Hi Michael,
The one thing that stands out about the snippet of code that you shared is that
there is no check to
if (cell->face(face)->at_boundary() == true && <ON BOUNDARY OF INTEREST>)...
Do you still have something like that?
Otherwise, after a cursory glance, everything appears to be alright with this.
It mimics what you’d do to get the deformation gradient at a QP in a cell.
To debug further, what happens when you apply a very small load? Maybe its not
scaled appropriately for the stiffness of the material. Also, if you’ve now
added a deformation dependent part to the load (i.e. the area transformation)
then you might need to consistently linearise this in order to attain
convergence for large loads.
Best,
Jean-Paul
> On 2. Aug 2021, at 18:03, Michael Li <lianxi...@gmail.com> wrote:
>
> Hi Jean-Paul,
>
> Thank you for your hints.
>
> I initialized a local variable solution_grads_u_face_total with
> fe_face_values_ref[u_fe].get_function_gradients to get the gradient of
> displacement at the quadrature point on the face (see codes below). But the
> gradient acquired is not sensible and the resultant deformation is totally
> wrong.
>
> void assemble_neumann_contribution_one_cell(…)
> {
> …………….
> const FEValuesExtractors::Vector &u_fe = data.solid->u_fe;
>
> std::vector<Tensor<2, dim,NumberType> >
> solution_grads_u_face_total(data.solid->qf_face.size());
>
> scratch.fe_face_values_ref.reinit(cell, face);
>
>
> scratch.fe_face_values_ref[u_fe].get_function_gradients(scratch.solution_total,
>
> solution_grads_u_face_total);
> for (unsigned int face = 0; face < GeometryInfo<dim>::faces_per_cell;
> ++face)
> {
> for (unsigned int f_q_point = 0; f_q_point < n_q_points_f; ++f_q_point)
> {
> const Tensor<2,dim,NumberType> &grad_u =
> solution_grads_u_face_total[f_q_point];
> const Tensor<2,dim,NumberType> F =
> Physics::Elasticity::Kinematics::F(grad_u);
> ………….
> }
> ………..
> }
> ………..
> }
>
> Can you tell me what’s wrong with the code above?
>
> Thank you!
> Michael
>
>
> From: Jean-Paul Pelteret <mailto:jppelte...@gmail.com>
> Sent: Sunday, August 1, 2021 1:46 PM
> To: dealii@googlegroups.com <mailto:dealii@googlegroups.com>
> Subject: Re: [deal.II] Computing the solution gradient at the quadrature
> point on a face
>
> Hi Michael,
>
> The problem here is that “scratch.solution_grads_u_total” is initialised with
> the cell FEValues, and so has n_cell_quadrature_points entries. You need to
> pass
> "scratch.fe_face_values_ref[u_fe].get_function_gradients(scratch.solution_total,
> scratch.solution_grads_u_total);” something that has size
> n_face_quadrature_points. That’s what this error is informing you.
>
>
> As a side note, Physics::Transformations::nansons_formula()
> <https://dealii.org/developer/doxygen/deal.II/namespacePhysics_1_1Transformations.html#aa82925b742c3708f625a48a7abc440bc>
> can compute the transformation of the normal vector + area change for you,
> should you like the traction direction to follow the moving boundary surface
> as well.
>
> Best,
> Jean-Paul
>
>
> On 1. Aug 2021, at 20:05, Michael Lee <lianxi...@gmail.com
> <mailto:lianxi...@gmail.com>> wrote:
>
> fe_face_values.get_function_gradients returns a rank 2 tensor as the solution
> is the displacement vector.
>
> Let me be more specific. In the code gallery " Quasi-Static Finite-Strain
> Compressible Elasticity (The deal.II Library: The 'Quasi-Static Finite-Strain
> Compressible Elasticity' code gallery program (dealii.org)
> <https://www.dealii.org/current/doxygen/deal.II/code_gallery_Quasi_static_Finite_strain_Compressible_Elasticity.html>
> ). It does not consider the follower force as described in the
> documentation: "
> // We specify the traction in reference configuration.
> // For this problem, a defined total vertical force is applied
> // in the reference configuration.
> // The direction of the applied traction is assumed not to
> // evolve with the deformation of the domain."
>
> So I made a modification to consider the effect of the deformed area on the
> traction as follows according to the formula da/dA = J sqrt(N C^-1 N) .
>
> void
> assemble_neumann_contribution_one_cell(const typename
> DoFHandler<dim>::active_cell_iterator &cell,
> ScratchData_ASM &scratch,
> PerTaskData_ASM &data)
> {
> // Aliases for data referenced from the Solid class
> const unsigned int &n_q_points_f = data.solid->n_q_points_f;
> const unsigned int &dofs_per_cell = data.solid->dofs_per_cell;
> const Time &time = data.solid->time;
> const FESystem<dim> &fe = data.solid->fe;
> const unsigned int &u_dof = data.solid->u_dof;
> const FEValuesExtractors::Vector &u_fe = data.solid->u_fe;
>
> // Next we assemble the Neumann contribution. We first check to see it
> the
> // cell face exists on a boundary on which a traction is applied and add
> // the contribution if this is the case.
