solid_mechanics_model.cc
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Created: Sat, May 11, 21:12

solid_mechanics_model.cc
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	/**
	* @file solid_mechanics_model.cc
	*
	* @author Ramin Aghababaei <ramin.aghababaei@epfl.ch>
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Daniel Pino Muñoz <daniel.pinomunoz@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Clement Roux <clement.roux@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Tue Jul 27 2010
	* @date last modification: Tue Jan 19 2016
	*
	* @brief Implementation of the SolidMechanicsModel class
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2012, 2014, 2015 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"
	#include "integrator_gauss.hh"
	#include "shape_lagrange.hh"

	#include "element_synchronizer.hh"
	#include "sparse_matrix.hh"
	#include "static_communicator.hh"
	#include "synchronizer_registry.hh"

	#include "dumpable_inline_impl.hh"
	#ifdef AKANTU_USE_IOHELPER
	#include "dumper_paraview.hh"
	#endif

	#include "material_non_local.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	/**
	* A solid mechanics model need a mesh and a dimension to be created. the model
	* by it self can not do a lot, the good init functions should be called in
	* order to configure the model depending on what we want to do.
	*
	* @param mesh mesh representing the model we want to simulate
	* @param dim spatial dimension of the problem, if dim = 0 (default value) the
	* dimension of the problem is assumed to be the on of the mesh
	* @param id an id to identify the model
	*/
	SolidMechanicsModel::SolidMechanicsModel(Mesh & mesh, UInt dim, const ID & id,
	const MemoryID & memory_id)
	: Model(mesh, dim, id, memory_id), BoundaryCondition<SolidMechanicsModel>(),
	f_m2a(1.0), displacement(nullptr), previous_displacement(nullptr),
	displacement_increment(nullptr), mass(nullptr), velocity(nullptr),
	acceleration(nullptr), external_force(nullptr), internal_force(nullptr),
	blocked_dofs(nullptr), current_position(nullptr), mass_matrix(nullptr),
	velocity_damping_matrix(nullptr), stiffness_matrix(nullptr),
	jacobian_matrix(nullptr), material_index("material index", id, memory_id),
	material_local_numbering("material local numbering", id, memory_id),
	material_selector(new DefaultMaterialSelector(material_index)),
	is_default_material_selector(true), increment_flag(false),
	are_materials_instantiated(false) { //, pbc_synch(nullptr) {
	AKANTU_DEBUG_IN();

	this->registerFEEngineObject<MyFEEngineType>("SolidMechanicsFEEngine", mesh,
	Model::spatial_dimension);

	this->mesh.registerEventHandler(*this, _ehp_solid_mechanics_model);

	#if defined(AKANTU_USE_IOHELPER)
	this->mesh.registerDumper<DumperParaview>("paraview_all", id, true);
	this->mesh.addDumpMesh(mesh, Model::spatial_dimension, _not_ghost,
	_ek_regular);
	#endif

	this->initDOFManager();

	this->registerDataAccessor(*this);

	if (this->mesh.isDistributed()) {
	auto & synchronizer = this->mesh.getElementSynchronizer();
	this->registerSynchronizer(synchronizer, _gst_material_id);
	this->registerSynchronizer(synchronizer, _gst_smm_mass);
	this->registerSynchronizer(synchronizer, _gst_smm_stress);
	this->registerSynchronizer(synchronizer, _gst_smm_boundary);
	this->registerSynchronizer(synchronizer, _gst_for_dump);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	SolidMechanicsModel::~SolidMechanicsModel() {
	AKANTU_DEBUG_IN();

	if (is_default_material_selector) {
	delete material_selector;
	material_selector = nullptr;
	}

	for (auto & internal : this->registered_internals) {
	delete internal.second;
	}

	// delete pbc_synch;

	AKANTU_DEBUG_OUT();
	}

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

	#if defined(AKANTU_USE_IOHELPER)
	this->mesh.getDumper().setTimeStep(time_step);
	#endif
	}

	/* -------------------------------------------------------------------------- */
	/* Initialization */
	/* -------------------------------------------------------------------------- */
	/**
	* This function groups many of the initialization in on function. For most of
	* basics case the function should be enough. The functions initialize the
	* model, the internal vectors, set them to 0, and depending on the parameters
	* it also initialize the explicit or implicit solver.
	*
	* @param material_file the file containing the materials to use
	* @param method the analysis method wanted. See the akantu::AnalysisMethod for
	* the different possibilities
	*/
	void SolidMechanicsModel::initFull(const ModelOptions & options) {
	Model::initFull(options);

	const SolidMechanicsModelOptions & smm_options =
	dynamic_cast<const SolidMechanicsModelOptions &>(options);

	this->method = smm_options.analysis_method;

	// initialize the vectors
	this->initArrays();

	if (!this->hasDefaultSolver())
	this->initNewSolver(this->method);

	// initialize pbc
	if (this->pbc_pair.size() != 0)
	this->initPBC();

	// initialize the materials
	if (this->parser->getLastParsedFile() != "") {
	this->instantiateMaterials();
	}

