Re: [Getfem-users] Getfem-users Digest, Vol 116, Issue 6

[Yves Renard]

Dear Andy,

The primary level-set function describes the geometry of the crack : its 0 level-set should contain the crack itself.
The secondary level-set function describes the crack front, the crack correspond to the part of the domain where the level-set function is non-positive.
This is mostly explained for the 3D case in the paper.

Gravouil A, Moës N, Belytschko T. Non-planar 3D crack growth by the extended finite element and level sets. Part I and II. International Journal for Numerical Methods in Engineerin, 2002.

If you want a model for the enrichment and the adaptation of integration for the 3D case, you can have a look to the program
/contrib/delaminated_crack/delaminated_crack.cc

Best Regards,

Yves






Le 21/06/2016 04:12, Andrew Roberts a écrit :

Thank you Yves for that insight.  After researching the level set mathematics a bit more, including papers authored in part by you, I understand I am attempting to establish calculations through a "fictitious domain".  In the 2d crack problem (crack.cc), I see the following:

base_small_vector ls_function(const base_node P, int num = 0) {
  scalar_type x = P[0], y = P[1];
  base_small_vector res(2);
  switch (num) {
    case 0: {
      res[0] = y;
      res[1] = -.5 + x;
    } break;
    case 1: {
      res[0] = gmm::vect_dist2(P, base_node(0.5, 0.)) - .25;
      res[1] = gmm::vect_dist2(P, base_node(0.25, 0.0)) - 0.27;
    } break;
    case 2: {
      res[0] = x - 0.25;
      res[1] = gmm::vect_dist2(P, base_node(0.25, 0.0)) - 0.35;
    } break;
    default: assert(0);
  }
  return res;
}

How are these three level set functions determined as to correspond to physical phenomena and how can than be imposed onto 3d behavior.  I've tried just toying with these functions in my 3d code and I receive "segmentation fault".

Thank you,

Andy

On Thu, Jun 16, 2016 at 4:26 AM, Yves Renard <address@hidden> wrote:

Dear Andy,

First, just a remark for the future version of Getfem, the two lines

getfem::crack_singular_xy_function *s = new
getfem::crack_singular_xy_function(j);
vfunc[j] = getfem::global_function_on_level_set(ls, *s);

will have to be changed to

auto s = std::make_shared<getfem::crack_singular_xy_function>(j);
vfunc[j] = getfem::global_function_on_level_set(ls, s);


My first error in the code is in fact :

  what():  Error in ../../src/getfem_fem_global_function.cc, line 95 :
Convexes of different dimension: to be done

Indicating that there is both 2D and 3D elements in the mesh : may be
you should select only the 3D elements.


I look a bit into the code. For me the main mistake in the code is that

mls.adapt();
mfls.adapt();
mim.adapt();

are called but the level set value is not set. To be clear

getfem::level_set ls(mesh);

defined an invalid level set function which is zero everywhere. You have
to set its value using
ls.values(0) (see tests/crack.cc for instance) before calling adapt()
methods.


Best regards,

Yves.

