phase_field_model.cc
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Created: Fri, Nov 15, 13:19

phase_field_model.cc
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	/**
	* @file phase_field_model.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Wed Aug 01 2018
	* @date last modification: Wed Aug 01 2018
	*
	* @brief Implementation of PhaseFieldModel class
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2018 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 "phase_field_model.hh"
	#include "dumpable_inline_impl.hh"
	#include "element_synchronizer.hh"
	#include "fe_engine_template.hh"
	#include "generalized_trapezoidal.hh"
	#include "group_manager_inline_impl.cc"
	#include "integrator_gauss.hh"
	#include "mesh.hh"
	#include "parser.hh"
	#include "shape_lagrange.hh"

	#ifdef AKANTU_USE_IOHELPER
	#include "dumper_element_partition.hh"
	#include "dumper_elemental_field.hh"
	#include "dumper_internal_material_field.hh"
	#include "dumper_iohelper_paraview.hh"
	#endif

	/* -------------------------------------------------------------------------- */
	namespace akantu {

	namespace phasefield {
	namespace details {
	class ComputeDamageFunctor {
	public:
	ComputeDamageFunctor(const PhaseFieldModel & model) : model(model){};
	// material functor can be created
	void operator()(Matrix<Real> & rho, const Element &) const {
	rho.set(1.);
	}

	private:
	const PhaseFieldModel & model;
	};
	} // namespace details
	} // namespace phasefield

	/* -------------------------------------------------------------------------- */
	PhaseFieldModel::PhaseFieldModel(Mesh & mesh, UInt dim, const ID & id,
	const MemoryID & memory_id,
	const ModelType model_type)
	: Model(mesh, model_type, dim, id, memory_id),
	BoundaryCondition<PhaseFieldModel>(),
	damage_on_qpoints("damage_on_qpoints", id),
	damage_energy_on_qpoints("damage_energy_on_qpoints", id),
	damage_energy_density_on_qpoints("damage_energy_density_on_qpoints", id),
	damage_gradient("damage_gradient", id),
	strain_on_qpoints("strain_on_qpoints", id),
	driving_force_on_qpoints("driving_force_on_qpoints", id),
	phi_history_on_qpoints("phi_history_on_qpoints", id) {

	AKANTU_DEBUG_IN();

	this->registerFEEngineObject<FEEngineType>("PhaseFieldFEEngine", mesh,
	Model::spatial_dimension);

	#ifdef AKANTU_USE_IOHELPER
	this->mesh.registerDumper<DumperParaview>("phase_field", id, true);
	this->mesh.addDumpMesh(mesh, spatial_dimension, _not_ghost, _ek_regular);
	#endif // AKANTU_USE_IOHELPER

	this->initDOFManager();

	this->registerDataAccessor(*this);

	if (this->mesh.isDistributed()) {
	auto & synchronizer = this->mesh.getElementSynchronizer();
	this->registerSynchronizer(synchronizer, SynchronizationTag::_pfm_damage);
	this->registerSynchronizer(synchronizer,
	SynchronizationTag::_pfm_gradient_damage);
	}

	this->registerParam("l0", l_0, 0., _pat_parsmod, "length scale");
	this->registerParam("gc", g_c, _pat_parsmod,
	"critical local fracture energy density");
	this->registerParam("E", E, _pat_parsmod, "Young's modulus");
	this->registerParam("nu", nu, _pat_parsmod, "Poisson ratio");

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	PhaseFieldModel::~PhaseFieldModel() = default;