	//if (!smm_options.no_init_materials) {
	this->initMaterials();
	//}

	// if (increment_flag)
	this->initBC(this, displacement, displacement_increment, external_force);
	// else
	// this->initBC(this, displacement, *external_force);
	}

	/* -------------------------------------------------------------------------- */
	TimeStepSolverType SolidMechanicsModel::getDefaultSolverType() const {
	return _tsst_dynamic_lumped;
	}

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

	switch (type) {
	case _tsst_dynamic_lumped: {
	options.non_linear_solver_type = _nls_lumped;
	options.integration_scheme_type["displacement"] = _ist_central_difference;
	options.solution_type["displacement"] = IntegrationScheme::_acceleration;
	break;
	}
	case _tsst_static: {
	options.non_linear_solver_type = _nls_newton_raphson;
	options.integration_scheme_type["displacement"] = _ist_pseudo_time;
	options.solution_type["displacement"] = IntegrationScheme::_not_defined;
	break;
	}
	case _tsst_dynamic: {
	if (this->method == _explicit_consistent_mass) {
	options.non_linear_solver_type = _nls_newton_raphson;
	options.integration_scheme_type["displacement"] = _ist_central_difference;
	options.solution_type["displacement"] = IntegrationScheme::_acceleration;
	} else {
	options.non_linear_solver_type = _nls_newton_raphson;
	options.integration_scheme_type["displacement"] = _ist_trapezoidal_rule_2;
	options.solution_type["displacement"] = IntegrationScheme::_displacement;
	}
	break;
	}
	}

	return options;
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::initNewSolver(const AnalysisMethod & method) {
	ID solver_name;
	TimeStepSolverType tss_type;

	this->method = method;

	switch (this->method) {
	case _explicit_lumped_mass: {
	solver_name = "explicit_lumped";
	tss_type = _tsst_dynamic_lumped;
	break;
	}
	case _explicit_consistent_mass: {
	solver_name = "explicit";
	tss_type = _tsst_dynamic;
	break;
	}
	case _static: {
	solver_name = "static";
	tss_type = _tsst_static;
	break;
	}
	case _implicit_dynamic: {
	solver_name = "implicit";
	tss_type = _tsst_dynamic;
	break;
	}
	}

	if (!this->hasSolver(solver_name)) {
	ModelSolverOptions options = this->getDefaultSolverOptions(tss_type);
	this->getNewSolver(solver_name, tss_type, options.non_linear_solver_type);
	this->setIntegrationScheme(solver_name, "displacement",
	options.integration_scheme_type["displacement"],
	options.solution_type["displacement"]);
	this->setDefaultSolver(solver_name);
	}
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	void SolidMechanicsModel::allocNodalField(Array<T> *& array, const ID & name) {
	if (array == nullptr) {
	UInt nb_nodes = mesh.getNbNodes();
	std::stringstream sstr_disp;
	sstr_disp << id << ":" << name;

	array =
	&(alloc<T>(sstr_disp.str(), nb_nodes, Model::spatial_dimension, T()));
	}
	}

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

	/* ------------------------------------------------------------------------ */
	// for alloc type of solvers
	this->allocNodalField(this->displacement, "displacement");
	this->allocNodalField(this->previous_displacement, "previous_displacement");
	this->allocNodalField(this->displacement_increment, "displacement_increment");
	this->allocNodalField(this->internal_force, "internal_force");
	this->allocNodalField(this->external_force, "external_force");
	this->allocNodalField(this->blocked_dofs, "blocked_dofs");
	this->allocNodalField(this->current_position, "current_position");

	// initialize the current positions
	this->current_position->copy(this->mesh.getNodes());

	/* ------------------------------------------------------------------------ */
	if (!dof_manager.hasDOFs("displacement")) {
	dof_manager.registerDOFs("displacement", *this->displacement, _dst_nodal);
	dof_manager.registerBlockedDOFs("displacement", *this->blocked_dofs);
	dof_manager.registerDOFsIncrement("displacement",
	*this->displacement_increment);
	dof_manager.registerDOFsPrevious("displacement",
	*this->previous_displacement);
	}

	/* ------------------------------------------------------------------------ */
	// for dynamic
	if (time_step_solver_type == _tsst_dynamic \|\|
	time_step_solver_type == _tsst_dynamic_lumped) {
	this->allocNodalField(this->velocity, "velocity");
	this->allocNodalField(this->acceleration, "acceleration");

	if (!dof_manager.hasDOFsDerivatives("displacement", 1)) {
	dof_manager.registerDOFsDerivative("displacement", 1, *this->velocity);
	dof_manager.registerDOFsDerivative("displacement", 2,
	*this->acceleration);
	}
	}

	if (time_step_solver_type == _tsst_dynamic \|\|
	time_step_solver_type == _tsst_static) {
	if (!dof_manager.hasMatrix("K")) {
	dof_manager.getNewMatrix("K", _symmetric);
	}

	if (!dof_manager.hasMatrix("J")) {
	dof_manager.getNewMatrix("J", "K");
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	// void SolidMechanicsModel::initParallel(MeshPartition & partition,
	// DataAccessor<Element> * data_accessor)
	// {
	// AKANTU_DEBUG_IN();

