Total free energy going UP in Cahn-Hilliard simulation

[dschwen]

We have several reports of phase field simulations showing an increase in the total free energy. This should not happen. I was able to reproduce this issue with a simple input file (that utilizes ElasticFreeEnergy). I'm investigating this further.

Ping @tonkmr (as this may involve the TotalFreeEnergy Auxkernel)

[permcody]

Dude - you've discovered free energy! Forget nuclear power, dump all your money into this!
💰

[dschwen]

One issue are undeclared variable dependencies. This is an error a user can easily make. E.g. For a free energy F=c*V, where V is a chemical potential AuxVariable, we need to specify args = V to the CahnHilliard kernel. This is required for the kernel to 'see' the gradient of F due to the gradient of V.
I think my first move will be to add a runtime check that looks for potentially missing args. I cannot do that at construction time to populate args automatically, but I think I can at least add a check at initialSetup time to compare the set of existing derivative material properties and the specified args.
However, @tonkmr, there is another issue: The elastic energy depends on strain and free energy gradients can be introduced by strain gradients! I don't yet know how to compute the strain gradient yet and use it in the CahnHilliard kernel to generate the propper driving force. This is a huge issue right now.

Tagging @laagesen

[dschwen]

Let's look at a simple free energy, which is basically a ramped chemical potential

And lets assume so that the CH equation reduces to

Intuitively we'd expect a diffusion to the negative x direction, where the chemical potential is smallest. But looking at the CH equation the driving force seems to be zero! As

But in the weak form one differential operator is shifted to the test function and we get

Which does yield the anticipated result of evolving the concentration to shift to lower chemical potentials. Needless to say that I am confused.

Quicklatex.com

[jwpeterson]

@dschwen may be missing the boundary term,

[SudiptaBiswas]

Is this issue resolved? I noticed while coupling PhaseField and TensorMechanics, elastic energy goes up as applied load increases. This eventually leads to increase in total free energy and Cahn-Hilliard is not able to reduce it (probably tensor mechanics is governing). Is there anything needs to be taken care of in this case?

[dschwen]

We are working on this. Currently a term is missing in the elastic free energy derivatives. File this issue for further updates.

[SudiptaBiswas]

Thanks for the update @dschwen. I will keep an eye on this issue. Let me know if I can contribute to this in any way.

[dschwen]

@SudiptaBiswas we are working on this at #5631

[SudiptaBiswas]

Thanks @dschwen , I figured that out.

[dschwen]

Possibly related to not using displaced meshes. Cannot check due to bug #5750.

[dschwen]

I'm closing this, as we identified and fixed a number of issues here. Please open a new issue if this problem is encountered with a specific simulation setup.