Ah, sorry, I misread what you said. So no, you don't need to use the
add_periodicity() function that I suggested.
But I would highly recommend that you take a look at Miehe's paper (or some
equivalent, maybe from Prof Wrigger's, Prof Steinmann's or Prof Schroder's
groups for example) before spending too much time debugging your current
implementation. If you are trying to ensure a periodic deformation, then
"identity" periodic constraints that you're trying to enforce are not the
correct ones for your problem. They correct constraints are of the form
[[ \mathbf{u} ]] = \bar{\mathbf{F}} \cdot [[ \mathbf{X} ]]
where [[a]] represents a jump in a quantity over the periodic faces, *u* is
the displacement, \bar{*F*} is the macroscopic deformation gradient and *X*
is a reference coordinate.
If you're trying to enforce an anti-periodic traction condition then I
suppose thats achieved by another algorithm entirely.
On Wednesday, June 1, 2016 at 5:51:28 PM UTC+2, Bastien Lauras wrote:
>
> Hi Jean-Paul,
>
> Thank you for your answer. I am using deal.II 8.4.0. I've seen this
> add_periodicity()
> <https://www.dealii.org/8.4.0/doxygen/deal.II/classparallel_1_1distributed_1_1Triangulation.html#a9539cda687eeb08c602bceac11807987>
>
> function, but it appears to me, in step-45
> <https://dealii.org/developer/doxygen/deal.II/step_45.html>, that I
> should only use this if I were to use a
> parallel::distributed::Triangulation
> <https://www.dealii.org/8.4.0/doxygen/deal.II/classparallel_1_1distributed_1_1Triangulation.html#a9539cda687eeb08c602bceac11807987>.
>
> Is it true?
> Maybe I didn't manage to adapt step-45 well to my problem because I am
> trying to implement periodic boundary conditions on a time-dependent
> loading and for each timestep, a Newton-Raphson algorithm. As in step-44
> <https://dealii.org/developer/doxygen/deal.II/step_44.html> obviously.
> Shall I add this add_periodicity()
> <https://www.dealii.org/8.4.0/doxygen/deal.II/classparallel_1_1distributed_1_1Triangulation.html#a9539cda687eeb08c602bceac11807987>
>
> function after initializing my mesh?
>
> Thanks again for your help,
>
> Bastien
>
> Thank you for the paper, I'll take a look at it and discuss of everything
> with my tutor.
>
> On Wednesday, June 1, 2016 at 1:20:25 AM UTC-5, Jean-Paul Pelteret wrote:
>>
>> Hi Bastien,
>>
>> Which version of deal.II are you using? There is the recently added
>> add_periodicity()
>> <https://www.dealii.org/8.4.0/doxygen/deal.II/classparallel_1_1distributed_1_1Triangulation.html#a9539cda687eeb08c602bceac11807987>
>> function
>> that helps join otherwise unrelated faces for distributed triangulations.
>> See also step-45
>> <https://www.dealii.org/8.4.0/doxygen/deal.II/step_45.html> for an
>> example as to how it is used.
>>
>> On a tangential but related note, this type of "periodic" boundary
>> condition is in all likelihood not appropriate for elasticity. See, for
>> example,
>> @Article{Miehe2003a,
>> Title = {Computational micro-to-macro transitions
>> for discretized micro-structures of heterogeneous materials at finite
>> strains based on the minimization of averaged incremental energy},
>> Author = {Miehe, Christian},
>> Journal = {Computer Methods in Applied Mechanics and
>> Engineering},
>> Year = {2003},
>> Number = {5},
>> Pages = {559--591},
>> Volume = {192}
>> }
>> for the correct definition of the periodicity constraint (namely a
>> periodic displacement jump based on the macroscopic deformation gradient)
>> for elasticity.
>>
>> I hope that this helps,
>> J-P
>>
>>
>> On Wednesday, June 1, 2016 at 2:10:36 AM UTC+2, Bastien Lauras wrote:
>>>
>>> Hi,
>>>
>>> I am working on a 2D square, a incompressible neo-hookean material. I've
>>> used step 44 and modified it to work on a two field formulation (*u* and
>>> p).
>>> I am trying to implement periodic boundary conditions for the vertical
>>> displacement on lateral faces (right and left).
>>> My left face has boundary indicator 1, and my right face has boundary
>>> indicator 3.
>>>
>>> In the make_constraints function, I've added, after constraints.clear() :
>>>
>>> DoFTools::make_hanging_node_constraints (dof_handler_ref,
>>> constraints); // I have local refinement in my code
>>>
>>> std::vector<GridTools::PeriodicFacePair<typename
>>> DoFHandler<dim>::cell_iterator> >
>>> periodicity_vector;
>>>
>>> const unsigned int direction = 0; // I've tried 0 and 1, I didn't
>>> understan what it really was
>>>
>>> GridTools::collect_periodic_faces(dof_handler_ref, 1, 3, direction,
>>> periodicity_vector);
>>>
>>> const FEValuesExtractors::Scalar x_displacement(0);
>>> const FEValuesExtractors::Scalar y_displacement(1);
>>>
>>> DoFTools::make_periodicity_constraints<DoFHandler<dim> >
>>> (periodicity_vector, constraints,
>>> fe.component_mask(y_displacement));
>>>
>>>
>>> And then I apply Dirichlet boundary conditions on face 1 and 3 on the
>>> horizontal displacement (x_displacement).
>>> I've also added the command :
>>>
>>> DoFTools::make_hanging_node_constraints (dof_handler_ref, constraints);
>>>
>>> before making my sparsity pattern.
>>> My triangulation is not a parallel::distributed one. I'm working on
>>> multithreads with the workstream::run of step 44.
>>>
>>>
>>> The problem is that my periodic boundary conditions are not enforced.
>>> The make_periodicity_constraints command does not change the number of
>>> constrained degrees of freedom (that I compute using a loop over the DOFs
>>> and calling constraints.is_constrained(i)).
>>> And moreover, I can see on my outputs that there is definitely no
>>> periodicity on my vertical displacement.
>>>
>>> Where can the problem come from?
>>>
>>> Thanks a lot for your help beforehand!
>>>
>>> Bastien Lauras
>>>
>>>
>>
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