	// if (data_accessor == nullptr)
	// data_accessor = this;
	// synch_parallel = &createParallelSynch(partition, *data_accessor);

	// synch_registry->registerSynchronizer(*synch_parallel, _gst_material_id);
	// synch_registry->registerSynchronizer(*synch_parallel, _gst_smm_mass);
	// synch_registry->registerSynchronizer(*synch_parallel, _gst_smm_stress);
	// synch_registry->registerSynchronizer(*synch_parallel, _gst_smm_boundary);
	// synch_registry->registerSynchronizer(*synch_parallel, _gst_for_dump);

	// AKANTU_DEBUG_OUT();
	// }

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::initFEEngineBoundary() {
	FEEngine & fem_boundary = getFEEngineBoundary();
	fem_boundary.initShapeFunctions(_not_ghost);
	fem_boundary.initShapeFunctions(_ghost);

	fem_boundary.computeNormalsOnIntegrationPoints(_not_ghost);
	fem_boundary.computeNormalsOnIntegrationPoints(_ghost);
	}

	/* -------------------------------------------------------------------------- */
	/**
	* Allocate all the needed vectors. By default their are not necessarily set to
	* 0
	*/
	void SolidMechanicsModel::initArrays() {
	AKANTU_DEBUG_IN();

	for (auto ghost_type : ghost_types) {
	for (auto type : mesh.elementTypes(Model::spatial_dimension, ghost_type,
	_ek_not_defined)) {
	UInt nb_element = mesh.getNbElement(type, ghost_type);
	this->material_index.alloc(nb_element, 1, type, ghost_type);
	this->material_local_numbering.alloc(nb_element, 1, type, ghost_type);
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	/**
	* Initialize the model,basically it pre-compute the shapes, shapes derivatives
	* and jacobian
	*
	*/
	void SolidMechanicsModel::initModel() {
	/// \todo add the current position as a parameter to initShapeFunctions for
	/// large deformation
	getFEEngine().initShapeFunctions(_not_ghost);
	getFEEngine().initShapeFunctions(_ghost);
	}

	/* -------------------------------------------------------------------------- */
	// void SolidMechanicsModel::initPBC() {
	// Model::initPBC();
	// registerPBCSynchronizer();

	// // as long as there are ones on the diagonal of the matrix, we can put
	// // boudandary true for slaves
	// std::map<UInt, UInt>::iterator it = pbc_pair.begin();
	// std::map<UInt, UInt>::iterator end = pbc_pair.end();
	// UInt dim = mesh.getSpatialDimension();
	// while (it != end) {
	// for (UInt i = 0; i < dim; ++i)
	// (blocked_dofs)((it).first, i) = true;
	// ++it;
	// }
	// }

	// /* --------------------------------------------------------------------------
	// */
	// void SolidMechanicsModel::registerPBCSynchronizer() {
	// pbc_synch = new PBCSynchronizer(pbc_pair);
	// synch_registry->registerSynchronizer(*pbc_synch, _gst_smm_uv);
	// synch_registry->registerSynchronizer(*pbc_synch, _gst_smm_mass);
	// synch_registry->registerSynchronizer(*pbc_synch, _gst_smm_res);
	// synch_registry->registerSynchronizer(*pbc_synch, _gst_for_dump);
	// // changeLocalEquationNumberForPBC(pbc_pair, mesh.getSpatialDimension());
	// }

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::assembleResidual() {
	AKANTU_DEBUG_IN();

	/* ------------------------------------------------------------------------ */
	// computes the internal forces
	this->assembleInternalForces();

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

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::assembleJacobian() {
	this->assembleStiffnessMatrix();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::predictor() { ++displacement_release; }

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::corrector() { ++displacement_release; }

	/* -------------------------------------------------------------------------- */
	/**
	* This function computes the internal forces as F_{int} = \int_{\Omega} N
	* \sigma d\Omega@f$
	*/
	void SolidMechanicsModel::assembleInternalForces() {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_INFO("Assemble the internal forces");

	this->internal_force->clear();

	// compute the stresses of local elements
	AKANTU_DEBUG_INFO("Compute local stresses");
	for (auto & material : materials) {
	material->computeAllStresses(_not_ghost);
	}

	#ifdef AKANTU_DAMAGE_NON_LOCAL
	/* ------------------------------------------------------------------------ */
	/* Computation of the non local part */
	if(this->non_local_manager)
	this->non_local_manager->computeAllNonLocalStresses();
	#endif

	// communicate the stresses
	AKANTU_DEBUG_INFO("Send data for residual assembly");
	this->asynchronousSynchronize(_gst_smm_stress);

	// assemble the forces due to local stresses
	AKANTU_DEBUG_INFO("Assemble residual for local elements");
	for (auto & material : materials) {
	material->assembleInternalForces(_not_ghost);
	}

