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problem regarding critical initial time step in poroelastic material during consolidation process.

Dear all,

I have a problem regarding critical initial time step in poroelastic material during consolidation process.

As we know, for implicit integration method, it's unconditionally stable. But for the consolidation of poroelastic material,

there is a critical time step t_critical derived by Vermeer and Verruijt (1981), this has also been inclued in the abaqus software (http://129.25.22.58:2180/v6.7/books/exa/default.htm).

As far as I know, using a initial time step delta_t<t_critial, there will be ossolication in the pressure results.

But I read some paper "Ill-conditioning of finite element poroelastisity equations" by Massimiliano Ferronato et al (2001),

where they mentioned that, "the concept of t_critical is basically related to the difficulty of finding the solution rather than to the accuracy of the solution itself, which may prove qutie accurate also for time steps smaller than the t_critical provided that one is willing to pay a sufficienttly high computational cost".

 

From above statements, seems the problem with a initial time step deltat<t_critical is that it might be difficult to find the solution due to the ill-conditioning.

 

My problem  is more complex than that, I am aiming at modeling the brain CSF circulation system, using qutie different permeability for CSF filled regions (such as ventricle and Subarachnoid space) and brain tissue. Model CSF as purely Darcy's lay, and brain tissue as poroelastic material.

From the results, I didn't see any ossolication in my pressure solution. But should I trust the pressure result? I am interested in the pressure in 200 seconds, but according to the t_critical equation, the estimated t_critical might already be larger than 200 seconds, which is rather contradictory. This makes it impossible that I have a initial time step less than t_critical.

According to Massimiliano Ferronato et al (2001), seems it's trustable, but according to the Abaqus manual, one should always have a time step larger than the t_critical?

 

Would appreciate if can get some suggestions on this.

Thanks a lot.

BR,

X Li

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