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[GeoMechanicsApplication] Develop prototype of Coulomb model with several stress state types #14156

@avdg81

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@avdg81

At present the Coulomb model has been expressed completely in terms of $\sigma$ and $\tau$ (including the tension cut-off). In this way, the code could be shared between the constitutive law that applies to continuum elements (i.e. MohrCoulombWithTensionCutOff) as well as one that applies to discrete elements (i.e. InterfaceCoulombWithTensionCutOff). However, by adopting $\sigma$ and $\tau$ as the only acceptable stress state, two problems arise:

  1. We cannot transform a stress state in terms of $\sigma$ and $\tau$ back to principal stresses, since we have too little information. This is the problem that Gennady identified last week, and which needs to be resolved.
  2. We cannot express the compression cap in terms of $\sigma$ and $\tau$. That means we cannot add a compression cap to these two constitutive laws if we stick to a formulation in terms of $\sigma$ and $\tau$ only.

Therefore, we need to move towards an approach that can accept several stress states. This has implications for the individual yield surfaces (starting with CoulombYieldSurface and TensionCutoff) as well as the part where these yield surfaces are combined (i.e. class CoulombWithTensionCutOffImpl). It will have an impact on:

  • Calculating the yield function value (which receives a trial stress state).
  • Calculating the derivative of the flow function.
  • Determining the return zone corresponding to a given trial stress state.
  • Return-mapping the trial stress state on the corresponding yield surface.

We suspect that there will still be common parts, but they may look a bit different than how they look now. We've found it hard to write down which changes are needed exactly. Therefore, we propose to develop a prototype to simply experience all of the issues that we may run into. Once we've got a working prototype, we can write down which steps are needed for a clean implementation.

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