Labeling overlapping nodes automatically

[mallickrishg]

@brendanjmeade This is a problem related to automating the labeling of nodes of fault segments that intersect. Consider a geometry of a wavy fault in a rectangular box (attached image), I was wondering if you had suggestions for how to come up with a general scheme to label which fault nodes overlap between which fault elements? So far, this has been easy because I only dealt with sequential elements and the first and last fault elements had free/unconstrained nodes.

With closed loops, it's a bit different but possibly simpler since there are no unconstrained nodes - the first and last element end up sharing a node.

For intersecting faults however, I think this might be a problem. In the figure below, elements 32,33 & 38 have a common node and similarly 14,15 & 46. I will think about this today.

[brendanjmeade]

@mallickrishg I've created a modified triple junction notebook:

https://github.com/brendanjmeade/bemcs/blob/main/notebooks/example_triple_junctions_120.ipynb

Overview:

• The model geometry is now with each branch equally oriented at 120 degrees from one another
• There is now areal visualization of the displacements and stresses for each of the cases (displacement magnitudes and second stress invariant too)
• Many variables have been renamed for consistency. The most general change is that mat and vec indicating matrices and vectors appear as suffixes in variable names. It's getting there!
• The current model is set up with kinematically consistent slip.

Things I think I've learned:

• For the kinematically consistent slip rate case stresses are very, very nearly continuous at the triple junction
• For the kinematically consistent slip rate example exam Cases A, C, and D are effectively identical.
• If the slip rates are made inconsistent but the geometry retained Cases A, and D are effectively identical but Case C can be quite different.
• The stresses at the triple junction do not appear to go singular for any of these cases, even when the slip rates are set arbitrarily.

Questions and ideas:

• If you look at the bottom most cells you can see that I've tried to do the same calculation with constant slip elements. However I don't think we have a function that does the constant solution for elements with arbitrary orientations. I think we're still using the _no_rotation function for constant slip. Did you build a rotated constant slip function as you did for the quadratic case? We should have a notebook documenting the use of these for just a single element that is not aligned along the x-axis.
• Just above the attempt at a constant slip example, I've written in words some vague idea about a slightly different approach to solving this problem. Maybe it's case E. At any rate, I haven't even written out the algebra for this yet so don't look for any implementation.

All in all, I'm still not sure we have a solid solution to the triple junction problem. We may, and I just haven't realized it yet, but I'm just not sure.

[brendanjmeade]

Both of triple junction approaches built by @mallickrishg are looking good and now have comparisons with a constant slip model. Some findings:

• The constant slip model looks acceptable if all slip rates are chosen to be kinematically consistent, but it's got a strong center singularity otherwise.

• Case A, and D look very similar. Whichever is more generalizable may be the better one.

• Qualitatively, triple junctions are still interesting but stand out less (as compared with the constant slip case) with quadratic elements and @mallickrishg's continuity approach.

[mallickrishg]

Can we submit the 2nd invariant plots as new images for the rorschach test? Or at least a journal cover photo? It's beautiful!

[brendanjmeade]

There are so many technical details and pictures are going to be an important way to tell the story and draw people in to listen to the ideas!