	/* -------------------------------------------------------------------------- */
	MatrixType PhaseFieldModel::getMatrixType(const ID & matrix_id) {
	if (matrix_id == "K" or matrix_id == "M") {
	return _symmetric;
	}
	return _mt_not_defined;
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::initModel() {
	auto & fem = this->getFEEngine();
	fem.initShapeFunctions(_not_ghost);
	fem.initShapeFunctions(_ghost);

	damage_on_qpoints.initialize(fem, _nb_component = 1);
	damage_energy_on_qpoints.initialize(fem, _nb_component = spatial_dimension *
	spatial_dimension);
	damage_energy_density_on_qpoints.initialize(fem, _nb_component = 1);
	damage_gradient.initialize(fem, _nb_component = spatial_dimension);
	strain_on_qpoints.initialize(fem, _nb_component =
	spatial_dimension * spatial_dimension);
	driving_force_on_qpoints.initialize(fem, _nb_component = 1);
	phi_history_on_qpoints.initialize(fem, _nb_component = 1);
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::initFullImpl(const ModelOptions & options) {
	Model::initFullImpl(options);

	readMaterials();
	this->initBC(this, damage, *external_force);
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::readMaterials() {
	auto sect = this->getParserSection();

	if (not std::get<1>(sect)) {
	const auto & section = std::get<0>(sect);
	this->parseSection(section);
	}

	Matrix<double> d(spatial_dimension, spatial_dimension);
	d.eye(g_c * l_0);

	damage_energy_on_qpoints.set(d);
	this->updateInternalParameters();
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::updateInternalParameters() {
	this->lambda = this->nu * this->E / ((1 + this->nu) * (1 - 2 * this->nu));
	this->mu = this->E / (2 * (1 + this->nu));
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::assembleMatrix(const ID & matrix_id) {

	if (matrix_id == "K") {
	this->assembleStiffnessMatrix();
	} else {
	AKANTU_ERROR("Unknown Matrix ID for PhaseFieldModel : " << matrix_id);
	}
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::predictor() {
	// AKANTU_TO_IMPLEMENT();
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::corrector() {
	// AKANTU_TO_IMPLEMENT();
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::initSolver(TimeStepSolverType time_step_solver_type,
	NonLinearSolverType) {
	DOFManager & dof_manager = this->getDOFManager();

	this->allocNodalField(this->damage, 1, "damage");
	this->allocNodalField(this->external_force, 1, "external_force");
	this->allocNodalField(this->internal_force, 1, "internal_force");
	this->allocNodalField(this->blocked_dofs, 1, "blocked_dofs");
	this->allocNodalField(this->previous_damage, 1, "previous_damage");
	this->allocNodalField(this->damage_increment, 1, "damage_increment");

	if (!dof_manager.hasDOFs("damage")) {
	dof_manager.registerDOFs("damage", *this->damage, _dst_nodal);
	dof_manager.registerBlockedDOFs("damage", *this->blocked_dofs);
	dof_manager.registerDOFsIncrement("damage", *this->damage_increment);
	dof_manager.registerDOFsPrevious("damage", *this->previous_damage);
	}

	if (time_step_solver_type == TimeStepSolverType::_dynamic) {
	AKANTU_TO_IMPLEMENT();
	}
	}

	/* -------------------------------------------------------------------------- */
	FEEngine & PhaseFieldModel::getFEEngineBoundary(const ID & name) {
	return dynamic_cast<FEEngine &>(getFEEngineClassBoundary<FEEngineType>(name));
	}

	/* -------------------------------------------------------------------------- */
	std::tuple<ID, TimeStepSolverType>
	PhaseFieldModel::getDefaultSolverID(const AnalysisMethod & method) {
	switch (method) {
	case _explicit_lumped_mass: {
	return std::make_tuple("explicit_lumped",
	TimeStepSolverType::_dynamic_lumped);
	}
	case _static: {
	return std::make_tuple("static", TimeStepSolverType::_static);
	}
	case _implicit_dynamic: {
	return std::make_tuple("implicit", TimeStepSolverType::_dynamic);
	}
	default:
	return std::make_tuple("unknown", TimeStepSolverType::_not_defined);
	}
	}

