Quad dominant or all Quad mesh in 2D (preserving grain boundaries)

[MiguelVCarvalho]

Include the possibility of having Quad dominant meshes or All Quads meshes in 2D.

For example with the options:
-elttype quad_dominant
-elttype all_quad

Why: If studying intergranular fracture with cohesive elements, the grain geometry is of utmost importance. Currently, only triangular elements preserve the grain geometry, since with the option -elttype quad, a regular grid is created.
However, if the grains are modelled with an incompressible material (as it is the case of crystal plasticity), the standard tri 3 and tri 6 elements should not be used since they are highly prone to volumetric locking.
In this case, quad 4 (FBAR for example) or quad 8 elements should be used.

Case 1:
Gmsh enables the user to choose "Recombine all triangular meshes" while meshing a geometry. This will lead to a quad dominant mesh.
Example:

(in this case, it was able to generate only quad elements but sometimes, due to complex geometry, some triangular elements remain)

Case 2:
Gmsh enables the user to change the Subdivision algorithm to "All Quads" while meshing a geometry. This will lead to a mesh that only contains quad elements (the element size may reduce).
Example:

Disclaimer: These examples may not present the best meshes in terms of element quality but it was something done quite fast and only for demonstration purposes.

[MiguelVCarvalho]

To use the subdivision algorithm All Quads, the checkbox Recombine all triangular meshes has to be activated also. Otherwise, it will only break all triangles into 4 quads.

[Mahdieh-karami]

Sorry for asking too many questions but I faced this error for both .msh and .msh4 :

[rquey]

Update your Neper.

[Mahdieh-karami]

It worked, thanks. what about .geo file for 3D? Because the last .geo does not work on 3D.

[rquey]

It should... Maybe you need to adapt it, but a geo file works in 3D too.

[Mahdieh-karami]

Hi,
I tried to adapt it . I faced this errors but it gives a Msh file in which there are just finer Tet elements .

[rquey]

How would it translate in terms of entries in the .geo file? For tri/tet meshing, Neper uses this:

/* Options for the meshing: */
[...]
Mesh.Algorithm      = 6;
Mesh.Algorithm3D    = 4;
[...]
Mesh.SaveAll = 1;
Mesh.Optimize       = 1;

[MiguelVCarvalho]

Quad Dominant:

Mesh.RecombinationAlgorithm = 3; (blossom full-quad)
Mesh.RecombineAll = 1;

All Quads:
Mesh.RecombinationAlgorithm = 3; (blossom full-quad)
Mesh.RecombineAll = 1;
Mesh.SubdivisionAlgorithm = 1; (All quads)

Something like this might work.

[rquey]

@MiguelVCarvalho - As of version 3.5.3-29, a mesh can be written under format msh version 4, using -format msh4. The mesh file can then be processed externally (by Gmsh) to get a full-quad mesh.

Here is an example:

neper -T -n 2 -dim 2
neper -M n2-id1.tess -format msh4
gmsh -2 n2-quad.geo

This is only a start - it will be integrated to Neper more thoroughly.

n2-quad.geo:

Merge "n2-id1.msh4";
Mesh.RecombinationAlgorithm = 1;
RecombineMesh;
Mesh.SecondOrderLinear = 1;
Mesh.SubdivisionAlgorithm = 1;
RefineMesh;

[rquey]

I haven't done it more thoroughly yet, for good reasons it seems ;-). The solution above should still work.

[MiguelVCarvalho]

Hi @rquey , are you thinking of implementing this quad-dominant meshes more thoroughly in neper any time soon?

The solution above works more or less. I am creating the .geo file with neper -T and then using gmsh to create the .msh file. However, with periodic tesselations, periodic meshes are not obtained because using this external processing approach, the periodic information is missing and gmsh does not create periodic finite elements.

[rquey]

Hi @MiguelVCarvalho - Unfortunately no. Not high in the todo list...

[MiguelVCarvalho]

Thank you anyway @rquey ;)

Just out of curiosity, what type of element do you use when modelling crystal plasticity?

[rquey]

10-node tets ;)

[MiguelVCarvalho]

Don't you start having convergence problems (at the global equilibrium procedure) when the plastic deformation (incompressible) becomes dominant?

I have those problems for the tri6 and tet10.

(sorry, I know that this is not the place for this type of discussion)

[rquey]

@mkasemer could elaborate on this point, but no, we can go to large plastic strain (30-50%) no problem...

[mkasemer]

In general @rquey is correct: the proof is in the pudding, so to speak: the 10-node tets are demonstratively adept at modeling large deformation plasticity (let alone when plastic deformation becomes "dominant", which would imply 3-5% deformation for most metals). It is dependent on morphology of the microstructure and material system (and thus local mesh quality), but again @rquey is correct that FEPX can handle out to 30-50% deformation without the aid of re-meshing.

Regarding an historical perspective, I would not be the best to ask about this, but Paul Dawson would often cite early (1990s) issues when experimenting with 4-node linear tetrahedra---specifically shear locking phenomena---as the impetus to move to quadratic tets (10-node). The added degrees of freedom and ability to have non-linear shapes allowed for greatly reduced numerical over-stiffening (problems with 4-node tets), according to Dawson. Again, I have no first-hand experience with this.

Others have been moving to partial employ of brick elements recently, though I am skeptical of the absolute need for this.

Another question worth asking is: what quadrature rule are you using? FEPX's quadrature rules can be found in the source code. This could also influence stability of the solution.

[rquey]

As a quick follow-up to @mkasemer's response, Paul Dawson (@dplab) would also say that quad elements are less apt to large deformation - they generally diverge sooner. I think that FEPX had support for quad elements in the 90s - early 2000s, but it was then abandoned.

[dplab]

Hi Romain, Both statements are correct. paul ps I've been keeping an eye on your massive re-write of FEpX. Wow! The new version is going to be quite an upgrade. I look forward to trying it out.

[mkasemer]

Thanks Paul (@dplab)! I'm always a bit cautious when speaking for you :)