Paras,
I am working on homogenization of particulate nano-composites and thus have to
solve the finite deformation quasistatics problem on different
microstructures, such as one shown in the attachment pic-1.png.
In order to automate the generation of (2D & 3D) meshes for microstructures
comprising of randomly distributed filler particles of arbitrary radius, we
employ a self-written python code using GMSH for mesh generation. The setup
works well for 2D but for 3D, the resulting mesh (left) culminates in
irregularities in the stress contour as compared to that obtained with a
structured mesh (right) as can be seen from the attachment pic-2.png. Due to
the random spatial distribution and arbitrary size of particles, unstructured
mesh appeared as the feasible option.
In order to verify that the cause of such irregularities is the mesh and not
our solver (based on deal.ii), we tested the mesh in Abaqus and similar
irregularities were observed, cf. pic-3.png. Refining the mesh does not help
either.
That suggests that you are doing something wrong. I don't know what exactly
the problem is, and in particular how you assign material properties to cells,
but we know from theory that the finite element solution must converge to the
exact solution if you just refine the mesh often enough. If it doesn't for
you, then something is amiss.
This does not say anything about the *absolute level of accuracy*. I would not
be surprised if for a mesh like the one you show (in which pretty much every
hexahedron is poorly shaped), the solution is less than for the corresponding
tetrahedal mesh. But if you refine it a couple of times, you should get a more
accurate solution. Is this not the case?
Has anyone else working with unstructured Hex meshes, observed similar issues?
Any clues on how to deal with this issue or on other tools (preferably open
source) which one could use for generating better meshes in 3D would be of
great help.
The quality of meshes matters for the absolute level of error. The hex meshes
you get by subdividing tets are generally quite poor, though I know of people
who are using these routinely and report that they nevertheless get good
accuracy. A better approach is certainly to see if you can find ways to
*directly* create hex meshes. gmsh can do this to some degree. For the sphere
you show, deal.II can also generate a high-quality mesh itself.
Best
W.
--
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Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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