Hi Farzin, To complement what Daniel already said, I noted in this previous post <https://groups.google.com/g/dealii/c/kY1v-O70pvs/m/2myOVa9WAwAJ> an approach whereby you solve for the microscopic fluctuation field directly (i.e. using homogeneous periodic constraints) and then correct for the superimposed linear deformation field as a post-processing step. Although I’d previously approached the problem in the same general manner that you’ve described (specifically, introducing a Lagrangian periodicity frame to compute the inhomogeneity for the affine constraints), a colleague of mine found success using the simpler method of first solving for the fluctuation field.
I hope that this (well, the information in my prior post) helps a bit. Best, Jean-Paul > On 12. Mar 2021, at 22:44, Daniel Arndt <d.arndt.m...@gmail.com> wrote: > > Farzin, > > it appears what you want to do is almost what > DoFTools::make_periodicity_constraints(https://www.dealii.org/current/doxygen/deal.II/namespaceDoFTools.html#a929249499b1e5624728d212e90a8e037 > > <https://www.dealii.org/current/doxygen/deal.II/namespaceDoFTools.html#a929249499b1e5624728d212e90a8e037>) > gives you. > You "only" have to apply the additional displacement +H(\chi_+-\chi_-). You > can check for the support points of the constraints using > DoFTools::map_dofs_to_support_points(https://www.dealii.org/current/doxygen/deal.II/namespaceDoFTools.html#a5514e4f59ea659f63953d62ca429eaff > > <https://www.dealii.org/current/doxygen/deal.II/namespaceDoFTools.html#a5514e4f59ea659f63953d62ca429eaff>) > assuming that you are using a nodal finite element. With this information, > you should be able to calculate the displacement for each constrained dof pair > and add it using AffineConstraints::set_inhomogeneity > (https://www.dealii.org/current/doxygen/deal.II/classAffineConstraints.html#a370b2b485a03fe2bb82c1098a6bdfc4c > > <https://www.dealii.org/current/doxygen/deal.II/classAffineConstraints.html#a370b2b485a03fe2bb82c1098a6bdfc4c>). > > Best, > Daniel > > Am Fr., 12. März 2021 um 12:29 Uhr schrieb Farzin Mozafari > <mozafari.far...@gmail.com <mailto:mozafari.far...@gmail.com>>: > > > Dear all, > > > > I am a new user of Deal ii. I am going to solve a multiscale problem in solid > mechanics using Deal ii. To this end, I am going to model a simple cube with > a linear elastic material under periodic boundary condition as the RVE of the > material containing its microstructural features. Then by applying simple > shear and uniaxial strain-controlled boundary conditions, I am going to > determine the associated components of the averaged stress and elasticity > tensor. > > > > The way that usually people use is to involve an H matrix (as explained in > the attached file). In the literature, this method is called the generalized > periodic boundary condition. Indeed, this method makes us able to directly > apply shear and uniaxial loading through the H matrix components (i.e. > Displacement gradient matrix). I am not sure how can I implement this method > in deal II. > > > > I would be grateful if anyone gives me a piece of advice to carry it out > properly. > > > > Regards > > Farzin > > > > > > > -- > The deal.II project is located at http://www.dealii.org/ > <http://www.dealii.org/> > For mailing list/forum options, see > https://groups.google.com/d/forum/dealii?hl=en > <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 > <mailto:dealii+unsubscr...@googlegroups.com>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/dealii/7D60CE96-E78D-45FA-A5C7-C51AAD2E3918%40hxcore.ol > > <https://groups.google.com/d/msgid/dealii/7D60CE96-E78D-45FA-A5C7-C51AAD2E3918%40hxcore.ol?utm_medium=email&utm_source=footer>. > > -- > The deal.II project is located at http://www.dealii.org/ > <http://www.dealii.org/> > For mailing list/forum options, see > https://groups.google.com/d/forum/dealii?hl=en > <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 > <mailto:dealii+unsubscr...@googlegroups.com>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/dealii/CAOYDWbLbQmfrgPJxsoYc8k%2B54vF6rugJ%2B4hHuA61mfDv9HKA3A%40mail.gmail.com > > <https://groups.google.com/d/msgid/dealii/CAOYDWbLbQmfrgPJxsoYc8k%2B54vF6rugJ%2B4hHuA61mfDv9HKA3A%40mail.gmail.com?utm_medium=email&utm_source=footer>. -- 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/E2178AD6-280F-433B-A889-DBEEE70FB754%40gmail.com.