Le 15/06/2016 19:21, address@hidden a écrit :
> Hi Andrew,
>
> I already had this error message, a long time ago. If I remember well,
> this message can appear when the degree of the level-set is wrong, in view
> of the way the level-set is defined and/or used. This degree must be 1
> when it is a curve (in 2D), or 2 when it is a surface (in 3D):
>
> getfem::level_set ls(mesh, degree = 1, with_secondary = false);
>
> http://download.gna.org/getfem/html/homepage/userdoc/xfem.html
>
> In your code, by default the degree of the level-set is equal to 1, and in
> what follows it seems that we are in a 3D context.
>
> Maybe the problem comes also from the fact that you may have to specify
> secondary level-set functions. In that case your level-set object is not a
> scalar-type anymore, but a vector.
>
> Sincerely,
>
> S.C
>
>
>
> https://online.uni-graz.at/kfu_online/visitenkarte.show_vcard?pPersonenId=8E061E23CBE613F4&pPersonenGruppe=3
>
>
>
>
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>> Today's Topics:
>>
>>    1. Re: "level is zero!" (Andrew Roberts)
>>
>>
>> ----------------------------------------------------------------------
>>
>> Message: 1
>> Date: Tue, 14 Jun 2016 16:35:59 -0500
>> From: Andrew Roberts <address@hidden>
>> To: Yves Renard <address@hidden>
>> Cc: address@hidden
>> Subject: Re: [Getfem-users] "level is zero!"
>> Message-ID:
>>      <address@hidden>
>> Content-Type: text/plain; charset="utf-8"
>>
>> Hello again,
>>    I've been working diligently to understand as to why I receive "level
>> is
>> zero" error.  I'd appreciate any code review and advice.  The purpose is
>> just to demonstrate basic xfem behavior in the compact specimen mesh
>> (v4.gmsh.msh).
>>
>> Thank you,
>> Andy
>>
>>
>> /address@hidden compact.cc
>>    @brief compact specimen problem.
>>
>> */
>>
>> #include "getfem/getfem_model_solvers.h"
>> #include "getfem/getfem_export.h"
>> #include "gmm/gmm.h"
>> #include "getfem/getfem_import.h"
>> #include "getfem/getfem_assembling.h"
>> #include "getfem/getfem_generic_assembly.h"
>> #include "getfem/getfem_mesh_im_level_set.h"
>> #include "getfem/getfem_mesh_fem_level_set.h"
>> #include "getfem/getfem_mesh_fem_product.h"
>> #include "getfem/getfem_mesh_fem_global_function.h"
>> #include "getfem/getfem_mesh_fem_sum.h"
>> #include <string>
>> #include <cstring>
>> #include <sstream>
>> #include <iostream>
>>
>> using std::endl; using std::cout; using std::cerr;
>> using std::ends; using std::cin;
>>
>> using bgeot::size_type;
>> using bgeot::base_node;
>> using bgeot::base_small_vector;
>> typedef getfem::model_real_plain_vector plain_vector;
>>
>>
>> using bgeot::scalar_type; /* = double */
>>
>>
>>
>> int main(void) {
>>
>>
>> double E = 21E6;     // Young Modulus (N/cm^2)
>> double nu = 0.3;     // Poisson ratio
>> double clambda = E*nu/((1+nu)*(1-2*nu));
>> double cmu = E/(2*(1+nu));
>> double clambdastar = 2*clambda*cmu/(clambda+2*cmu);
>>
>>
>> double residual = 1E-9;
>>
>>
>> getfem::mesh mesh;
>> getfem::import_mesh("gmsh:v4.gmsh.msh",mesh);
>>
>>
>> getfem::mesh_fem mf(mesh);
>>
>>
>> getfem::level_set ls(mesh);
>> getfem::mesh_level_set mls(mesh);
>> mls.add_level_set(ls);
>>
>>
>> std::vector<getfem::pglobal_function> vfunc(4);
>>   for (unsigned j=0; j < 4; ++j) {
>>     getfem::crack_singular_xy_function *s =
>>       new getfem::crack_singular_xy_function(j);
>>     vfunc[j] = getfem::global_function_on_level_set(ls, *s);
>>   }
>>
>>
>> getfem::mesh_fem_level_set mfls(mls, mf);
>>
>>
>> getfem::mesh_fem_global_function mf_sing(mesh);