	/* -------------------------------------------------------------------------- */
	ModelSolverOptions PhaseFieldModel::getDefaultSolverOptions(
	const TimeStepSolverType & type) const {
	ModelSolverOptions options;

	switch (type) {
	case TimeStepSolverType::_static: {
	options.non_linear_solver_type = NonLinearSolverType::_linear;
	options.integration_scheme_type["damage"] =
	IntegrationSchemeType::_pseudo_time;
	options.solution_type["damage"] = IntegrationScheme::_not_defined;
	break;
	}
	case TimeStepSolverType::_dynamic: {
	options.non_linear_solver_type = NonLinearSolverType::_newton_raphson;
	options.integration_scheme_type["damage"] =
	IntegrationSchemeType::_backward_euler;
	options.solution_type["damage"] = IntegrationScheme::_damage;
	break;
	}
	default:
	AKANTU_EXCEPTION(type << " is not a valid time step solver type");
	}

	return options;
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::beforeSolveStep() {

	this->computePhiHistoryOnQuadPoints(_not_ghost);
	this->computeDamageEnergyDensityOnQuadPoints(_not_ghost);
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::afterSolveStep() {

	for (auto && values : zip(damage, previous_damage)) {
	auto & dam = std::get<0>(values);
	auto & prev_dam = std::get<1>(values);

	dam -= prev_dam;
	dam = std::min(1., 2 * dam - dam * dam);
	prev_dam = dam;
	}
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::assembleStiffnessMatrix() {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_INFO("Assemble the new stiffness matrix");

	if (!this->getDOFManager().hasMatrix("K")) {
	this->getDOFManager().getNewMatrix("K", getMatrixType("K"));
	}

	this->getDOFManager().clearMatrix("K");

	this->assembleDamageMatrix();
	this->assembleDamageGradMatrix();
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::assembleDamageMatrix() {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_INFO("Assemble the new damage matrix");

	switch (mesh.getSpatialDimension()) {
	case 1:
	this->assembleDamageMatrix<1>(_not_ghost);
	break;
	case 2:
	this->assembleDamageMatrix<2>(_not_ghost);
	break;
	case 3:
	this->assembleDamageMatrix<3>(_not_ghost);
	break;
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::assembleDamageGradMatrix() {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_INFO("Assemble the new damage gradient matrix");

	switch (mesh.getSpatialDimension()) {
	case 1:
	this->assembleDamageGradMatrix<1>(_not_ghost);
	break;
	case 2:
	this->assembleDamageGradMatrix<2>(_not_ghost);
	break;
	case 3:
	this->assembleDamageGradMatrix<3>(_not_ghost);
	break;
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	void PhaseFieldModel::assembleDamageMatrix(const GhostType & ghost_type) {

	AKANTU_DEBUG_IN();

	auto & fem = getFEEngineClass<FEEngineType>();

	for (auto && type : mesh.elementTypes(spatial_dimension, ghost_type)) {
	auto nb_element = mesh.getNbElement(type, ghost_type);
	auto nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
	auto nb_quadrature_points = fem.getNbIntegrationPoints(type, ghost_type);

	auto nt_b_n = std::make_unique<Array<Real>>(
	nb_element * nb_quadrature_points,
	nb_nodes_per_element * nb_nodes_per_element, "N^tbN");

	auto & damage_energy_density_on_qpoints_vect =
	damage_energy_density_on_qpoints(type, ghost_type);

	// damage_energy_on_qpoints = gc/l0 + phi = scalar
	fem.computeNtbN(damage_energy_density_on_qpoints_vect, *nt_b_n, 2, type,
	ghost_type);

	/// compute @f$ K_{\grad d} = \int_e \mathbf{N}^t * \mathbf{w} *
	/// \mathbf{N}@f$
	auto K_n = std::make_unique<Array<Real>>(
	nb_element, nb_nodes_per_element * nb_nodes_per_element, "K_n");

	fem.integrate(nt_b_n, K_n, nb_nodes_per_element * nb_nodes_per_element,
	type, ghost_type);

	this->getDOFManager().assembleElementalMatricesToMatrix(
	"K", "damage", *K_n, type, ghost_type, _symmetric);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	void PhaseFieldModel::assembleDamageGradMatrix(const GhostType & ghost_type) {

