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material.cc
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			/**
			* @file material.cc
			*
			* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
			* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
			* @author Daniel Pino Muñoz <daniel.pinomunoz@epfl.ch>
			* @author Nicolas Richart <nicolas.richart@epfl.ch>
			* @author Marco Vocialta <marco.vocialta@epfl.ch>
			*
			* @date creation: Tue Jul 27 2010
			* @date last modification: Wed Feb 21 2018
			*
			* @brief Implementation of the common part of the material 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 "material.hh"
			#include "solid_mechanics_model.hh"
			/* -------------------------------------------------------------------------- */

			namespace akantu {

			/* -------------------------------------------------------------------------- */
			Material::Material(SolidMechanicsModel & model, const ID & id)
			: Memory(id, model.getMemoryID()), Parsable(ParserType::_material, id),
			is_init(false), fem(model.getFEEngine()), finite_deformation(false),
			name(""), model(model),
			spatial_dimension(this->model.getSpatialDimension()),
			element_filter("element_filter", id, this->memory_id),
			stress("stress", this), eigengradu("eigen_grad_u", this),
			gradu("grad_u", this), green_strain("green_strain", this),
			piola_kirchhoff_2("piola_kirchhoff_2", *this),
			potential_energy("potential_energy", *this), is_non_local(false),
			use_previous_stress(false), use_previous_gradu(false),
			interpolation_inverse_coordinates("interpolation inverse coordinates",
			*this),
			interpolation_points_matrices("interpolation points matrices", *this) {
			AKANTU_DEBUG_IN();

			/// for each connectivity types allocate the element filer array of the
			/// material
			element_filter.initialize(model.getMesh(),
			_spatial_dimension = spatial_dimension,
			_element_kind = _ek_regular);
			this->initialize();

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			Material::Material(SolidMechanicsModel & model, UInt dim, const Mesh & mesh,
			FEEngine & fe_engine, const ID & id)
			: Memory(id, model.getMemoryID()), Parsable(ParserType::_material, id),
			is_init(false), fem(fe_engine), finite_deformation(false), name(""),
			model(model), spatial_dimension(dim),
			element_filter("element_filter", id, this->memory_id),
			stress("stress", *this, dim, fe_engine, this->element_filter),
			eigengradu("eigen_grad_u", *this, dim, fe_engine, this->element_filter),
			gradu("gradu", *this, dim, fe_engine, this->element_filter),
			green_strain("green_strain", *this, dim, fe_engine, this->element_filter),
			piola_kirchhoff_2("piola_kirchhoff_2", *this, dim, fe_engine,
			this->element_filter),
			potential_energy("potential_energy", *this, dim, fe_engine,
			this->element_filter),
			is_non_local(false), use_previous_stress(false),
			use_previous_gradu(false),
			interpolation_inverse_coordinates("interpolation inverse_coordinates",
			*this, dim, fe_engine,
			this->element_filter),
			interpolation_points_matrices("interpolation points matrices", *this, dim,
			fe_engine, this->element_filter) {

			AKANTU_DEBUG_IN();

			element_filter.initialize(mesh, _spatial_dimension = spatial_dimension,
			_element_kind = _ek_regular);

			this->initialize();
			AKANTU_DEBUG_OUT();
			}

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

			/* -------------------------------------------------------------------------- */
			void Material::initialize() {
			registerParam("rho", rho, Real(0.), _pat_parsable \| _pat_modifiable,
			"Density");
			registerParam("name", name, std::string(), _pat_parsable \| _pat_readable);
			registerParam("finite_deformation", finite_deformation, false,
			_pat_parsable \| _pat_readable, "Is finite deformation");
			registerParam("inelastic_deformation", inelastic_deformation, false,
			_pat_internal, "Is inelastic deformation");

			/// allocate gradu stress for local elements
			eigengradu.initialize(spatial_dimension * spatial_dimension);
			gradu.initialize(spatial_dimension * spatial_dimension);
			stress.initialize(spatial_dimension * spatial_dimension);

			potential_energy.initialize(1);

			this->model.registerEventHandler(*this);
			}

			/* -------------------------------------------------------------------------- */
			void Material::initMaterial() {
			AKANTU_DEBUG_IN();

			if (finite_deformation) {
			this->piola_kirchhoff_2.initialize(spatial_dimension * spatial_dimension);
			if (use_previous_stress)
			this->piola_kirchhoff_2.initializeHistory();
			this->green_strain.initialize(spatial_dimension * spatial_dimension);
			}

			if (use_previous_stress)
			this->stress.initializeHistory();
			if (use_previous_gradu)
			this->gradu.initializeHistory();

			this->resizeInternals();

			is_init = true;

			updateInternalParameters();

