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test_phase_solid_coupling.cc
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test_phase_solid_coupling.cc
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/**
* @file test_phase_solid_coupling.cc
*
* @author Mohit Pundir <mohit.pundir@epfl.ch>
*
* @date creation: Sun Jan 06 2019
* @date last modification: Wed Mar 03 2021
*
* @brief test of the class PhaseFieldModel on the 2d square
*
*
* @section LICENSE
*
* Copyright (©) 2018-2021 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 "aka_common.hh"
#include "material.hh"
#include "material_phasefield.hh"
#include "non_linear_solver.hh"
#include "phase_field_model.hh"
#include "solid_mechanics_model.hh"
/* -------------------------------------------------------------------------- */
#include <fstream>
#include <iostream>
/* -------------------------------------------------------------------------- */
using namespace akantu;
const UInt spatial_dimension = 2;
/* -------------------------------------------------------------------------- */
void applyDisplacement(SolidMechanicsModel &, Real &);
void computeStrainOnQuadPoints(SolidMechanicsModel &, PhaseFieldModel &,
const GhostType &);
void computeDamageOnQuadPoints(SolidMechanicsModel &, PhaseFieldModel &,
const GhostType &);
void gradUToEpsilon(const Matrix<Real> &, Matrix<Real> &);
/* -------------------------------------------------------------------------- */
int main(int argc, char * argv[]) {
std::ofstream os("data.csv");
os << "#strain stress damage analytical_sigma analytical_damage" << std::endl;
initialize("material_coupling.dat", argc, argv);
Mesh mesh(spatial_dimension);
mesh.read("test_one_element.msh");
SolidMechanicsModel model(mesh);
model.initFull(_analysis_method = _static);
PhaseFieldModel phase(mesh);
auto && selector = std::make_shared<MeshDataPhaseFieldSelector<std::string>>(
"physical_names", phase);
phase.setPhaseFieldSelector(selector);
phase.initFull(_analysis_method = _static);
model.setBaseName("phase_solid");
model.addDumpField("stress");
model.addDumpField("grad_u");
model.addDumpFieldVector("displacement");
model.addDumpField("damage");
model.dump();
UInt nbSteps = 1000;
Real increment = 1e-4;
auto & stress = model.getMaterial(0).getArray<Real>("stress", _quadrangle_4);
auto & damage = model.getMaterial(0).getArray<Real>("damage", _quadrangle_4);
Real analytical_damage{0.};
Real analytical_sigma{0.};
auto & phasefield = phase.getPhaseField(0);
const Real E = phasefield.getParam("E");
const Real nu = phasefield.getParam("nu");
Real c22 = E * (1 - nu) / ((1 + nu) * (1 - 2 * nu));
const Real gc = phasefield.getParam("gc");
const Real l0 = phasefield.getParam("l0");
Real error_stress{0.};
Real error_damage{0.};
for (UInt s = 0; s < nbSteps; ++s) {
Real axial_strain = increment * s;
applyDisplacement(model, axial_strain);
model.solveStep();
computeStrainOnQuadPoints(model, phase, _not_ghost);
phase.solveStep();
computeDamageOnQuadPoints(model, phase, _not_ghost);
model.assembleInternalForces();
analytical_damage = axial_strain * axial_strain * c22 /
(gc / l0 + axial_strain * axial_strain * c22);
analytical_sigma =
c22 * axial_strain * (1 - analytical_damage) * (1 - analytical_damage);
error_stress = std::abs(analytical_sigma - stress(0, 3)) / analytical_sigma;
error_damage = std::abs(analytical_damage - damage(0)) / analytical_damage;
if (error_damage > 1e-8 and error_stress > 1e-8) {
return EXIT_FAILURE;
}
os << axial_strain << " " << stress(0, 3) << " " << damage(0) << " "
<< analytical_sigma << " " << analytical_damage << " " << error_stress
<< " " << error_damage << std::endl;
model.dump();
}
os.close();
finalize();
return EXIT_SUCCESS;
}
