I have a 2D system for which I create the stiffness tensor of an isotropic material, but for each finite element I create it with a different shear modulus. The shear modulus is random for each element (I use an exponential distribution, but any distribution leads to the same behavior as long as the std is high), with no structure such as layers or anything else. In this case, the system should clearly be macroscopically isotropic (up to statistical fluctuations due to the random properties) for symmetry reasons.
On Thursday, 9 July 2020 05:03:45 UTC+2, Wolfgang Bangerth wrote: > > On 7/2/20 10:06 PM, David F wrote: > > > > *_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. > > I don't know how exactly you choose your coefficient, but if you alternate > layers of isotropic materials, then you get an anisotropic material. Think > about layering styrofoam plates with steel plates -- the resulting stack > of > layers is essentially incompressible under loads from the side (because > the > steel plates provide the stiffness), but is quite compressible if you load > it > from top and bottom (because the styrofoam layers will simply collapse). > > Best > W. > > -- > ------------------------------------------------------------------------ > Wolfgang Bangerth email: bang...@colostate.edu > <javascript:> > www: http://www.math.colostate.edu/~bangerth/ > > -- 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/ef939354-6b36-4b8d-aaa8-f15e5d6aca3bo%40googlegroups.com.
