*u'; (where, u' is the velocity)

i*eta*K'*u =i* Beta*K'*w*u

Hence,

Beta = eta/w

Therefore, complex viscoelastic model may be equivalently expressed with Rayleigh damping having Alpha = 0, and Beta = eta/w