	// finalize communications
	AKANTU_DEBUG_INFO("Wait distant stresses");
	this->waitEndSynchronize(_gst_smm_stress);

	// assemble the stresses due to ghost elements
	AKANTU_DEBUG_INFO("Assemble residual for ghost elements");
	for (auto & material : materials) {
	material->assembleInternalForces(_ghost);
	}

	AKANTU_DEBUG_OUT();
	}

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

	AKANTU_DEBUG_INFO("Assemble the new stiffness matrix.");

	// Check if materials need to recompute the matrix
	bool need_to_reassemble = false;

	for (auto & material : materials) {
	need_to_reassemble \|= material->hasStiffnessMatrixChanged();
	}

	if (need_to_reassemble) {
	this->getDOFManager().getMatrix("K").clear();

	// call compute stiffness matrix on each local elements
	for (auto & material : materials) {
	material->assembleStiffnessMatrix(_not_ghost);
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::updateCurrentPosition() {
	if (this->current_position_release == this->displacement_release)
	return;

	this->current_position->copy(this->mesh.getNodes());

	auto cpos_it = this->current_position->begin(Model::spatial_dimension);
	auto cpos_end = this->current_position->end(Model::spatial_dimension);
	auto disp_it = this->displacement->begin(Model::spatial_dimension);

	for (; cpos_it != cpos_end; ++cpos_it, ++disp_it) {
	cpos_it += disp_it;
	}

	this->current_position_release = this->displacement_release;
	}

	/* -------------------------------------------------------------------------- */
	const Array<Real> & SolidMechanicsModel::getCurrentPosition() {
	this->updateCurrentPosition();
	return *this->current_position;
	}

	/* -------------------------------------------------------------------------- */
	// void SolidMechanicsModel::initializeUpdateResidualData() {
	// AKANTU_DEBUG_IN();
	// UInt nb_nodes = mesh.getNbNodes();
	// internal_force->resize(nb_nodes);

	// /// copy the forces in residual for boundary conditions
	// this->getDOFManager().assembleToResidual("displacement",
	// *this->external_force);

	// // start synchronization
	// this->asynchronousSynchronize(_gst_smm_uv);
	// this->waitEndSynchronize(_gst_smm_uv);

	// this->updateCurrentPosition();

	// AKANTU_DEBUG_OUT();
	// }

	/* -------------------------------------------------------------------------- */
	/* Explicit scheme */
	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	// void SolidMechanicsModel::computeStresses() {
	// if (isExplicit()) {
	// // start synchronization
	// this->asynchronousSynchronize(_gst_smm_uv);
	// this->waitEndSynchronize(_gst_smm_uv);

	// // compute stresses on all local elements for each materials
	// std::vector<Material *>::iterator mat_it;
	// for (mat_it = materials.begin(); mat_it != materials.end(); ++mat_it) {
	// Material & mat = **mat_it;
	// mat.computeAllStresses(_not_ghost);
	// }

	// #ifdef AKANTU_DAMAGE_NON_LOCAL
	// /* Computation of the non local part */
	// this->non_local_manager->computeAllNonLocalStresses();
	// #endif
	// } else {
	// std::vector<Material *>::iterator mat_it;
	// for (mat_it = materials.begin(); mat_it != materials.end(); ++mat_it) {
	// Material & mat = **mat_it;
	// mat.computeAllStressesFromTangentModuli(_not_ghost);
	// }
	// }
	// }

	/* -------------------------------------------------------------------------- */
	/* Implicit scheme */
	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	// /**
	// * Initialize the solver and create the sparse matrices needed.
	// *
	// */
	// void SolidMechanicsModel::initSolver(__attribute__((unused))
	// SolverOptions & options) {
	// UInt nb_global_nodes = mesh.getNbGlobalNodes();

	// jacobian_matrix = &(this->getDOFManager().getNewMatrix("jacobian",
	// _symmetric));

	// // jacobian_matrix->buildProfile(mesh, *dof_synchronizer,
	// spatial_dimension);

	// if (!isExplicit()) {
	// delete stiffness_matrix;
	// std::stringstream sstr_sti;
	// sstr_sti << id << ":stiffness_matrix";

	// stiffness_matrix = &(this->getDOFManager().getNewMatrix("stiffness",
	// _symmetric));
	// }

	// if (solver) solver->initialize(options);
	// }

	// /* --------------------------------------------------------------------------
	// */
	// void SolidMechanicsModel::initJacobianMatrix() {
	// // @todo make it more flexible: this is an ugly patch to treat the case of
	// non
	// // fix profile of the K matrix
	// delete jacobian_matrix;

	// jacobian_matrix = &(this->getDOFManager().getNewMatrix("jacobian",
	// "stiffness"));

	// std::stringstream sstr_solv; sstr_solv << id << ":solver";
	// delete solver;
	// solver = new SolverMumps(*jacobian_matrix, sstr_solv.str());
	// if(solver)
	// solver->initialize(_solver_no_options);
	// }