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void Material::savePreviousState() {
			AKANTU_DEBUG_IN();

			for (auto pair : internal_vectors_real)
			if (pair.second->hasHistory())
			pair.second->saveCurrentValues();

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void Material::restorePreviousState() {
			AKANTU_DEBUG_IN();

			for (auto pair : internal_vectors_real)
			if (pair.second->hasHistory())
			pair.second->restorePreviousValues();

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			/**
			* Compute the residual by assembling @f$\int_{e} \sigma_e \frac{\partial
			* \varphi}{\partial X} dX @f$
			*
			* @param[in] displacements nodes displacements
			* @param[in] ghost_type compute the residual for _ghost or _not_ghost element
			*/
			// void Material::updateResidual(GhostType ghost_type) {
			// AKANTU_DEBUG_IN();

			// computeAllStresses(ghost_type);
			// assembleResidual(ghost_type);

			// AKANTU_DEBUG_OUT();
			// }

			/* -------------------------------------------------------------------------- */
			void Material::assembleInternalForces(GhostType ghost_type) {
			AKANTU_DEBUG_IN();

			UInt spatial_dimension = model.getSpatialDimension();

			if (!finite_deformation) {

			auto & internal_force = const_cast<Array<Real> &>(model.getInternalForce());

			// Mesh & mesh = fem.getMesh();
			for (auto && type :
			element_filter.elementTypes(spatial_dimension, ghost_type)) {
			Array<UInt> & elem_filter = element_filter(type, ghost_type);
			UInt nb_element = elem_filter.size();

			if (nb_element == 0)
			continue;

			const Array<Real> & shapes_derivatives =
			fem.getShapesDerivatives(type, ghost_type);

			UInt size_of_shapes_derivatives = shapes_derivatives.getNbComponent();
			UInt nb_quadrature_points = fem.getNbIntegrationPoints(type, ghost_type);
			UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);

			/// compute @f$\sigma \frac{\partial \varphi}{\partial X}@f$ by
			/// @f$\mathbf{B}^t \mathbf{\sigma}_q@f$
			Array<Real> * sigma_dphi_dx =
			new Array<Real>(nb_element * nb_quadrature_points,
			size_of_shapes_derivatives, "sigma_x_dphi_/_dX");

			fem.computeBtD(stress(type, ghost_type), *sigma_dphi_dx, type, ghost_type,
			elem_filter);

			/**
			* compute @f$\int \sigma * \frac{\partial \varphi}{\partial X}dX@f$ by
			* @f$ \sum_q \mathbf{B}^t
			* \mathbf{\sigma}_q \overline w_q J_q@f$
			*/
			Array<Real> * int_sigma_dphi_dx =
			new Array<Real>(nb_element, nb_nodes_per_element * spatial_dimension,
			"int_sigma_x_dphi_/_dX");

			fem.integrate(sigma_dphi_dx, int_sigma_dphi_dx,
			size_of_shapes_derivatives, type, ghost_type, elem_filter);
			delete sigma_dphi_dx;

			/// assemble
			model.getDOFManager().assembleElementalArrayLocalArray(
			*int_sigma_dphi_dx, internal_force, type, ghost_type, -1,
			elem_filter);
			delete int_sigma_dphi_dx;
			}
			} else {
			switch (spatial_dimension) {
			case 1:
			this->assembleInternalForces<1>(ghost_type);
			break;
			case 2:
			this->assembleInternalForces<2>(ghost_type);
			break;
			case 3:
			this->assembleInternalForces<3>(ghost_type);
			break;
			}
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			/**
			* Compute the stress from the gradu
			*
			* @param[in] current_position nodes postition + displacements
			* @param[in] ghost_type compute the residual for _ghost or _not_ghost element
			*/
			void Material::computeAllStresses(GhostType ghost_type) {
			AKANTU_DEBUG_IN();

			UInt spatial_dimension = model.getSpatialDimension();

			for (const auto & type :
			element_filter.elementTypes(spatial_dimension, ghost_type)) {
			Array<UInt> & elem_filter = element_filter(type, ghost_type);

			if (elem_filter.size() == 0)
			continue;
			Array<Real> & gradu_vect = gradu(type, ghost_type);

			/// compute @f$\nabla u@f$
			fem.gradientOnIntegrationPoints(model.getDisplacement(), gradu_vect,
			spatial_dimension, type, ghost_type,
			elem_filter);

			gradu_vect -= eigengradu(type, ghost_type);