	AKANTU_DEBUG_IN();

	auto & fem = this->getFEEngine();

	for (auto && type : mesh.elementTypes(spatial_dimension, ghost_type)) {
	auto nb_element = mesh.getNbElement(type, ghost_type);
	auto nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
	auto nb_quadrature_points = fem.getNbIntegrationPoints(type, ghost_type);

	auto bt_d_b = std::make_unique<Array<Real>>(
	nb_element * nb_quadrature_points,
	nb_nodes_per_element * nb_nodes_per_element, "B^tDB");

	auto & damage_energy_on_qpoints_vect =
	damage_energy_on_qpoints(type, ghost_type);

	// damage_energy_on_qpoints = gc*l0 = scalar
	fem.computeBtDB(damage_energy_on_qpoints_vect, *bt_d_b, 2, type,
	ghost_type);

	/// compute @f$ K_{\grad d} = \int_e \mathbf{B}^t * \mathbf{W} *
	/// \mathbf{B}@f$
	auto K_b = std::make_unique<Array<Real>>(
	nb_element, nb_nodes_per_element * nb_nodes_per_element, "K_b");

	fem.integrate(bt_d_b, K_b, nb_nodes_per_element * nb_nodes_per_element,
	type, ghost_type);

	this->getDOFManager().assembleElementalMatricesToMatrix(
	"K", "damage", *K_b, type, ghost_type, _symmetric);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::computeDamageEnergyDensityOnQuadPoints(
	const GhostType & ghost_type) {

	AKANTU_DEBUG_IN();

	for (auto & type : mesh.elementTypes(spatial_dimension, ghost_type)) {
	for (auto && values :
	zip(make_view(damage_energy_density_on_qpoints(type, ghost_type)),
	make_view(phi_history_on_qpoints(type, ghost_type)))) {

	auto & dam_energy_density = std::get<0>(values);
	auto & phi_history = std::get<1>(values);
	dam_energy_density = g_c / l_0 + 2.0 * phi_history;
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::computePhiHistoryOnQuadPoints(
	const GhostType & ghost_type) {

	Matrix<Real> strain_plus(spatial_dimension, spatial_dimension);
	Matrix<Real> strain_minus(spatial_dimension, spatial_dimension);
	Matrix<Real> strain_dir(spatial_dimension, spatial_dimension);
	Matrix<Real> strain_diag_plus(spatial_dimension, spatial_dimension);
	Matrix<Real> strain_diag_minus(spatial_dimension, spatial_dimension);

	Vector<Real> strain_values(spatial_dimension);

	Real trace_plus, trace_minus, phi_plus;

	for (auto & type : mesh.elementTypes(spatial_dimension, ghost_type)) {

	for (auto && values :
	zip(make_view(strain_on_qpoints(type, ghost_type), spatial_dimension,
	spatial_dimension),
	make_view(phi_history_on_qpoints(type, ghost_type)))) {

	auto & strain = std::get<0>(values);
	auto & phi_history = std::get<1>(values);

	strain_plus.clear();
	strain_minus.clear();
	strain_dir.clear();
	strain_values.clear();
	strain_diag_plus.clear();
	strain_diag_minus.clear();

	strain.eig(strain_values, strain_dir);

	for (UInt i = 0; i < spatial_dimension; i++) {
	strain_diag_plus(i, i) = std::max(Real(0.), strain_values(i));
	strain_diag_minus(i, i) = std::min(Real(0.), strain_values(i));
	}

	Matrix<Real> mat_tmp(spatial_dimension, spatial_dimension);
	Matrix<Real> sigma_plus(spatial_dimension, spatial_dimension);
	Matrix<Real> sigma_minus(spatial_dimension, spatial_dimension);

	mat_tmp.mul<false, true>(strain_diag_plus, strain_dir);
	strain_plus.mul<false, false>(strain_dir, mat_tmp);
	mat_tmp.mul<false, true>(strain_diag_minus, strain_dir);
	strain_minus.mul<false, true>(strain_dir, mat_tmp);

	trace_plus = std::max(Real(0.), strain.trace());
	trace_minus = std::min(Real(0.), strain.trace());

	for (UInt i = 0; i < spatial_dimension; i++) {
	for (UInt j = 0; j < spatial_dimension; j++) {
	sigma_plus(i, j) =
	(i == j) * lambda * trace_plus + 2 * mu * strain_plus(i, j);
	sigma_minus(i, j) =
	(i == j) * lambda * trace_minus + 2 * mu * strain_minus(i, j);
	}
	}

	phi_plus = 1. / 2 * sigma_plus.doubleDot(strain);

	if (phi_plus > phi_history) {
	phi_history = phi_plus;
	}
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::assembleResidual() {