	/* -------------------------------------------------------------------------- */
	/**
	* Initialize the implicit solver, either for dynamic or static cases,
	*
	* @param dynamic
	*/
	// void SolidMechanicsModel::initImplicit(bool dynamic) {
	// AKANTU_DEBUG_IN();

	// method = dynamic ? _implicit_dynamic : _static;

	// if (!increment)
	// setIncrementFlagOn();

	// initSolver();

	// // if(method == _implicit_dynamic) {
	// // if(integrator) delete integrator;
	// // integrator = new TrapezoidalRule2();
	// // }

	// AKANTU_DEBUG_OUT();
	// }

	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	// SparseMatrix & SolidMechanicsModel::initVelocityDampingMatrix() {
	// return this->getDOFManager().getNewMatrix("velocity_damping", "jacobian");
	// }

	// /* --------------------------------------------------------------------------
	// */
	// void SolidMechanicsModel::implicitPred() {
	// AKANTU_DEBUG_IN();

	// if(previous_displacement) previous_displacement->copy(*displacement);

	// if(method == _implicit_dynamic)
	// integrator->integrationSchemePred(time_step,
	// *displacement,
	// *velocity,
	// *acceleration,
	// *blocked_dofs);

	// AKANTU_DEBUG_OUT();
	// }

	// /* --------------------------------------------------------------------------
	// */
	// void SolidMechanicsModel::implicitCorr() {
	// AKANTU_DEBUG_IN();

	// if(method == _implicit_dynamic) {
	// integrator->integrationSchemeCorrDispl(time_step,
	// *displacement,
	// *velocity,
	// *acceleration,
	// *blocked_dofs,
	// *increment);
	// } else {
	// UInt nb_nodes = displacement->size();
	// UInt nb_degree_of_freedom = displacement->getNbComponent() * nb_nodes;

	// Real * incr_val = increment->storage();
	// Real * disp_val = displacement->storage();
	// bool * boun_val = blocked_dofs->storage();

	// for (UInt j = 0; j < nb_degree_of_freedom; ++j, ++disp_val, ++incr_val,
	// ++boun_val){
	// incr_val = (1. - *boun_val);
	// disp_val += incr_val;
	// }
	// }

	// AKANTU_DEBUG_OUT();
	// }

	/* -------------------------------------------------------------------------- */
	// void SolidMechanicsModel::updateIncrement() {
	// AKANTU_DEBUG_IN();

	// auto incr_it = this->displacement_increment->begin(spatial_dimension);
	// auto incr_end = this->displacement_increment->end(spatial_dimension);
	// auto disp_it = this->displacement->begin(spatial_dimension);
	// auto prev_disp_it = this->previous_displacement->begin(spatial_dimension);

	// for (; incr_it != incr_end; ++incr_it) {
	// incr_it = disp_it;
	// incr_it -= prev_disp_it;
	// }

	// AKANTU_DEBUG_OUT();
	// }

	// /* --------------------------------------------------------------------------
	// */ void SolidMechanicsModel::updatePreviousDisplacement() {
	// AKANTU_DEBUG_IN();

	// AKANTU_DEBUG_ASSERT(
	// previous_displacement,
	// "The previous displacement has to be initialized."
	// << " Are you working with Finite or Ineslactic deformations?");

	// previous_displacement->copy(*displacement);

	// AKANTU_DEBUG_OUT();
	// }

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::updateDataForNonLocalCriterion(
	ElementTypeMapReal & criterion) {
	const ID field_name = criterion.getName();
	for (auto & material : materials) {
	if (!material->isInternal<Real>(field_name, _ek_regular))
	continue;

	for (auto ghost_type : ghost_types) {
	material->flattenInternal(field_name, criterion, ghost_type, _ek_regular);
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	/* Information */
	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	// void SolidMechanicsModel::synchronizeBoundaries() {
	// AKANTU_DEBUG_IN();
	// this->synchronize(_gst_smm_boundary);
	// AKANTU_DEBUG_OUT();
	// }

	// /* --------------------------------------------------------------------------
	// */ void SolidMechanicsModel::synchronizeResidual() {
	// AKANTU_DEBUG_IN();
	// this->synchronize(_gst_smm_res);
	// AKANTU_DEBUG_OUT();
	// }

	/* -------------------------------------------------------------------------- */
	// void SolidMechanicsModel::setIncrementFlagOn() {
	// AKANTU_DEBUG_IN();

	// if (!displacement_increment) {
	// this->allocNodalField(displacement_increment, spatial_dimension,
	// "displacement_increment");

	// this->getDOFManager().registerDOFsIncrement("displacement",
	// *this->displacement_increment);
	// }

	// increment_flag = true;

	// AKANTU_DEBUG_OUT();
	// }

	/* -------------------------------------------------------------------------- */
	Real SolidMechanicsModel::getStableTimeStep() {
	AKANTU_DEBUG_IN();

	Real min_dt = getStableTimeStep(_not_ghost);

