Dear H.B. For this mesh and deformation field, you can expect to run into this problem regardless of whether you use the total or updated Lagrangian formulation. As you can see, with your updated formulation you run into an issue when the mapping Jacobian becomes singular (due to element skewness/inversion). For the total Lagrangian approach, the same problem would manifest itself in that the deformation gradient would be non-invertible i.e. det(F) <= 0. You only really have two "easy" options here: 1. Perform some mesh adaptivity 2. Change your initial mesh, keeping in mind the expected deformation.
A third option would be to use an ALE solid formulation <http://www.sciencedirect.com/science/article/pii/S0045782598001078>, but I have no experience with this so I have no idea how hard it is to do. What I suggest might help is if you make some sort of c-grid <http://jullio.pe.kr/fluent6.1/help/html/ug/node123.htm> that focusses on the crack tip. That way the mesh opens up as the crack does, rather than thins out like you have here. I hope this helps, J-P On Wednesday, January 25, 2017 at 9:02:01 PM UTC+1, [email protected] wrote: > > Dear all > > > I am working on a solid material model with large deformation using a > updated Lagrangian formulation. In each time step and Newton iteration the > mesh is moved. The mesh is highly deformed and and the deformation > localized in a narrow band(due to the nature of the material behavior). So > some element is distorted and the following error occurs: > > > An error occurred in line <2587> of file > </home/hojat/deal/dealii-8.4.1/source/fe/mapping_q_generic.cc> in function > > dealii::CellSimilarity::Similarity dealii::MappingQGeneric<dim, > spacedim>::fill_fe_values(const typename dealii::Triangulation<dim, > spacedim>::cell_iterator&, dealii::CellSimilarity::Similarity, const > dealii::Quadrature<dim>&, const typename dealii::Mapping<dim, > spacedim>::InternalDataBase&, > dealii::internal::FEValues::MappingRelatedData<dim, spacedim>&) const [with > int dim = 2; int spacedim = 2; typename dealii::Triangulation<dim, > spacedim>::cell_iterator = dealii::TriaIterator<dealii::CellAccessor<2, 2> > >; typename dealii::Mapping<dim, spacedim>::InternalDataBase = > dealii::Mapping<2, 2>::InternalDataBase] > > The violated condition was: > > det > 1e-12*Utilities::fixed_power<dim>(cell->diameter()/ > std::sqrt(double(dim))) > > The name and call sequence of the exception was: > > (typename > Mapping<dim,spacedim>::ExcDistortedMappedCell(cell->center(), det, point)) > > Additional Information: > > The image of the mapping applied to cell with center [0.295666 0.850622] > is distorted. The cell geometry or the mapping are invalid, giving a > non-positive volume fraction of -0.000119973 in quadrature point 0. > > > Stacktrace: > > ----------- > > #0 /home/hojat/deal/install_8.4.1/lib/libdeal_II.g.so.8.4.1: > dealii::MappingQGeneric<2, > 2>::fill_fe_values(dealii::TriaIterator<dealii::CellAccessor<2, 2> > > const&, dealii::CellSimilarity::Similarity, dealii::Quadrature<2> const&, > dealii::Mapping<2, 2>::InternalDataBase const&, > dealii::internal::FEValues::MappingRelatedData<2, 2>&) const > > #1 /home/hojat/deal/install_8.4.1/lib/libdeal_II.g.so.8.4.1: > dealii::FEValues<2, 2>::do_reinit() > > #2 /home/hojat/deal/install_8.4.1/lib/libdeal_II.g.so.8.4.1: void > dealii::FEValues<2, 2>::reinit<dealii::DoFHandler, > false>(dealii::TriaIterator<dealii::DoFCellAccessor<dealii::DoFHandler<2, > 2>, false> > const&) > > #3 /home/hojat/deal/install_8.4.1/examples/HB/: > FEM<2>::assemble_large_deformation() > > > The attached figures show the deformed and initial mesh. How to solve > this problem (without adaptive mesh refinement)? Can I use the update > Lagrangian formulation in Deal.II without moving the mesh? Do you think > that the total Lagrangian formulation is a solution? > > > Best Regards, > > H.B > -- 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 [email protected]. For more options, visit https://groups.google.com/d/optout.
