David, Unfortunately this is really not my domain of expertise but maybe you can randomize the cells https://dealii.org/current/doxygen/deal.II/namespaceGridTools.html#aec039d544c93a6e810427ad45ba0c84f instead of randomizing the quadrature points (which you cannot easily do).
Best, Bruno On Friday, July 3, 2020 at 12:06:04 AM UTC-4, David F wrote: > > Hello everyone, > > I'm trying to solve a 2D solid mechanics homogenization problem, in which > I have element-wise constant elastic properties, which are inhomogeneous > and isotropic from element to element (i.e., I am assembling the system > using the same 4-rank stiffness tensor for all the quadrature points of a > certain element, but that tensor is different for each element). For this > system, I would like to compute its effective elastic properties, which I > do by loading the system under several different loading conditions as is > done in standard homogenization approaches. The system should behave as an > isotropic solid. However, I observe significant anisotropy (and clearly not > due to random fluctuations that might arise because the element-to-element > inhomogeneous properties are randomly distributed). I attribute this to a > mesh dependency of the solution, since I have solved the same problem with > a unstructured triangular mesh with another FEM package and I don't observe > this issue. I believe the structured quadrilateral mesh induces some > artificial elastic anisotropy, which is not there in the case of the > unstructured triangular mesh due to its topological disorder. > > I've thought of a way that might palliate this issue, which is to set > different elastic properties at the quadrature points themselves (i.e., the > properties are no longer element-wise constant). This seems to work to some > extent since the system becomes less anisotropic, however it is not good > enough. > > > *Q1:* is there a preferred way in dealII in which I could randomly > distort a bit the location of the quadrature points? I think this extra > distortion might help get rid of the mesh artifacts. Is is possible to do > it with the in-built Lagrange linear FE or another type of FE is more > suitable within dealII for this task? Basically I have no idea where to > start from to do something like this, so any suggestion is welcome. > > *Q2:* why the system behaves as anisotropic if its local inhomogeneous > elastic properties are isotropic? If you have any comment or suggestion > about the problem of mesh-induced elastic anistropy in FEM, I would like to > know it. > > > Thanks in advance, > David. > > -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to dealii+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/eba8c7df-b614-4a7b-807b-9f158ced85afo%40googlegroups.com.
