Periodic Tesselations with Flat Surfaces

[lkuna24]

To create a tesselation/mesh such that the resulting structure is still a square/cube with flat surface but has periodicity. To elaborate, the +z face of the cube it would be exactly the same as the -z face, and for all the sides etc.
Resulting cube would have tesselations periodic across all faces.

[rquey]

The reason why non-cubic periodic tessellations have been preferred is that cells are not cut, and therefore there is no additional surfaces, etc. This is easier for generation, regularization (although it is not implemented yet) and meshing. Moreover, and from a general point of view, this should not cause problems from the solver side - the loading just has to be defined a little differently.

[yguilhem]

@rquey is right because "cutting" the topology of the grains with the planes corresponding to the cube limits will "artificially" add supplementary small edges. That would not be a problem if you are able to mesh (and compute) with a very small element size (smaller than the small edges emanating from the cut). Otherwise you will suffer from potential flat elements and/or varying element size.
Anyway it will for sure be less efficient than the current periodic tesselation method.

[xinliu09]

@yguilhem Thank you for the answer. It makes sense to me if considering the mesh quality and efficiency.

[yguilhem]

As a complement to my answer, small edges/faces emanating from the cut could vanish by applying regularization (not implemented for periodic tessellations). Nevertheless, regularization may lead to face flatness fault which is another source of difficulties for mesh generation.
Especially if too many small edges are identified by this process and have to be fused into a single vertex (and small faces fused into a single edge).

[xinliu09]

@yguilhem Thank you for the clarification. I was thinking about the voxel mesh approach. I know voxel mesh has been used in many RVEs with complex geometries. The good part of voxel mesh is that the mesh quality can be controlled, but it will cause the inaccuracy in the real geometries and maybe unrealistic stress along the interfaces.
Looks like the current design in Neper is the best one, it is just not very intuitive at first glance.

[rquey]

@xinliu09, note that even with a non-cubic periodic tessellation, the "voxel mesh" (-elt hex) will be cubic.

[RoadToDream]

May I ask why regularization is not implemented for periodicity case? Is there any concerns for implementation or it's just due to the schedule. I would love to help to implement this if there will be some guidance provided.

[dilekguzel]

Hi everyone,
To obtain Neper-based periodic microstructures on unit domains (with flat surfaces), we have developed an open-source software, Neper-Mosaic.
The goal is to use Neper-based tesselations and do the relevant cutting operations so that we generate a unit square/cubic periodic RVEs/microstructures automatically.

Learn more:
Code and Documentation: Neper-Mosaic
Detailed Explanation: Publication