Mesh Sensitivity for pile-soil interaction

[[email protected]]

Dear STKO team,

The soil model behaves correctly next to the contact. See figure below. I have plotted until reloading. The soil is in failure at the top and retains residual strength until unloading. I do not see any issues with the behavior. Except if the plastic flow state causes the mesh sensitivity issue, which it should not.

Stress-Strain_PIMY.png (23.46 KiB) Viewed 4456 times

However, after examining the original model I uploaded (Newmark integration + skewed rectangular mesh refinement) I found that the constitutive behavior in that model was a mess as we got further from the interface (top graph in Figure below; moving away from the pile as: black line->green line->blue line->etc.).
I found a similar phenomenon happening in the improved model as well. (TRBDF2 integration + circular refinement) As I plotted the stress-strain response at the "interface" between the circular portion and the rectangular portion of the model it showed a reversed loading compared to what would be expected (2nd graph pink line : bordering element in the circle refinement) and it continues this bizarre reversed stress behavior outside of the refined zone as well. (cyan, blue, green lines) (red and black are for elements inside the refined circle)

Stress-strain2.png (58.72 KiB) Viewed 4456 times

Perhaps a circular geometry for the entire model would be the way to go?

Bence

[STKO Team]

Oh maybe I got where the issue is... however I do not know this model very well.
As you can see you have a softening branch (even if small).

As you may know, when you have softening, the strain tends to localize in a narrow band (localization band) that, due to the locality of the Finite Element Method, coincides with a layer of elements. So the band will always have a size equal to the characteristic length of an element.

So, upon mesh refinement, your band becomes thinner, and your material shows a more brittle behavior. This is very common in concrete or masonry modeling. That's why we use the so called "Fracture energy regularization".

Now you have a problem:
You do not define any softening, because the backbone curve is hyperbolic until gamma_max and flat after that limit value.
However, also perfect plasticity is dangerous as softening for strain localization, with an extra problem: you cannot regularize the fracture energy because it is infinite.
Also you may ask: whay sigma13 is showing softening while my backbone curve is flat after gamma_max ? Well your model is 3D, and what happens in sigma13 is not exactly what happens in the backbone, which is in fact the octahedral stress-strain.

unfortunately, if you use the autogenerated surfaces, you cannot avoid the last flat part of the backbone curve. You can isntead define a very high value for gamma_max so that you octahedral stress will only approach tau max, thus always showing a hardening.
Otherwise you can define your own backbone curve.

Also can you do something?
Plot the displacement (in the point with max disp) versus time-step-id
Plot the sigma_13-gamma_13 versus time-step-id (near the same point)
normalize both of them (Y axis with respect to their max value)
superimpose those 2 graph, and let's see if the displacement starts diverging close to the peak point.

[[email protected]]

Sadly I only have one model that I ran for enough time steps to show meaningful results. A model with the coarsest mesh. To test sensitivity I only ran the denser models to a point where I already saw large difference in lateral displacements compared to the coarser models.
The displacements don't diverge within a single model, actually. The displacements diverge with increasing mesh density only. So when a coarse model is compared to a dense one the dense will always have much larger displacements which is also obvious from comparing the two figures posted below.
Nevertheless, here are the plots you mentioned for Two models. Coarse model ran for almost a full load-uload cycle:

plots.png (48.68 KiB) Viewed 4439 times

And a denser model ran until 75% of the loading (contains no unloading)

plots_Denser.png (43.51 KiB) Viewed 4441 times

Bence

[STKO Team]

This is exactly what I meant.

From this plots you've seen that the displacements and strains in each model, start increasing on the onset of softening.
What I think is that, in the denser model, the rate of increase in displacement is larger.

if you superimpose the plots (displacement or strain only) from the corse mesh (first figure) with the plots from the dense mesh (second figure) , without normalizing them, probably you will see small differences before the softening point, and larger differences after.

If this is the case then you should try to review your backbone curves.

[[email protected]]

Thank you a lot for the helpful suggestions!

Bence

[STKO Team]

You are welcome!