	AKANTU_DEBUG_IN();

	this->assembleInternalForces();

	this->getDOFManager().assembleToResidual("damage", *this->external_force, 1);
	this->getDOFManager().assembleToResidual("damage", *this->internal_force, 1);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::assembleInternalForces() {
	AKANTU_DEBUG_IN();

	this->internal_force->clear();

	this->synchronize(SynchronizationTag::_pfm_damage);
	auto & fem = this->getFEEngine();

	for (auto ghost_type : ghost_types) {

	computeDrivingForce(ghost_type);

	for (auto type : mesh.elementTypes(spatial_dimension, ghost_type)) {
	UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);

	auto & driving_force_on_qpoints_vect =
	driving_force_on_qpoints(type, ghost_type);

	UInt nb_quad_points = driving_force_on_qpoints_vect.size();
	Array<Real> nt_driving_force(nb_quad_points, nb_nodes_per_element);
	fem.computeNtb(driving_force_on_qpoints_vect, nt_driving_force, type,
	ghost_type);

	UInt nb_elements = mesh.getNbElement(type, ghost_type);
	Array<Real> int_nt_driving_force(nb_elements, nb_nodes_per_element);

	fem.integrate(nt_driving_force, int_nt_driving_force,
	nb_nodes_per_element, type, ghost_type);

	this->getDOFManager().assembleElementalArrayLocalArray(
	int_nt_driving_force, *this->internal_force, type, ghost_type, 1);
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::assembleLumpedMatrix(const ID & matrix_id) {}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::setTimeStep(Real time_step, const ID & solver_id) {
	Model::setTimeStep(time_step, solver_id);

	#if defined(AKANTU_USE_IOHELPER)
	this->mesh.getDumper("phase_field").setTimeStep(time_step);
	#endif
	}
	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::computeDrivingForce(const GhostType & ghost_type) {

	for (auto & type : mesh.elementTypes(spatial_dimension, ghost_type)) {

	for (auto && values :
	zip(make_view(phi_history_on_qpoints(type, ghost_type)),
	make_view(driving_force_on_qpoints(type, ghost_type)))) {
	auto & phi_history = std::get<0>(values);
	auto & driving_force = std::get<1>(values);

	driving_force = 2.0 * phi_history;
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::computeDamageOnQuadPoints(const GhostType & ghost_type) {

	AKANTU_DEBUG_IN();

	auto & fem = this->getFEEngine();

	for (auto & type : mesh.elementTypes(spatial_dimension, ghost_type)) {
	auto & damage_on_qpoints_vect = damage_on_qpoints(type, ghost_type);
	fem.interpolateOnIntegrationPoints(*damage, damage_on_qpoints_vect, 1, type,
	ghost_type);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	UInt PhaseFieldModel::getNbData(const Array<Element> & elements,
	const SynchronizationTag & tag) const {

	AKANTU_DEBUG_IN();

	UInt size = 0;
	UInt nb_nodes_per_element = 0;

	for (const Element & el : elements) {
	nb_nodes_per_element += Mesh::getNbNodesPerElement(el.type);
	}

	switch (tag) {
	case SynchronizationTag::_pfm_damage: {
	size += nb_nodes_per_element * sizeof(Real); // damage
	break;
	}
	case SynchronizationTag::_pfm_gradient_damage: {
	size += getNbIntegrationPoints(elements) * spatial_dimension * sizeof(Real);
	size += nb_nodes_per_element * sizeof(Real);
	break;
	}
	default: { AKANTU_ERROR("Unknown ghost synchronization tag : " << tag); }
	}