	/// reduction min over all processors
	StaticCommunicator::getStaticCommunicator().allReduce(min_dt, _so_min);

	AKANTU_DEBUG_OUT();
	return min_dt;
	}

	/* -------------------------------------------------------------------------- */
	Real SolidMechanicsModel::getStableTimeStep(const GhostType & ghost_type) {
	AKANTU_DEBUG_IN();

	Real min_dt = std::numeric_limits<Real>::max();

	this->updateCurrentPosition();

	Element elem;
	elem.ghost_type = ghost_type;
	elem.kind = _ek_regular;

	for (auto type :
	mesh.elementTypes(Model::spatial_dimension, ghost_type, _ek_regular)) {
	elem.type = type;
	UInt nb_nodes_per_element = mesh.getNbNodesPerElement(type);
	UInt nb_element = mesh.getNbElement(type);

	auto mat_indexes = material_index(type, ghost_type).begin();
	auto mat_loc_num = material_local_numbering(type, ghost_type).begin();

	Array<Real> X(0, nb_nodes_per_element * Model::spatial_dimension);
	FEEngine::extractNodalToElementField(mesh, *current_position, X, type,
	_not_ghost);

	auto X_el = X.begin(Model::spatial_dimension, nb_nodes_per_element);

	for (UInt el = 0; el < nb_element;
	++el, ++X_el, ++mat_indexes, ++mat_loc_num) {
	elem.element = *mat_loc_num;
	Real el_h = getFEEngine().getElementInradius(*X_el, type);
	Real el_c = this->materials[*mat_indexes]->getCelerity(elem);
	Real el_dt = el_h / el_c;

	min_dt = std::min(min_dt, el_dt);
	}
	}

	AKANTU_DEBUG_OUT();
	return min_dt;
	}

	/* -------------------------------------------------------------------------- */
	Real SolidMechanicsModel::getKineticEnergy() {
	AKANTU_DEBUG_IN();

	Real ekin = 0.;
	UInt nb_nodes = mesh.getNbNodes();

	if (this->getDOFManager().hasLumpedMatrix("M")) {
	auto m_it = this->mass->begin(Model::spatial_dimension);
	auto m_end = this->mass->end(Model::spatial_dimension);
	auto v_it = this->velocity->begin(Model::spatial_dimension);

	for (UInt n = 0; m_it != m_end; ++n, ++m_it, ++v_it) {
	const Vector<Real> & v = *v_it;
	const Vector<Real> & m = *m_it;

	Real mv2 = 0;
	bool is_local_node = mesh.isLocalOrMasterNode(n);
	// bool is_not_pbc_slave_node = !isPBCSlaveNode(n);
	bool count_node = is_local_node; // && is_not_pbc_slave_node;
	if (count_node) {
	for (UInt i = 0; i < Model::spatial_dimension; ++i) {
	if (m(i) > std::numeric_limits<Real>::epsilon())
	mv2 += v(i) * v(i) * m(i);
	}
	}

	ekin += mv2;
	}
	} else if (this->getDOFManager().hasMatrix("M")) {
	Array<Real> Mv(nb_nodes, Model::spatial_dimension);
	this->getDOFManager().getMatrix("M").matVecMul(*this->velocity, Mv);

	auto mv_it = Mv.begin(Model::spatial_dimension);
	auto mv_end = Mv.end(Model::spatial_dimension);
	auto v_it = this->velocity->begin(Model::spatial_dimension);

	for (; mv_it != mv_end; ++mv_it, ++v_it) {
	ekin += v_it->dot(*mv_it);
	}
	} else {
	AKANTU_DEBUG_ERROR("No function called to assemble the mass matrix.");
	}

	StaticCommunicator::getStaticCommunicator().allReduce(ekin, _so_sum);

	AKANTU_DEBUG_OUT();
	return ekin * .5;
	}

	/* -------------------------------------------------------------------------- */
	Real SolidMechanicsModel::getKineticEnergy(const ElementType & type,
	UInt index) {
	AKANTU_DEBUG_IN();

	UInt nb_quadrature_points = getFEEngine().getNbIntegrationPoints(type);

	Array<Real> vel_on_quad(nb_quadrature_points, Model::spatial_dimension);
	Array<UInt> filter_element(1, 1, index);

	getFEEngine().interpolateOnIntegrationPoints(*velocity, vel_on_quad,
	Model::spatial_dimension, type,
	_not_ghost, filter_element);

	Array<Real>::vector_iterator vit =
	vel_on_quad.begin(Model::spatial_dimension);
	Array<Real>::vector_iterator vend = vel_on_quad.end(Model::spatial_dimension);

	Vector<Real> rho_v2(nb_quadrature_points);

	Real rho = materials[material_index(type)(index)]->getRho();

	for (UInt q = 0; vit != vend; ++vit, ++q) {
	rho_v2(q) = rho * vit->dot(*vit);
	}