/* -------------------------------------------------------------------------- */
void applyDisplacement(SolidMechanicsModel & model, Real & increment) {
auto & displacement = model.getDisplacement();
auto & positions = model.getMesh().getNodes();
auto & blocked_dofs = model.getBlockedDOFs();
for (UInt n = 0; n < model.getMesh().getNbNodes(); ++n) {
if (positions(n, 1) == -0.5) {
displacement(n, 0) = 0;
displacement(n, 1) = 0;
blocked_dofs(n, 0) = true;
blocked_dofs(n, 1) = true;
} else {
displacement(n, 0) = 0;
displacement(n, 1) = increment;
blocked_dofs(n, 0) = true;
blocked_dofs(n, 1) = true;
}
}
}
/* -------------------------------------------------------------------------- */
void computeStrainOnQuadPoints(SolidMechanicsModel & solid,
PhaseFieldModel & phase,
const GhostType & ghost_type) {
auto & mesh = solid.getMesh();
auto nb_materials = solid.getNbMaterials();
auto nb_phasefields = phase.getNbPhaseFields();
AKANTU_DEBUG_ASSERT(
nb_phasefields == nb_materials,
"The number of phasefields and materials should be equal");
for (auto index : arange(nb_materials)) {
auto & material = solid.getMaterial(index);
for (auto index2 : arange(nb_phasefields)) {
auto & phasefield = phase.getPhaseField(index2);
if (phasefield.getName() == material.getName()) {
auto & strain_on_qpoints = phasefield.getStrain();
auto & gradu_on_qpoints = material.getGradU();
for (auto & type : mesh.elementTypes(spatial_dimension, ghost_type)) {
auto & strain_on_qpoints_vect = strain_on_qpoints(type, ghost_type);
auto & gradu_on_qpoints_vect = gradu_on_qpoints(type, ghost_type);
for (auto && values :
zip(make_view(strain_on_qpoints_vect, spatial_dimension,
spatial_dimension),
make_view(gradu_on_qpoints_vect, spatial_dimension,
spatial_dimension))) {
auto & strain = std::get<0>(values);
auto & grad_u = std::get<1>(values);
gradUToEpsilon(grad_u, strain);
}
}
break;
}
}
}
}
/* -------------------------------------------------------------------------- */
void computeDamageOnQuadPoints(SolidMechanicsModel & solid,
PhaseFieldModel & phase,
const GhostType & ghost_type) {
auto & fem = phase.getFEEngine();
auto & mesh = phase.getMesh();
auto nb_materials = solid.getNbMaterials();
auto nb_phasefields = phase.getNbPhaseFields();
AKANTU_DEBUG_ASSERT(
nb_phasefields == nb_materials,
"The number of phasefields and materials should be equal");
for (auto index : arange(nb_materials)) {
auto & material = solid.getMaterial(index);
for (auto index2 : arange(nb_phasefields)) {
auto & phasefield = phase.getPhaseField(index2);
if (phasefield.getName() == material.getName()) {
switch (spatial_dimension) {
case 1: {
auto & mat = static_cast<MaterialPhaseField<1> &>(material);
auto & solid_damage = mat.getDamage();
for (auto & type : mesh.elementTypes(spatial_dimension, ghost_type)) {
auto & damage_on_qpoints_vect = solid_damage(type, ghost_type);
fem.interpolateOnIntegrationPoints(
phase.getDamage(), damage_on_qpoints_vect, 1, type, ghost_type);
}
break;
}
case 2: {
auto & mat = static_cast<MaterialPhaseField<2> &>(material);
auto & solid_damage = mat.getDamage();
for (auto & type : mesh.elementTypes(spatial_dimension, ghost_type)) {
auto & damage_on_qpoints_vect = solid_damage(type, ghost_type);
fem.interpolateOnIntegrationPoints(
phase.getDamage(), damage_on_qpoints_vect, 1, type, ghost_type);
}
break;
}
default:
break;
}
}
}
}
}
/* -------------------------------------------------------------------------- */
void gradUToEpsilon(const Matrix<Real> & grad_u, Matrix<Real> & epsilon) {
for (UInt i = 0; i < spatial_dimension; ++i) {
for (UInt j = 0; j < spatial_dimension; ++j)
epsilon(i, j) = 0.5 * (grad_u(i, j) + grad_u(j, i));
}
}

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