	AKANTU_DEBUG_OUT();
	return size;
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::packData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) const {

	switch (tag) {
	case SynchronizationTag::_pfm_damage: {
	packNodalDataHelper(*damage, buffer, elements, mesh);
	break;
	}
	case SynchronizationTag::_pfm_gradient_damage: {
	packElementalDataHelper(damage_gradient, buffer, elements, true,
	getFEEngine());
	packNodalDataHelper(*damage, buffer, elements, mesh);
	break;
	}
	default: { AKANTU_ERROR("Unknown ghost synchronization tag : " << tag); }
	}
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::unpackData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) {

	switch (tag) {
	case SynchronizationTag::_pfm_damage: {
	unpackNodalDataHelper(*damage, buffer, elements, mesh);
	break;
	}
	case SynchronizationTag::_pfm_gradient_damage: {
	unpackElementalDataHelper(damage_gradient, buffer, elements, true,
	getFEEngine());
	unpackNodalDataHelper(*damage, buffer, elements, mesh);
	break;
	}
	default: { AKANTU_ERROR("Unknown ghost synchronization tag : " << tag); }
	}
	}

	/* -------------------------------------------------------------------------- */
	UInt PhaseFieldModel::getNbData(const Array<UInt> & indexes,
	const SynchronizationTag & tag) const {

	AKANTU_DEBUG_IN();

	UInt size = 0;
	UInt nb_nodes = indexes.size();

	switch (tag) {
	case SynchronizationTag::_pfm_damage: {
	size += nb_nodes * sizeof(Real);
	break;
	}
	default: { AKANTU_ERROR("Unknown ghost synchronization tag : " << tag); }
	}

	AKANTU_DEBUG_OUT();
	return size;
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::packData(CommunicationBuffer & buffer,
	const Array<UInt> & indexes,
	const SynchronizationTag & tag) const {

	AKANTU_DEBUG_IN();

	for (auto index : indexes) {
	switch (tag) {
	case SynchronizationTag::_pfm_damage: {
	buffer << (*damage)(index);
	break;
	}
	default: { AKANTU_ERROR("Unknown ghost synchronization tag : " << tag); }
	}
	}
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::unpackData(CommunicationBuffer & buffer,
	const Array<UInt> & indexes,
	const SynchronizationTag & tag) {

	AKANTU_DEBUG_IN();

	for (auto index : indexes) {
	switch (tag) {
	case SynchronizationTag::_pfm_damage: {
	buffer >> (*damage)(index);
	break;
	}
	default: { AKANTU_ERROR("Unknown ghost synchronization tag : " << tag); }
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	/* -------------------------------------------------------------------------- */
	#ifdef AKANTU_USE_IOHELPER

	std::shared_ptr<dumper::Field>
	PhaseFieldModel::createNodalFieldBool(const std::string & field_name,
	const std::string & group_name,
	bool /padding_flag/) {

	std::map<std::string, Array<bool> *> uint_nodal_fields;
	uint_nodal_fields["blocked_dofs"] = blocked_dofs;

	return mesh.createNodalField(uint_nodal_fields[field_name], group_name);

	std::shared_ptr<dumper::Field> field;
	return field;
	}

	/* -------------------------------------------------------------------------- */
	std::shared_ptr<dumper::Field>
	PhaseFieldModel::createNodalFieldReal(const std::string & field_name,
	const std::string & group_name,
	bool /padding_flag/) {

	if (field_name == "capacity_lumped") {
	AKANTU_EXCEPTION(
	"Capacity lumped is a nodal field now stored in the DOF manager."
	"Therefore it cannot be used by a dumper anymore");
	}

	std::map<std::string, Array<Real> *> real_nodal_fields;
	real_nodal_fields["damage"] = damage;
	real_nodal_fields["external_force"] = external_force;
	real_nodal_fields["internal_force"] = internal_force;

	return mesh.createNodalField(real_nodal_fields[field_name], group_name);

	std::shared_ptr<dumper::Field> field;
	return field;
	}

	/* -------------------------------------------------------------------------- */
	std::shared_ptr<dumper::Field> PhaseFieldModel::createElementalField(
	const std::string & field_name, const std::string & group_name,
	bool /padding_flag/, const UInt & spatial_dimension,
	const ElementKind & element_kind) {

