Voigt material

Hi,



I am trying to modeling the shear wave propagation in a Voigt
viscoelastic material. I am using Abaqus CAE 6.8.3. The shear wave speed as a
function of frequency is of my main interest.



The way I input the
viscoelatic parameters in CAE is Domain->Frequency, Frequency->Tabular,
Type=Iosotropic, preload=None. The "Omega g* real" and "Omega g* imag" entries
are calculated as below.



Since the complex shear modulus of a Voigt
material is G* = mu1 + i*omega*mu2, where mu1 and mu2 are the shear elasticity
and shear viscosity.



Then the storage modulus Gs, loss modulus Gl, long
term modulus Ginf are:



Gs = mu1

Gl = omega*mu2

Ginf =
mu1





Then



"Omega g* real" = Gl/Ginf = omega*mu2/mu1

"Omega
g* imag" = (Ginf-Gs)/Ginf = 0



For example, if mu1 = 3 kPa and mu2 = 4
PaS, then the "Omega g* real" and "Omega g* imag" in 100-500 Hz
are



"Omega g* real"      "Omega g* imag"    f

0.8378                   0                            100

1.6755                   0
                           200

2.5133                   0                            300

3.3510                   0                            400

4.1888                   0                            500



I can try the
simulations but if I calculate the shear wave speed, the speed dispersion does
not behave like a Voigt material. Below are the shear speed for simulation and
theory:





f             Abaqus       Theory

100          1.752          2.105

200          1.719          2.782

300
         1.708          3.442

400          1.683          4.039

500          1.654          4.579





If you need more
information or the input file, please let know. Thanks!