# [CIG-SHORT] on the viscosity coefficient

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

```Dear Charles,

> 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.

Yuta
```