	AKANTU_DEBUG_OUT();

	return .5 * getFEEngine().integrate(rho_v2, type, index);
	}

	/* -------------------------------------------------------------------------- */
	Real SolidMechanicsModel::getExternalWork() {
	AKANTU_DEBUG_IN();

	auto incr_or_velo_it = this->velocity->begin(Model::spatial_dimension);
	if (this->method == _static) {
	incr_or_velo_it =
	this->displacement_increment->begin(Model::spatial_dimension);
	}

	auto ext_force_it = external_force->begin(Model::spatial_dimension);
	auto int_force_it = internal_force->begin(Model::spatial_dimension);
	auto boun_it = blocked_dofs->begin(Model::spatial_dimension);

	Real work = 0.;

	UInt nb_nodes = this->mesh.getNbNodes();

	for (UInt n = 0; n < nb_nodes;
	++n, ++ext_force_it, ++int_force_it, ++boun_it, ++incr_or_velo_it) {
	const auto & int_force = *int_force_it;
	const auto & ext_force = *ext_force_it;
	const auto & boun = *boun_it;
	const auto & incr_or_velo = *incr_or_velo_it;

	bool is_local_node = this->mesh.isLocalOrMasterNode(n);
	// bool is_not_pbc_slave_node = !this->isPBCSlaveNode(n);
	bool count_node = is_local_node; // && is_not_pbc_slave_node;

	if (count_node) {
	for (UInt i = 0; i < Model::spatial_dimension; ++i) {
	if (boun(i))
	work -= int_force(i) * incr_or_velo(i);
	else
	work += ext_force(i) * incr_or_velo(i);
	}
	}
	}

	StaticCommunicator::getStaticCommunicator().allReduce(work, _so_sum);

	if (this->method != _static)
	work *= this->getTimeStep();
	AKANTU_DEBUG_OUT();
	return work;
	}

	/* -------------------------------------------------------------------------- */
	Real SolidMechanicsModel::getEnergy(const std::string & energy_id) {
	AKANTU_DEBUG_IN();

	if (energy_id == "kinetic") {
	return getKineticEnergy();
	} else if (energy_id == "external work") {
	return getExternalWork();
	}

	Real energy = 0.;
	for (auto & material : materials)
	energy += material->getEnergy(energy_id);

	/// reduction sum over all processors
	StaticCommunicator::getStaticCommunicator().allReduce(energy, _so_sum);

	AKANTU_DEBUG_OUT();
	return energy;
	}
	/* -------------------------------------------------------------------------- */
	Real SolidMechanicsModel::getEnergy(const std::string & energy_id,
	const ElementType & type, UInt index) {
	AKANTU_DEBUG_IN();

	if (energy_id == "kinetic") {
	return getKineticEnergy(type, index);
	}

	UInt mat_index = this->material_index(type, _not_ghost)(index);
	UInt mat_loc_num = this->material_local_numbering(type, _not_ghost)(index);
	Real energy =
	this->materials[mat_index]->getEnergy(energy_id, type, mat_loc_num);

	AKANTU_DEBUG_OUT();
	return energy;
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::onElementsAdded(const Array<Element> & element_list,
	const NewElementsEvent & event) {
	AKANTU_DEBUG_IN();

	for (auto ghost_type : ghost_types) {
	for (auto type : mesh.elementTypes(Model::spatial_dimension, ghost_type,
	_ek_not_defined)) {
	UInt nb_element = this->mesh.getNbElement(type, ghost_type);

	if (!material_index.exists(type, ghost_type)) {
	this->material_index.alloc(nb_element, 1, type, ghost_type);
	this->material_local_numbering.alloc(nb_element, 1, type, ghost_type);
	} else {
	this->material_index(type, ghost_type).resize(nb_element);
	this->material_local_numbering(type, ghost_type).resize(nb_element);
	}
	}
	}

	ElementTypeMapArray<UInt> filter("new_element_filter", this->getID(),
	this->getMemoryID());

	for (auto & elem : element_list) {
	if (!filter.exists(elem.type, elem.ghost_type))
	filter.alloc(0, 1, elem.type, elem.ghost_type);

	filter(elem.type, elem.ghost_type).push_back(elem.element);
	}

	this->assignMaterialToElements(&filter);

	for (auto & material : materials)
	material->onElementsAdded(element_list, event);


	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::onElementsRemoved(
	__attribute__((unused)) const Array<Element> & element_list,
	const ElementTypeMapArray<UInt> & new_numbering,
	const RemovedElementsEvent & event) {
	this->getFEEngine().initShapeFunctions(_not_ghost);
	this->getFEEngine().initShapeFunctions(_ghost);

	for (auto & material : materials) {
	material->onElementsRemoved(element_list, new_numbering, event);
	}
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::onNodesAdded(const Array<UInt> & nodes_list,
	__attribute__((unused))
	const NewNodesEvent & event) {
	AKANTU_DEBUG_IN();
	UInt nb_nodes = mesh.getNbNodes();