> for (unsigned int face = 0; face < GeometryInfo<dim>::faces_per_cell;
> ++face)
> if (cell->face(face)->at_boundary() == true
> && cell->face(face)->boundary_id() == 11)
> {
> scratch.fe_face_values_ref.reinit(cell, face);
>
> scratch.fe_face_values_ref[u_fe].get_function_gradients(scratch.solution_total,
>
> scratch.solution_grads_u_total);
>
> for (unsigned int f_q_point = 0; f_q_point < n_q_points_f;
> ++f_q_point)
> {
> // Note that the contributions to the right hand side vector
> we
> // compute here only exist in the displacement components of
> the
> // vector.
> const double time_ramp = (time.current() / time.end());
> const double magnitude = 0.5*1.95*1000*0.32*0.32*time_ramp;
> // (Total force) / (RHS surface area)
> Tensor<1,dim> dir;
> dir[0] = 1.0;
> Tensor<1,dim> face_normal =
> scratch.fe_face_values_ref.normal_vector(f_q_point);
>
> const Tensor<2,dim,NumberType> &grad_u =
> scratch.solution_grads_u_total[f_q_point];
> const Tensor<2,dim,NumberType> F =
> Physics::Elasticity::Kinematics::F(grad_u);
> const SymmetricTensor<2,dim,NumberType> C =
> Physics::Elasticity::Kinematics::C(F);
> const SymmetricTensor<2,dim,NumberType> C_inv = invert(C);
> const Tensor<1, dim> traction = magnitude*dir;
>
> for (unsigned int i = 0; i < dofs_per_cell; ++i)
> {
> const unsigned int i_group =
> fe.system_to_base_index(i).first.first;
>
> if (i_group == u_dof)
> {
> const unsigned int component_i =
> fe.system_to_component_index(i).first;
> const double Ni =
> scratch.fe_face_values_ref.shape_value(i,
> f_q_point);
> const double JxW =
> scratch.fe_face_values_ref.JxW(f_q_point);
>
> data.cell_rhs(i) += (Ni * traction[component_i])
> * sqrt(face_normal * C_inv *
> face_normal)
> * JxW;
> }
> }
> }
> }
> }
>
>
> The errors I got are as follows:
> If I set the parameters as: set Polynomial degree = 2 set Quadrature
> order = 2
> An error occurred in line <645> of file
> </home/michael/dealii-9.2.0/source/fe/fe_values.cc <http://fe_values.cc/>> in
> function
> void dealii::FEValuesViews::internal::do_function_derivatives(const
> dealii::ArrayView<Number>&, const dealii::Table<2, dealii::Tensor<order,
> spacedim> >&, const std::vector<typename dealii::FEValuesViews::Vector<dim,
> spacedim>::ShapeFunctionData>&, std::vector<typename
> dealii::ProductType<Number, dealii::Tensor<(order + 1), spacedim> >::type>&)
> [with int order = 1; int dim = 3; int spacedim = 3; Number = double; typename
> dealii::FEValuesViews::Vector<dim, spacedim>::ShapeFunctionData =
> dealii::FEValuesViews::Vector<3, 3>::ShapeFunctionData; typename
> dealii::ProductType<Number, dealii::Tensor<(order + 1), spacedim> >::type =
> dealii::Tensor<2, 3, double>]
> The violated condition was:
> static_cast<typename ::dealii::internal::argument_type<void( typename
> std::common_type<decltype(derivatives.size()),
> decltype(n_quadrature_points)>::type)>::type>(derivatives.size()) ==
> static_cast<typename ::dealii::internal::argument_type<void( typename
> std::common_type<decltype(derivatives.size()),
> decltype(n_quadrature_points)>::type)>::type>(n_quadrature_points)
> Additional information:
> Dimension 8 not equal to 4.
>
> If I use set Polynomial degree = 2 set Quadrature order = 1
> An error occurred in line <335> of file
> </home/michael/dealii-9.2.0/source/lac/sparse_direct.cc
> <http://sparse_direct.cc/>> in function
> void dealii::SparseDirectUMFPACK::factorize(const Matrix&) [with Matrix =
> dealii::SparseMatrix<double>]
> The violated condition was:
> status == UMFPACK_OK
> Additional information:
> UMFPACK routine umfpack_dl_numeric returned error status 1.
>
> On Sunday, August 1, 2021 at 12:08:37 AM UTC-6 peterr...@gmail.com
> <http://gmail.com/> wrote:
> The return type should be `Tensor<2,dim,NumberType>` shouldn't it?
>
> Hope this helps. If not, could describe how the code does not work? It it not
> compiling? Is the result wrong?
>
> PM
>
> On Sunday, 1 August 2021 at 04:09:45 UTC+2 lian...@gmail.com wrote:
> Dear All,
>
> I want to do a surface integration which needs to evaluate the gradients of
> the solution on the face. The following code does not work
>
> fe_face_values.get_function_gradients(solution, solution_grads);
> for (unsigned int f_q_point = 0; f_q_point < n_q_points_f;
> ++f_q_point)
> {
> const Tensor<2,dim,NumberType> &grad_u =
> solution_grads[f_q_point];
> ...
> }
>
> Can anybody give a hint on that?
>
> Thanks,
> Michael
>
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