>>
>>
>> mf_sing.set_functions(vfunc);
>>
>>
>> getfem::mesh_fem_sum mfu(mesh);
>>
>>
>> mfu.set_mesh_fems(mf_sing, mfls);
>>
>> getfem::mesh_im_level_set mim(mls,
>> getfem::mesh_im_level_set::INTEGRATE_ALL,
>> getfem::int_method_descriptor("IM_TETRAHEDRON(6)"),
>> getfem::int_method_descriptor("IM_QUASI_POLAR(IM_TETRAHEDRON(8), 2)"));
>>
>>
>> mls.adapt();
>> mfls.adapt();
>> mim.adapt();
>>
>>
>> getfem::mesh_fem mfvm(mesh, 1);
>>
>> mfvm.set_classical_discontinuous_finite_element(1);
>>
>>
>> getfem::model md;
>> md.add_fem_variable("u", mfu);
>>
>>
>> md.add_initialized_scalar_data("cmu", cmu);
>> md.add_initialized_scalar_data("clambdastar", clambdastar);
>>
>>
>> getfem::add_isotropic_linearized_elasticity_brick
>>     (md, mim, "u", "clambdastar", "cmu");
>>
>>
>>
>> getfem::add_normal_Dirichlet_condition_with_multipliers(md,mim,"u", 1,
>> 109);
>>
>> getfem::add_source_term_brick(md,mim,"u","[0,1640,0]", 108);
>>
>>
>> gmm::iteration iter(residual, 1, 50);
>> getfem::standard_solve(md, iter,
>> getfem::rselect_linear_solver(md,"superlu"));
>>
>>
>>
>> plain_vector U(mfu.nb_dof()); gmm::copy(md.real_variable("u"), U);
>> plain_vector VM(mfvm.nb_dof());
>> getfem::compute_isotropic_linearized_Von_Mises_or_Tresca
>>     (md, "u", "clamabdastar", "cmu", mfvm, VM, false);
>>
>>
>> getfem::vtk_export exp2("d_w_vm.vtk", false);
>> exp2.exporting(mfu);
>> exp2.write_point_data(mfu, U, "displacement");
>> exp2.write_point_data(mfvm, VM, "Von Mises stress");
>>
>>
>> }
>>
>> On Mon, Jun 13, 2016 at 7:03 AM, Yves Renard <address@hidden>
>> wrote:
>>
>>> Dear Andrew,
>>>
>>> This message appear when the level_set function is identically zero on
>>> an
>>> element (the level set function have to be "close" to a signed
>>> distance).
>>> Are you sure you initialized your level-set function with a correct
>>> value ?
>>>
>>> Best regards,
>>>
>>> Yves.
>>>
>>>
>>> Le 12/06/2016 23:33, Andrew Roberts a écrit :
>>>
>>> Working to demo 3d XFEM crack propagation of a steel compact specimen
>>> top-half (gmsh import).
>>>
>>> It compiles fine but the executable throws a "level is zero" error which
>>> I'm uncertain of the source of this error.  Code attached below.
>>>
>>> /address@hidden compact.cc
>>>>    @brief three-dimensional XFEM crack propagation.
>>>>
>>>> */
>>>>
>>>> #include "getfem/getfem_model_solvers.h"
>>>> #include "getfem/getfem_export.h"
>>>> #include "gmm/gmm.h"
>>>> #include "getfem/getfem_import.h"
>>>> #include "getfem/getfem_assembling.h"
>>>> #include "getfem/getfem_generic_assembly.h"
>>>> #include "getfem/getfem_mesh_im_level_set.h"
>>>> #include "getfem/getfem_mesh_fem_level_set.h"
>>>> #include "getfem/getfem_mesh_fem_product.h"
>>>> #include "getfem/getfem_mesh_fem_global_function.h"
>>>> #include "getfem/getfem_mesh_fem_sum.h"
>>>> #include <string>
>>>> #include <cstring>
>>>> #include <sstream>
>>>> #include <iostream>
>>>>
>>>> using std::endl; using std::cout; using std::cerr;
>>>> using std::ends; using std::cin;
>>>>
>>>> using bgeot::size_type;
>>>> using bgeot::base_node;
>>>> using bgeot::base_small_vector;
>>>> typedef getfem::model_real_plain_vector plain_vector;
>>>>
>>>>
>>>> using bgeot::scalar_type; /* = double */
>>>>
>>>> int main(void) {
>>>>
>>>> double E = 21E6;     // Young Modulus (N/cm^2)
>>>> double nu = 0.3;     // Poisson ratio
>>>> double clambda = E*nu/((1+nu)*(1-2*nu));
>>>> double cmu = E/(2*(1+nu));
>>>> double clambdastar = 2*clambda*cmu/(clambda+2*cmu);
>>>>
>>>> double residual = 1E-9;
>>>>
