[CIG-SHORT] sensitivity of Drucker-Prager yielding to time step

[Eric Lindsey]

Hi Brad,

In all cases (except possibly the dt=1yr case) it's yielding significantly
before the yield condition that I calculate. My initial stress state has no
shear stress, so it should be plenty far from the yield condition. The
initial isotropic compression is -100MPa, and the friction angle is 30
degrees -- for an inscribed Drucker-Prager yield condition, I found that
this implies yielding when the shear stress reaches 69.3 MPa. None of the
models yielded at that value (i.e. at the first time step that exceeded
that level).

I do have one confusion about the initial stress state. I was setting
sigma_zz_initial equal to the other two compressional stresses (isotropic
compression), but this technically violates the plane strain assumption
that sigma_zz = poisson_ratio*(sigma_xx + sigma_yy). Is this a problem? My
poisson ratio is 0.25, so I re-ran a few of the models and the calculation
of equation 5.101 for the case where sigma_zz_initial=-50MPa, in which case
I predicted that yielding should occur at a shear stress of 111.8 MPa. But
I get yielding at 40MPa for the dt=50years case, and 41MPa for dt=10years.

Sorry to send so much detail about this issue... your help is much
appreciated!

Eric


On Fri, Jul 11, 2014 at 1:41 PM, Brad Aagaard <baagaard at usgs.gov> wrote:

> Eric,
>
> How close is your initial stress state to the yield condition? At what
> time do you expect yielding to occur? Have you computed the yield condition
> (equation 5.101 on page 88/252 in the PyLith manual) from the PyLith output
> to see if it matches your expectations of when yielding should occur?
>
> My guess is that your load increment might be too big, so larger time
> steps push the response much further outside the yield surface. Intuitively
> I would think this would give a higher shear stress at yielding at larger
> time steps but that is the opposite of what you see. This is why I suggest
> going back to the yield criterion and starting from there.
>
> Brad
>
>
>
>
> On 07/10/2014 06:11 PM, Eric Lindsey wrote:
>
>> Hi all,
>>
>> I'm getting some strange results with the DruckerPragerPlaneStrain
>> material. In short, I'm finding that the value of shear stress at which
>> yielding/failure of the material occurs depends on my timestep...
>>
>> I have a 2D box and apply Dirichlet boundary conditions on all 4 sides,
>> and
>> an initial isotropic compression -- including the zz component as required
>> for models with plasticity. There is zero initial displacement, then I
>> apply simple shear to the domain, such that the stresses remain uniform
>> everywhere as shear stress increases.
>>
>> It turns out that the point at which yielding occurs depends significantly
>> on the time step. Initial compression is -100MPa. The shear modulus
>> (30GPa), displacement rate (1m/yr), and domain size (150km) implies a
>> stressing rate of 0.2MPa/year. Here is a table of some results:
>>
>> timestep dt (yr)         shear stress at yielding (MPa)
>> 50                               30
>> 10                               36
>> 5                                 58
>> 1                                 76.6
>>
>> The log file doesn't indicate convergence problems, but could this be a
>> tolerance issue? Or a more subtle solver problem? My .cfg files and a log
>> of the screen output are attached.
>>
>> Thanks,
>> Eric
>>
>>
>>
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