[mfront] Implement the CamClay stress potential

[thelfer]

@MManicaM, @cbsilver, @nagelt, would you have a look at this page: https://thelfer.github.io/tfel/web/CamClayStressPotential.html

[cbsilver]

Dear @thelfer , thank you very much for setting up this nice overview! Here are my remarks/comments:

1.1) This is, in my eyes, the standard convention in continuum mechanics and thermodynamics. That's fine. To the contrary, in geomechanics it can be confusing when some so-called "mean stress" p is defined with opposite sign. But we don't do that.

1.2 & 1.3) The word "pressure" seems to be missing at several places. (...the hydrostatic is ...)

1.2 and further) It might be more convenient to use the quantity v=1+e_0 which is defined as Total volume per solid volume ( = 1 + pore number e_0). Further, v (or e) evolve with (elastic) deformation. So it is our assumption to keep this constant or handle the v explicitly during a time step. We need to state this somewhere.

1.5) It might be a bit confusing using the tensor s both for deviatoric stress and strain. Why not call the deviatoric strain \mathbf{eps}^{\text{el}}_{\text{D}}? That would improve clarity.

1.5.1) Maybe add in the headline mu=const. 1.5.2) Maybe add that... ...this spurious pressure-shear-coupling for MCC is questionable and might not be intended. ...unsymmetric stiffness tensor implies energy sinks or sources. Hence, it should be clear for the reader that this case should really be avoided.

2) In all the Cam clay literature I read so far, kappa is always called swelling line slope. We should do so too, but of course keep the nice explanation as unloading/reloading slope.

[thelfer]

Thanks for the feed-backs @cbsilver !

1.1) This is, in my eyes, the standard convention in continuum mechanics and thermodynamics. That's fine. To the contrary, in geomechanics it can be confusing when some so-called "mean stress" p is defined with opposite sign. But we don't do that.

I have always used the other convention, in particular in ductile failure.

1.2 & 1.3) The word "pressure" seems to be missing at several places. (...the hydrostatic is ...)

I have fixed this.

1.2 and further) It might be more convenient to use the quantity v=1+e_0 which is defined as Total volume per solid volume ( = 1 + pore number e_0). Further, v (or e) evolve with (elastic) deformation. So it is our assumption to keep this constant or handle the v explicitly during a time step. We need to state this somewhere.

That an interesting point. This may mean that one shall add an option associated with this hypothesis. @nagelt, @MManicaM, any interest to support the general case. Note also the in-progress work that we started with @kuateric here: https://thelfer.github.io/MFrontGallery/web/CrushedSaltKorthausBehaviour.html which shows how we could take the evolution of the porosity into account.

1.5.1) Maybe add in the headline mu=const. 1.5.2) Maybe add that... ...this spurious pressure-shear-coupling for MCC is questionable and might not be intended. ...unsymmetric stiffness tensor implies energy sinks or sources. Hence, it should be clear for the reader that this case should really be avoided.

@nagelt, @MManicaM, it would be very nice if we could have your insights about this discussion. Bibliographic references would be great too. In particular, I would like to exhibit the unrealistic results obtained by keeping mu constant.

2. In all the Cam clay literature I read so far, kappa is always called swelling line slope. We should do so too, but of course keep the nice explanation as unloading/reloading slope.

To be honest, I don't have enough experience to choose. @nagelt, @MManicaM, what do you think ?

I would be great if one of you could take the time to discuss the physical meaning of those kappa and maybe discuss how to identify it (and maybe describe an MTest test that could be used to interpret classical data to find kappa, for example).

[thelfer]

@cbsilver BTW, if the void ratio is not considered constant, we also loose the ability to define a non incremental behaviour and all the thermodynamic framework is also lost.

[cbsilver]

Yes, I am aware of this. However, I am assuming the void ratio to be constant during a time step. Of course, this way the formulation is explicit w.r.t. the void ratio. But this is fine as long as the void ratio changes only slightly during the time step, which is most the case.

[thelfer]

Yes, I am aware of this. However, I am assuming the void ratio to be constant during a time step. Of course, this way the formulation is explicit w.r.t. the void ratio. But this is fine as long as the void ratio changes only slightly during the time step, which is most the case.

It does not change the fact that I will not be able to use a non incremental form in this case.