Dear Greg, 

>>To clarify the loading question, in my case this is equivalent to a
>>body force -- the temperature gradient -- over which I have no control
>>since it arises from the solution of mass and energy conservation
>>equations. How could the arc-length method be applied in this case?
>>Can you give me an example or reference?
>
>Arc-length is normally applied to incremental displacement and
>load vectors during Newton-Raphson type iterations and it can be applied =
>to any process. It is a method of controlling both load and incremental =
>displacement during Newton type iterations.

The driving physical process is an inflow of hot fluid at depth. The
rock matrix in contact with the fluid heats up and expands. This is a
dynamic process and solution proceeds by marching forward in time
together with Newton-Raphson iteration within timesteps. So the "load"
for the stress equilibrium equation is really a body force arising from
the temperature (and pressure) gradient. I am solving simultaneously
for 4 unknowns, fluid pressure, temperature, and 2 components of
displacement.

Are you suggesting that I should employ the arc-length method _in addition_
to time-stepping? That would mean employing it within timesteps?  Maybe
I have not understood the meaning of the arc-length method. Can you
give me a reference to an application, preferably of a similar type?
I read about the arc-length method in Kardestuncer section 4.70.


>>I agree with you that there is clearly instability. When things go
>>wrong the usual pattern is that the iterations appear to converge for
>>a while but then diverge. The timestep is cut back maybe several times
>>then perhaps the solution will converge once or twice then it fails
>>again and so on. Finally I end up with very small timesteps and
>>unphysical results, eg negative pressures.
>
>This description may indicate that some negative terms appeared in
>your material stiffness matrix (softening, the matrix is not positive
>definite). This may also be the case of if E modulus becomes very
>small.  Problems with material stiffness matrix could easily explain
>change of pressure from possitive to negative or other erratic
>phenomena

Pressure here is fluid pressure which is normally of the order of
100 bars (at 1 km depth). So yes, something is seriously screwy
when the fluid pressure becomes negative!! My solution method
uses Gaussian elimination with pivoting. There are checks in place
for the matrix being singular or nearly singular. So far none of
these have been flagged. But I agree, there is something funny
going on in the matrix... 

Thanks for your insight into my problem,

Cheers,
Roger.
[log in to unmask] 



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%