[CIG-SHORT] Kelvin-Voigt viscoelasticity

[okuyama.satoshi]

Charles,

Thank you for quick reply.

> The solution is to use a large value for the overall shear modulus, and 
> then assign the ratios appropriately.  Please let us know if you require 
> additional assistance.

How smart... I will never think of such solution by myself. I appreciate 
your advice.

Befor I try your suggestion, I will give an example in case someone do 
similar analysis in the future. Please correct me if I do something wrong.

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Vp and Vs can be written as follows;

Vp^2 = 2*mu*(1-nu) / ((1-2*nu)*rho)
Vs^2 = mu/rho

(mu, nu, rho) = (rigidity, Poisson's ratio, density)

So, for the material whose mu, nu, rho are 30GPa, 0.25, 2700kg/m**3,

Vp = 5773 m/s
Vs = 3333 m/s

If I consider another material, whose properties are

mu'  = 1000*mu
nu'  = nu
rho' = rho

then velocities are 

Vp' = 182574 m/s
Vs' = 105409 m/s

Thus, for kelvin-voigt material whose parameters are (vp=5773*m/s, vs=3333*m/s, 
density=2700*kg/m**3, viscosity=1e+18), I give following values as GenMaxwell 
model parameters;

vp            = 182574*m/s
vs            = 105409*m/s
density       = 2700*kg/m*3
shear-ratio-1 = 0.999
shear-ratio-2 = 0
shear-ratio-3 = 0
viscosity-1   = 1e+18
viscosity-2   = 0
viscosity-3   = 0

Parameter shear-ratio-1 is set to 0.999 so that the remain (0.001) corresponds to 
original mu (30GPa). 

I am not sure if mu'=1000*mu is huge enough. If not, mu' should be increased 
to, say, 100000*mu. But what I need is not mu' but the value of original mu. 
Using too large mu' may lead to loss of significant digits.
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Again, thank you for smart (and simple) solution!


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Satoshi Okuyama