[Getfem-users] Adding an initialized fem data in a hyperelastic problem

[David Danan]

Dear Getfem users,

i would like to take into account the fiber direction in my model;
to do so i computed the vector associated to each point of the mesh in the order given by mf.point_of_basic_dof, stored it in a vector, used an initialized fem data

  model.add_initialized_fem_data("fibre",mf_u,Param_fibre);

and included it in the model (basically, add the component T_a*fibre*fibre^T to the second Piola-Kirchhoff tensor in the reference configuration)
      getfem::add_nonlinear_generic_assembly_brick(model, mim,"T_a*(Id(3)+Grad_u)*[fibre(1)*fibre(1),fibre(1)*fibre(2),fibre(1)*fibre(3);fibre(2)*fibre(1),fibre(2)*fibre(2),fibre(2)*fibre(3);fibre(3)*fibre(1),fibre(3)*fibre(2),fibre(3)*fibre(3)]:Grad_Test_u");

(this is where i have some doubts)

The results i obtained are qualitatively correct but a visible difference still remains between the reference solution and my own solution.

It corresponds to the last problem described in this article
http://rspa.royalsocietypublishing.org/content/471/2184/20150641#sec-15

the first two were already validated, so such a difference should (a priori) come from the fiber i guess.

I have tried naively to interpolate the fiber data computed on a P3 mesh on the original P2 mesh but it didn't change anything.

Some help will be really appreciated, i may have overlooked something.

Thanks in advance,

David.

PS: Please, find enclosed the reference solution (deformed.vtk) and the solution obtained (Fibre.vtk)

Fibre.vtk
Description: Binary data

deformed.vtk
Description: Binary data