[CIG-SHORT] problems about the Kelvin model

[Brad Aagaard]

FengLi-

It appears that you are trying to create a Kelvin-Voigt model 
(http://en.wikipedia.org/wiki/Kelvin-Voigt_material), a spring in 
parallel with a damper. In a Kelvin-Voigt model

   Strain = Strain_spring = Strain_damper
   Stress = Stress_spring + Stress_damper

This leads to

   Stress = 2*mu*Strain + 2*viscosity*Strain_rate

where mu is the shear modulus. The strain time history for a constant 
step in stress, Stress0 is

   Strain(t) = Stress0/(2*mu) * (1.0 - exp(t/tm))

where tm is the Maxwell time, tm = viscosity/mu.

In the generalized Maxwell implementation in PyLith, the Maxwell time 
for Maxwell element i is tm_i = viscosity_i/(mu*muFrac_i). We formulate 
it this way because muFrac_i corresponds to the fraction of the total 
elastic response associated with the viscosity of the Maxwell element.

If you set muFrac=0 for all of the Maxwell elements, then the Maxwell 
time is infinite and you end up with a purely elastic response. You need 
to adjust the muFrac parameter for one of the Maxwell elements to give 
you the Maxwell time that you want. Another way to think of this is that 
is the fraction of the shear modulus that decreases to 0 as time 
approaches infinity at a rate corresponding to the viscosity.

Brad


On 04/28/2011 06:23 AM, lf1981 at mail.ustc.edu.cn wrote:
> Dear sir : As the instructions of the Pylith manual,the Kelvin model
> may be obtained from Generalized Maxwell Models by setting the shear
> moduli of various springs to zero.  As you known, the KeLvin model is
> one spring in parallel with a dashpot.In order to obtain the Kelvin
> model,I set various parameters in the attached mat.spatialdb,and the
> 'dt' is 0.1 year, however ,it display the properties of elastic
> materials in the end. can you give me some instructions ?  Thank
> you.
>
>
> FengLi
>