Newton method for plastic dilation #5953
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This PR adds dilation-relevant terms to the Newton solver for both AMG and GMG methods. It has also modified the Drucker-Prager model to allow the user to specify a dilation angle.
I have carried out experiments on the strip-footing problem with the following parameter file:
strip_footing.prm.txt
strip_footing.cc.txt
It turns out that when using Picard method (and also the Defect Correction method) the relative residual can only be reduced to ~0.01, while the Newton solver can reduce the residual to ~0.0001 within 30 iterations. The different convergence behavior is reflected in the effective viscosity, as shown below.
However, the plastic dilation model is far from the best shape, because (1) the Newton solver only converges when "Newton residual scaling method" is turned on; (2) it cannot produce shear bands as sharp as elASPECT. Currently I don't know why.
There is another problem about the plastic dilation model: it works correctly only when the material is compressible. This can be explained by the derivation in the following pdf (Remark 1):
dilation.pdf
However, I tried to modify the effective viscosity by Eq. (26), but the result is incorrect. Again, I don't know why.
Anyway, I think this PR has made some progress. Please let me know if it is worth being merged @naliboff @bobmyhill @cedrict .