Dilatational Free Surface Boundary Conditions

[smithht]

Hi Damask users,

I have been trying to emulate free surface boundary conditions in the X and Z directions in my simulations. The Y direction is the loading axis, and I would like to keep that direction as a periodic solid material. To emulate these free surface boundary conditions, I have been trying to mimic the work done in the paper titled "Fourier-based spectral method solution to finite strain crystal plasticity with free surfaces." In this paper, a very low stiffness elastic material and a dilatational material are used as free surfaces. One of the samples in this paper uses an encapsulating dilatational boundary layer, which is very similar to what I am trying to accomplish.

I have been able to get a dilatational boundary layer working with a 10x10x10 voxel mesh:

5 voxel thick dilatational layer (red) added to mesh:

I am applying 1% strain over 100 seconds and 100 time steps. Simulation files can be accessed here:
https://panthers-my.sharepoint.com/:f:/g/personal/smithht_uwm_edu/IgCjp0UvVpC8TpILN6prCQ0tAdKnl0ZsbgHmZU6vZRL-UHk?e=6n6hJ2

I haven't been able to get a similar setup working on a larger sized simulation. This project I am working on has a mesh size of 234x351x237 voxels. I have scaled this down by a quarter to 58x87x59 to try to get a moderately-sized simulation running. Running this mesh on its own without the dilatational boundary works perfectly normal. It is just when I introduce the dilatational boundary layer that it stops working. I have tried adjusting the dilatational boundary thickness from 5 voxels up to 50 voxels on each side, adjusting the number of time steps, and adjusting the amount of strain being applied (down to 0.1% strain). I have even tried running a simulation that applies no load at all. All of these scenarios converge for about 10-50% of their time steps, and then it starts failing to converge. The only error I have received from Damask (other than max cutbacks taken) has been: "crystallite responds elastically, inversion error in analytic tangent calculation, at phase 3" (dilatational phase). Simulation files can be viewed here:
https://panthers-my.sharepoint.com/:f:/g/personal/smithht_uwm_edu/IgDvw0fmaXUBQpJZdTeLIuCKARUZqumArZPapHJ_g-f1B74?e=NItxE6

I am out of ideas to try getting these free surface boundary conditions working. Thanks in advance for your time and help!

[eisenlohr]

I am not fully certain which boundary conditions (BCs) you are actually applying, but would suggest to only use deformation BCs, i.e., avoid restricting the stress to explicit zero. The dilatational envelope will accomplish this...

Secondly, it seems that your elastic stiffness of the envelope material is much too high. The elastic and plastic properties should be match in such a way that the yield stress of the enveloping material is reached at a similar strain than the actual material that you are considering. So, if the envelope is a factor of 100 softer than the central material, then its stiffness also needs to be (about) a factor of 100 lower than the actual material's.

[smithht]

Thank you, @eisenlohr ! Using purely deformation BCs and proportionally matching the stiffness and yield stress fixed my convergence problems. Much appreciated

[tmaiti26]

Adding to what Dr. Eisenlohr, already suggested earlier. Couple of changes recommended

a) switch to spectral_polarization solver
b) reduced the magnitude of difference between elastic & plastic properties of the buffer layer

F101_t100_N100_f10.yaml changes

$ diff original/F101_t100_N100_f10.yaml modified/F101_t100_N100_f10.yaml 
1c1
< solver: {mechanical: spectral_basic}
---
> solver: {mechanical: spectral_polarization}

dislowin_IN625.yaml changes

$ diff original/dislotwin_IN625.yaml modified/dislowin_IN625.yaml 
38,39c38,39
<         xi_0: 300000.0
<         xi_inf: 600000.0
---
>         xi_0: 3000000.0
>         xi_inf: 6000000.0
41c41
<         h_0: 1000000.0
---
>         h_0: 10000000.0
129a130
> 

Result

 ===========================================================================

 increment 1000 converged

 ... saving results ........................................................

 ###########################################################################

 DAMASK terminated on:
   Date: 08/03/2026
   Time: 17:43:04

[smithht]

Thank you, @tmaiti26 ! These fixes help my convergence issues.