[CIG-SHORT] Kelvin-Voigt viscoelasticity

[Charles Williams]

Dear Satoshi,

The setup you describe below looks correct to me.  The one problem you may encounter is that with a large shear modulus you will end up with a very short Maxwell time.  This will unfortunately restrict your calculations to very small time step sizes.

Cheers,
Charles


> On 7/01/2016, at 2:11 PM, okuyama.satoshi <okuyama.satoshi at jaea.go.jp> wrote:
> 
> 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.
> 
> -------------------------------------------------------------------------
> 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.
> -------------------------------------------------------------------------
> 
> Again, thank you for smart (and simple) solution!
> 
> 
> ---
> Satoshi Okuyama
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Charles A. Williams
Scientist
GNS Science
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PO Box 30368
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New Zealand
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C.Williams at gns.cri.nz


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