[CIG-SHORT] on the viscosity coefficient

Yuta Abe yuta-abe at aist.go.jp
Sun Mar 7 21:34:46 PST 2010

Dear Charles,

Thanks for your reply.

> I'm glad the final output matches the analytical solution.  Would it  
> be possible for you to describe the problem?  It may be useful as an  
> example problem or benchmark.

  On this problem, I applied Dirichlet's boundary conditions to a 3D  
medium, 330 km x 550 km x 132 km in volume, and solved for the  
relaxation of stress. The boundary conditions are as shown in Table 1.  
The analytical solution for the deviator stress tensor s_33 at time t  
is given by the following equation:

s_33(t)=( (n-1)*2*A*G*t + (2*G*e_33(0) )**(1-n) )**(1/(1-n))

where n is the power-law-exponent, A is the power-law-coefficient, G  
is the rigidity modulus and e_33 is the deviator strain tensor. By the  
way, the physical properties are as shown in Table 2.

Table 1
U=0 at X=X_min
U=0 at X=X_max
V=0 at Y=Y_min
V=0 at Y=Y_max
W=0 at Z=Z_min
W=39.6m at Z=Z_max

Table 2
Vp : 5291.502622 (m/s)
Vs : 3000 (m/s)
mass density : 2500 (kg/m**3)
n : 2.4
A : 3.17e-30 (Pa**-n/s)
e_33(0) : 2e-4

I hope these pieces of information are helpful.


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