	if (displacement) {
	displacement->resize(nb_nodes, 0.);
	++displacement_release;
	}
	if (mass)
	mass->resize(nb_nodes, 0.);
	if (velocity)
	velocity->resize(nb_nodes, 0.);
	if (acceleration)
	acceleration->resize(nb_nodes, 0.);
	if (external_force)
	external_force->resize(nb_nodes, 0.);
	if (internal_force)
	internal_force->resize(nb_nodes, 0.);
	if (blocked_dofs)
	blocked_dofs->resize(nb_nodes, 0.);
	if (current_position)
	current_position->resize(nb_nodes, 0.);

	if (previous_displacement)
	previous_displacement->resize(nb_nodes, 0.);
	if (displacement_increment)
	displacement_increment->resize(nb_nodes, 0.);

	for (auto & material : materials) {
	material->onNodesAdded(nodes_list, event);
	}

	if(this->getDOFManager().hasMatrix("M")) {
	this->assembleMass(nodes_list);
	}

	if(this->getDOFManager().hasLumpedMatrix("M")) {
	this->assembleMassLumped(nodes_list);
	}


	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::onNodesRemoved(__attribute__((unused))
	const Array<UInt> & element_list,
	const Array<UInt> & new_numbering,
	__attribute__((unused))
	const RemovedNodesEvent & event) {
	if (displacement) {
	mesh.removeNodesFromArray(*displacement, new_numbering);
	++displacement_release;
	}
	if (mass)
	mesh.removeNodesFromArray(*mass, new_numbering);
	if (velocity)
	mesh.removeNodesFromArray(*velocity, new_numbering);
	if (acceleration)
	mesh.removeNodesFromArray(*acceleration, new_numbering);
	if (internal_force)
	mesh.removeNodesFromArray(*internal_force, new_numbering);
	if (external_force)
	mesh.removeNodesFromArray(*external_force, new_numbering);
	if (blocked_dofs)
	mesh.removeNodesFromArray(*blocked_dofs, new_numbering);

	// if (increment_acceleration)
	// mesh.removeNodesFromArray(*increment_acceleration, new_numbering);
	if (displacement_increment)
	mesh.removeNodesFromArray(*displacement_increment, new_numbering);

	if (previous_displacement)
	mesh.removeNodesFromArray(*previous_displacement, new_numbering);

	// if (method != _explicit_lumped_mass) {
	// this->initSolver();
	// }
	}

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

	stream << space << "Solid Mechanics 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;
	displacement->printself(stream, indent + 2);
	mass->printself(stream, indent + 2);
	velocity->printself(stream, indent + 2);
	acceleration->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;
	material_index.printself(stream, indent + 2);
	stream << space << AKANTU_INDENT << "]" << std::endl;

	stream << space << " + materials [" << std::endl;
	for (auto & material : materials) {
	material->printself(stream, indent + 1);
	}
	stream << space << AKANTU_INDENT << "]" << std::endl;

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

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::insertIntegrationPointsInNeighborhoods(
	const GhostType & ghost_type) {
	for (auto & mat : materials) {
	try {
	ElementTypeMapArray<Real> quadrature_points_coordinates(
	"quadrature_points_coordinates_tmp_nl", this->id, this->memory_id);
	quadrature_points_coordinates.initialize(
	this->getFEEngine(), _spatial_dimension = Model::spatial_dimension,
	_nb_component = Model::spatial_dimension, _ghost_type = ghost_type);
	for (auto & type : quadrature_points_coordinates.elementTypes(
	Model::spatial_dimension, ghost_type)) {
	this->getFEEngine().computeIntegrationPointsCoordinates(
	quadrature_points_coordinates(type, ghost_type), type, ghost_type);
	}

	auto & mat_non_local = dynamic_cast<MaterialNonLocalInterface &>(*mat);
	mat_non_local.insertIntegrationPointsInNeighborhoods(
	ghost_type, quadrature_points_coordinates);
	} catch (std::bad_cast &) {
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::computeNonLocalStresses(
	const GhostType & ghost_type) {
	for (auto & mat : materials) {
	try {
	auto & mat_non_local = dynamic_cast<MaterialNonLocalInterface &>(*mat);
	mat_non_local.computeNonLocalStresses(ghost_type);
	} catch (std::bad_cast &) {
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::updateLocalInternal(
	ElementTypeMapReal & internal_flat, const GhostType & ghost_type,
	const ElementKind & kind) {
	const ID field_name = internal_flat.getName();
	for (auto & material : materials) {
	if (material->isInternal<Real>(field_name, kind))
	material->flattenInternal(field_name, internal_flat, ghost_type, kind);
	}
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::updateNonLocalInternal(
	ElementTypeMapReal & internal_flat, const GhostType & ghost_type,
	const ElementKind & kind) {

	const ID field_name = internal_flat.getName();

	for (auto & mat : materials) {
	try {
	auto & mat_non_local = dynamic_cast<MaterialNonLocalInterface &>(*mat);
	mat_non_local.updateNonLocalInternals(internal_flat, field_name,
	ghost_type, kind);
	} catch (std::bad_cast &) {
	}
	}
	}

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

	} // namespace akantu

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