Orthotropic elasticity

[endJunction]

Use local coordinate system for the coordinate transformations. If no coordinate system is provided, the usual cartesian coordinate system is assumed.

Only 3D case is implemented and rudimentary tested in this PR.
Another unfortunate thing is that the local coordinate system must be passed through the process' interfaces to the solid material creation. This can be resolved by creating the materials independent of the process; definitely not this PR.

Commit-wise review is easier, I think.

Changelog updated.

[nagelt]

at this stage, i.e. after back-rotation, you can toss out the last two columns & rows in the 2D/AXI calculations ... then we have made no further assumption on coordinate systems.
So Q and S would remain 6D, and you return the block (Q S_inv Q)<4,4>

Alternative is to always have 3 coincide with z, for example ..

[codecov]

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[wenqing]

It is better to add the following explantation:

Note: \f$\nu_{21}\f$, \f$\nu_{32}\f$, and \f$\nu_{31}\f$ are calculated by the symmetry property as
\f$\nv_{21}E_1=\nv_{12}E_2\f$, \f$\nv_{32}E_2=\nv_{23}E_3\f$, and \f$\nv_{31}E_1=\nv_{13}E_3\f$ 

[ThieJan]

Should be poissons_ratios.name.c_str() here

[ThieJan]

I have been testing it with one of the Benchmarks in the 2018 book. Without setting of local coordinate system the benchmark looks fine. I will add it soon to the test set.

Switching the canonical directions to incorporate the local coordinate system gives unexpected results. For example I changed the test in this PR only by setting

...
    <local_coordinate_system>
        <basis_vector_0>e2</basis_vector_0>
        <basis_vector_1>e0</basis_vector_1>
        <basis_vector_2>e1</basis_vector_2>
    </local_coordinate_system>
...

and displayed the elasticity tensor C in SmallDeformationFEM.h:271. The output is

0.234279 0.320592   1.1344        0        0        0
0.591862   0.2836 0.234279        0        0        0
  0.2836  1.17756 0.320592        0        0        0
       0        0        0        0        0        2
       0        0        0        2        0        0
       0        0        0        0        2        0

I think it should be at least symmetric?

[endJunction]

@ThieJan Thanks! It's an error in my code. Pushing fixed implementation with the original test now extended to coordinate permutations (xyz -> yzx -> zxy) and updated Poissons ratios and Young's moduli.

Keeping 'WIP' tag until first non-trivial example with skewed coordinate system is running.

[TomFischer]

The source code looks reasonable. Didn't check the tests. ⏩

[ThieJan]

I succesfully checked the current implementation with two examples of transversal anisotropy from the 2018 benchmark book.

You could merge them from my copy of this branch: https://github.com/ThieJan/ogs/tree/OrthotropicElasticity

One of the variations uses coordinate vector permutation while the other is rotated by a non trivial transformation. All four are checked against the analytical solutions presented in the book. So far, documentation for the web page is missing.

Writing the project file, I came up with a feature request ;-) It would be nice to add a possible input for transversal anisotropy to the project file. I found the parametrization of the full orthotropc elasticity tensor sufficiently error prone to add a tested project file interface for the current implemenation.

[endJunction]

All tests included, and code rebased.

[ogsbot]

OpenGeoSys development has been moved to GitLab.

See this pull request on GitLab.