	if (field_name == "partitions") {
	return mesh.createElementalField<UInt, dumper::ElementPartitionField>(
	mesh.getConnectivities(), group_name, this->spatial_dimension,
	element_kind);
	} else if (field_name == "damage_gradient") {
	ElementTypeMap<UInt> nb_data_per_elem =
	this->mesh.getNbDataPerElem(damage_gradient);

	return mesh.createElementalField<Real, dumper::InternalMaterialField>(
	damage_gradient, group_name, this->spatial_dimension, element_kind,
	nb_data_per_elem);
	} else if (field_name == "damage_energy") {
	ElementTypeMap<UInt> nb_data_per_elem =
	this->mesh.getNbDataPerElem(damage_energy_on_qpoints);

	return mesh.createElementalField<Real, dumper::InternalMaterialField>(
	damage_energy_on_qpoints, group_name, this->spatial_dimension,
	element_kind, nb_data_per_elem);
	}

	std::shared_ptr<dumper::Field> field;
	return field;
	}

	/* -------------------------------------------------------------------------- */
	#else
	/* -------------------------------------------------------------------------- */
	std::shared_ptr<dumper::Field> PhaseFieldModel::createElementalField(
	const std::string & /field_name/, const std::string & /group_name/,
	bool /padding_flag/, const ElementKind & /element_kind/) {
	return nullptr;
	}

	/* -------------------------------------------------------------------------- */
	std::shared_ptr<dumper::Field>
	PhaseFieldModel::createNodalFieldBool(const std::string & /field_name/,
	const std::string & /group_name/,
	bool /padding_flag/) {
	return nullptr;
	}

	/* -------------------------------------------------------------------------- */
	std::shared_ptr<dumper::Field>
	PhaseFieldModel::createNodalFieldReal(const std::string & /field_name/,
	const std::string & /group_name/,
	bool /padding_flag/) {
	return nullptr;
	}
	#endif

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::dump(const std::string & dumper_name) {
	mesh.dump(dumper_name);
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::dump(const std::string & dumper_name, UInt step) {
	mesh.dump(dumper_name, step);
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::dump(const std::string & dumper_name, Real time,
	UInt step) {
	mesh.dump(dumper_name, time, step);
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::dump() { mesh.dump(); }

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::dump(UInt step) { mesh.dump(step); }

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::dump(Real time, UInt step) { mesh.dump(time, step); }

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::printself(std::ostream & stream, int indent) const {
	std::string space;
	for (Int i = 0; i < indent; i++, space += AKANTU_INDENT)
	;

	stream << space << "Phase Field Model [" << std::endl;
	stream << space << " + id : " << id << std::endl;
	stream << space << " + spatial dimension : " << Model::spatial_dimension
	<< std::endl;
	stream << space << " + fem [" << std::endl;
	getFEEngine().printself(stream, indent + 2);
	stream << space << AKANTU_INDENT << "]" << std::endl;
	stream << space << " + nodals information [" << std::endl;
	damage->printself(stream, indent + 2);
	external_force->printself(stream, indent + 2);
	internal_force->printself(stream, indent + 2);
	blocked_dofs->printself(stream, indent + 2);
	stream << space << AKANTU_INDENT << "]" << std::endl;

	stream << space << " + material information [" << std::endl;
	stream << space << AKANTU_INDENT << "]" << std::endl;

	stream << space << " + materials [" << std::endl;
	stream << space << " length scale parameter : " << l_0 << std::endl;
	stream << space << " critical energy release rate : " << g_c << std::endl;
	stream << space << " Young's modulus : " << E << std::endl;
	stream << space << " Poisson's ratio : " << nu << std::endl;
	stream << space << " Lame's first parameter : " << lambda << std::endl;
	stream << space << " Lame's second parameter : " << mu << std::endl;
	stream << space << AKANTU_INDENT << "]" << std::endl;

	stream << space << "]" << std::endl;
	}

	} // namespace akantu

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