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test_solid_mechanics_model_material_eigenstrain.cc
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test_solid_mechanics_model_material_eigenstrain.cc
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/**
* @file test_solid_mechanics_model_material_eigenstrain.cc
*
* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Mon Feb 10 2014
* @date last modification: Thu Jun 05 2014
*
* @brief test the internal field prestrain
*
* @section LICENSE
*
* Copyright (©) 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
* Akantu is free software: you can redistribute it and/or modify it under the
* terms of the GNU Lesser General Public License as published by the Free
* Software Foundation, either version 3 of the License, or (at your option) any
* later version.
*
* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
* details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
*
*/
/* -------------------------------------------------------------------------- */
#include "solid_mechanics_model.hh"
using namespace akantu;
Real alpha [3][4] = { { 0.01, 0.02, 0.03, 0.04 },
{ 0.05, 0.06, 0.07, 0.08 },
{ 0.09, 0.10, 0.11, 0.12 } };
/* -------------------------------------------------------------------------- */
template<ElementType type, bool is_plane_strain>
static Matrix<Real> prescribed_strain() {
UInt spatial_dimension = ElementClass<type>::getSpatialDimension();
Matrix<Real> strain(spatial_dimension, spatial_dimension);
for (UInt i = 0; i < spatial_dimension; ++i) {
for (UInt j = 0; j < spatial_dimension; ++j) {
strain(i, j) = alpha[i][j + 1];
}
}
return strain;
}
template<ElementType type, bool is_plane_strain>
static Matrix<Real> prescribed_stress(Matrix<Real> prescribed_eigenstrain) {
UInt spatial_dimension = ElementClass<type>::getSpatialDimension();
Matrix<Real> stress(spatial_dimension, spatial_dimension);
//plane strain in 2d
Matrix<Real> strain(spatial_dimension, spatial_dimension);
Matrix<Real> pstrain;
pstrain = prescribed_strain<type, is_plane_strain>();
Real nu = 0.3;
Real E = 2.1e11;
Real trace = 0;
/// symetric part of the strain tensor
for (UInt i = 0; i < spatial_dimension; ++i)
for (UInt j = 0; j < spatial_dimension; ++j)
strain(i,j) = 0.5 * (pstrain(i, j) + pstrain(j, i));
// elastic strain is equal to elastic strain minus the eigenstrain
strain -= prescribed_eigenstrain;
for (UInt i = 0; i < spatial_dimension; ++i) trace += strain(i,i);
Real lambda = nu * E / ((1 + nu) * (1 - 2*nu));
Real mu = E / (2 * (1 + nu));
if(!is_plane_strain) {
std::cout << "toto" << std::endl;
lambda = nu * E / (1 - nu*nu);
}
if(spatial_dimension == 1) {
stress(0, 0) = E * strain(0, 0);
} else {
for (UInt i = 0; i < spatial_dimension; ++i)
for (UInt j = 0; j < spatial_dimension; ++j) {
stress(i, j) = (i == j)*lambda*trace + 2*mu*strain(i, j);
}
}
return stress;
}
/* -------------------------------------------------------------------------- */
/* -------------------------------------------------------------------------- */
int main(int argc, char *argv[])
{
initialize("material_elastic_plane_strain.dat", argc, argv);
UInt dim = 3;
const ElementType element_type = _tetrahedron_4;
const bool plane_strain = true;
Matrix<Real> prescribed_eigenstrain(dim, dim);
prescribed_eigenstrain.clear();
for (UInt i = 0; i < dim; ++i) {
for (UInt j = 0; j < dim; ++j)
prescribed_eigenstrain(i,j) += 0.1;
}
/// load mesh
Mesh my_mesh(dim);
std::stringstream filename; filename << "cube_3d_tet_4.msh";
my_mesh.read(filename.str());
/// declaration of model
SolidMechanicsModel my_model(my_mesh);
/// model initialization
my_model.initFull(SolidMechanicsModelOptions(_static));
const Array<Real> & coordinates = my_mesh.getNodes();
Array<Real> & displacement = my_model.getDisplacement();
Array<bool> & boundary = my_model.getBlockedDOFs();
MeshUtils::buildFacets(my_mesh);
my_mesh.createBoundaryGroupFromGeometry();
// Loop over (Sub)Boundar(ies)
for(GroupManager::const_element_group_iterator it(my_mesh.element_group_begin());
it != my_mesh.element_group_end(); ++it) {
for(ElementGroup::const_node_iterator nodes_it(it->second->node_begin());
nodes_it!= it->second->node_end(); ++nodes_it) {
UInt n(*nodes_it);
std::cout << "Node " << *nodes_it << std::endl;
for (UInt i = 0; i < dim; ++i) {
displacement(n, i) = alpha[i][0];
for (UInt j = 0; j < dim; ++j) {
displacement(n, i) += alpha[i][j + 1] * coordinates(n, j);
}
boundary(n, i) = true;
}
}
}
/* ------------------------------------------------------------------------ */
/* Apply eigenstrain in each element */
/* ------------------------------------------------------------------------ */
Array<Real> & eigenstrain_vect = const_cast<Array<Real> &>(my_model.getMaterial(0).getInternal("eigenstrain")(element_type));
Array<Real>::iterator< Matrix<Real> > eigenstrain_it = eigenstrain_vect.begin(dim, dim);
Array<Real>::iterator< Matrix<Real> > eigenstrain_end = eigenstrain_vect.end(dim, dim);
for (; eigenstrain_it != eigenstrain_end; ++eigenstrain_it) {
for (UInt i = 0; i < dim; ++i)
for (UInt j = 0; j < dim; ++j)
(*eigenstrain_it)(i,j) += prescribed_eigenstrain(i,j);
}
/* ------------------------------------------------------------------------ */
/* Static solve */
/* ------------------------------------------------------------------------ */
my_model.solveStep<_scm_newton_raphson_tangent_modified, _scc_residual>(2e-4, 2);
/* ------------------------------------------------------------------------ */
/* Checks */
/* ------------------------------------------------------------------------ */
Array<Real> & stress_vect = const_cast<Array<Real> &>(my_model.getMaterial(0).getStress(element_type));
Array<Real>::iterator< Matrix<Real> > stress_it = stress_vect.begin(dim, dim);
Array<Real>::iterator< Matrix<Real> > stress_end = stress_vect.end(dim, dim);
Matrix<Real> presc_stress;
presc_stress = prescribed_stress<element_type, plane_strain>(prescribed_eigenstrain);
Real stress_tolerance = 1e-13;
for (; stress_it != stress_end; ++stress_it) {
Matrix<Real> & stress = *stress_it;
Matrix<Real> diff(dim, dim);
diff = stress;
diff -= presc_stress;
Real stress_error = diff.norm<L_inf>() / stress.norm<L_inf>();
if(stress_error > stress_tolerance) {
std::cerr << "stress error: " << stress_error << " > " << stress_tolerance << std::endl;
std::cerr << "stress: " << stress << std::endl
<< "prescribed stress: " << presc_stress << std::endl;
return EXIT_FAILURE;
} else {
std::cerr << "stress error: " << stress_error << " < " << stress_tolerance << std::endl;
}
}
finalize();
return EXIT_SUCCESS;
}

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