>>>> getfem::mesh mesh;
>>>> getfem::import_mesh("gmsh:v4.gmsh.msh",mesh);
>>>>
>>>>
>>>> getfem::mesh_fem mf(mesh, 3);
>>>>
>>>> getfem::mesh_fem mfvm(mesh, 1);
>>>>
>>>> mf.set_finite_element(mesh.convex_index(),
>>>> getfem::fem_descriptor("FEM_PK(3,2)"));
>>>>
>>>> mfvm.set_classical_discontinuous_finite_element(1);
>>>>
>>>> getfem::level_set ls(mesh, 1, true);
>>>> getfem::mesh_level_set mls(mesh);
>>>> mls.add_level_set(ls);
>>>> mls.adapt();
>>>>
>>>> std::vector<getfem::pglobal_function> vfunc(6);
>>>> for (unsigned i = 0; i < vfunc.size(); ++i){
>>>>     getfem::abstract_xy_function *s =
>>>>         new getfem::crack_singular_xy_function(i);
>>>>     getfem::abstract_xy_function *c =
>>>>         new getfem::cutoff_xy_function(0, .2,.01,.49);
>>>>     s = new getfem::product_of_xy_functions(*s, *c);
>>>>       vfunc[i] = getfem::global_function_on_level_set(ls, *s);
>>>> }
>>>>
>>>> getfem::mesh_fem_level_set mfls(mls, mf);
>>>>
>>>> getfem::mesh_fem_global_function mf_sing(mesh,3);
>>>>
>>>> mf_sing.set_functions(vfunc);
>>>>
>>>> getfem::mesh_fem_product mf_asympt(mfls, mf_sing);
>>>>
>>>> getfem::mesh_fem_product mfu(mf_asympt);
>>>>
>>>> getfem::mesh_im_level_set mim(mls,
>>>> getfem::mesh_im_level_set::INTEGRATE_ALL,
>>>> getfem::int_method_descriptor("IM_TETRAHEDRON(6)"),
>>>> getfem::int_method_descriptor("IM_QUASI_POLAR(IM_TETRAHEDRON(8), 2)"));
>>>>
>>>>
>>>>
>>>> getfem::model md;
>>>> md.add_fem_variable("u", mfu);
>>>>
>>>>
>>>> md.add_initialized_scalar_data("cmu", cmu);
>>>> md.add_initialized_scalar_data("clambdastar", clambdastar);
>>>>
>>>> getfem::add_isotropic_linearized_elasticity_brick
>>>>     (md, mim, "u", "clambdastar", "cmu");
>>>>
>>>>
>>>> getfem::add_normal_Dirichlet_condition_with_multipliers(md,mim,"u", 1,
>>>> 109);
>>>>
>>>> getfem::add_source_term_brick(md,mim,"u","[0,1640,0]", 108);
>>>>
>>>> gmm::iteration iter(residual, 1, 50);
>>>> getfem::standard_solve(md, iter,
>>>> getfem::rselect_linear_solver(md,"superlu"));
>>>>
>>>> getfem::standard_solve(md, iter);
>>>>
>>>> plain_vector U(mfu.nb_dof()); gmm::copy(md.real_variable("u"), U);
>>>> plain_vector VM(mfvm.nb_dof());
>>>> getfem::compute_isotropic_linearized_Von_Mises_or_Tresca
>>>>     (md, "u", "clamabdastar", "cmu", mfvm, VM, false);
>>>>
>>>>
>>>> getfem::vtk_export exp2("d_w_vm.vtk", false);
>>>> exp2.exporting(mfu);
>>>> exp2.write_point_data(mfu, U, "displacement");
>>>> exp2.write_point_data(mfvm, VM, "Von Mises stress");
>>>>
>>>>
>>>> }
>>>>
>>> Thank you for any help in advance,
>>>
>>> Andy
>>>
>>>
>>> _______________________________________________
>>> Getfem-users mailing
>>> address@hidden://mail.gna.org/listinfo/getfem-users
>>>
>>>
>>>
>>> --
>>>
>>>   Yves Renard (address@hidden)       tel : (33) 04.72.43.87.08
>>>   Pole de Mathematiques, INSA-Lyon             fax : (33) 04.72.43.85.29
>>>   20, rue Albert Einstein
>>>   69621 Villeurbanne Cedex, FRANCE
>>>   http://math.univ-lyon1.fr/~renard
>>>
>>> ---------
>>>
>>>
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--

  Yves Renard (address@hidden)       tel : (33) 04.72.43.87.08
  Pole de Mathematiques, INSA-Lyon             fax : (33) 04.72.43.85.29
  20, rue Albert Einstein
  69621 Villeurbanne Cedex, FRANCE
  http://math.univ-lyon1.fr/~renard

---------

-- 

  Yves Renard (address@hidden)       tel : (33) 04.72.43.87.08
  Pole de Mathematiques, INSA-Lyon             fax : (33) 04.72.43.85.29
  20, rue Albert Einstein
  69621 Villeurbanne Cedex, FRANCE
  http://math.univ-lyon1.fr/~renard

---------