			/// compute @f$\mathbf{\sigma}_q@f$ from @f$\nabla u@f$
			computeStress(type, ghost_type);
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void Material::computeAllCauchyStresses(GhostType ghost_type) {
			AKANTU_DEBUG_IN();

			AKANTU_DEBUG_ASSERT(finite_deformation, "The Cauchy stress can only be "
			"computed if you are working in "
			"finite deformation.");

			for (auto type : element_filter.elementTypes(spatial_dimension, ghost_type)) {
			switch (spatial_dimension) {
			case 1:
			this->StoCauchy<1>(type, ghost_type);
			break;
			case 2:
			this->StoCauchy<2>(type, ghost_type);
			break;
			case 3:
			this->StoCauchy<3>(type, ghost_type);
			break;
			}
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			template <UInt dim>
			void Material::StoCauchy(ElementType el_type, GhostType ghost_type) {
			AKANTU_DEBUG_IN();

			auto gradu_it = this->gradu(el_type, ghost_type).begin(dim, dim);

			auto gradu_end = this->gradu(el_type, ghost_type).end(dim, dim);

			auto piola_it = this->piola_kirchhoff_2(el_type, ghost_type).begin(dim, dim);

			auto stress_it = this->stress(el_type, ghost_type).begin(dim, dim);

			for (; gradu_it != gradu_end; ++gradu_it, ++piola_it, ++stress_it) {
			Matrix<Real> & grad_u = *gradu_it;
			Matrix<Real> & piola = *piola_it;
			Matrix<Real> & sigma = *stress_it;

			auto F_tensor = gradUToF<dim>(grad_u);
			this->StoCauchy<dim>(F_tensor, piola, sigma);
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void Material::setToSteadyState(GhostType ghost_type) {
			AKANTU_DEBUG_IN();

			const Array<Real> & displacement = model.getDisplacement();

			// resizeInternalArray(gradu);

			UInt spatial_dimension = model.getSpatialDimension();

			for (auto type : element_filter.elementTypes(spatial_dimension, ghost_type)) {
			Array<UInt> & elem_filter = element_filter(type, ghost_type);
			Array<Real> & gradu_vect = gradu(type, ghost_type);

			/// compute @f$\nabla u@f$
			fem.gradientOnIntegrationPoints(displacement, gradu_vect, spatial_dimension,
			type, ghost_type, elem_filter);

			setToSteadyState(type, ghost_type);
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			/**
			* Compute the stiffness matrix by assembling @f$\int_{\omega} B^t \times D
			* \times B d\omega @f$
			*
			* @param[in] current_position nodes postition + displacements
			* @param[in] ghost_type compute the residual for _ghost or _not_ghost element
			*/
			void Material::assembleStiffnessMatrix(GhostType ghost_type) {
			AKANTU_DEBUG_IN();

			UInt spatial_dimension = model.getSpatialDimension();

			for (auto type : element_filter.elementTypes(spatial_dimension, ghost_type)) {
			if (finite_deformation) {
			switch (spatial_dimension) {
			case 1: {
			assembleStiffnessMatrixNL<1>(type, ghost_type);
			assembleStiffnessMatrixL2<1>(type, ghost_type);
			break;
			}
			case 2: {
			assembleStiffnessMatrixNL<2>(type, ghost_type);
			assembleStiffnessMatrixL2<2>(type, ghost_type);
			break;
			}
			case 3: {
			assembleStiffnessMatrixNL<3>(type, ghost_type);
			assembleStiffnessMatrixL2<3>(type, ghost_type);
			break;
			}
			}
			} else {
			switch (spatial_dimension) {
			case 1: {
			assembleStiffnessMatrix<1>(type, ghost_type);
			break;
			}
			case 2: {
			assembleStiffnessMatrix<2>(type, ghost_type);
			break;
			}
			case 3: {
			assembleStiffnessMatrix<3>(type, ghost_type);
			break;
			}
			}
			}
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			template <UInt dim>
			void Material::assembleStiffnessMatrix(const ElementType & type,
			GhostType ghost_type) {
			AKANTU_DEBUG_IN();

			Array<UInt> & elem_filter = element_filter(type, ghost_type);
			if (elem_filter.size() == 0) {
			AKANTU_DEBUG_OUT();
			return;
			}

			// const Array<Real> & shapes_derivatives =
			// fem.getShapesDerivatives(type, ghost_type);

			Array<Real> & gradu_vect = gradu(type, ghost_type);

			UInt nb_element = elem_filter.size();
			UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
			UInt nb_quadrature_points = fem.getNbIntegrationPoints(type, ghost_type);

			gradu_vect.resize(nb_quadrature_points * nb_element);

			fem.gradientOnIntegrationPoints(model.getDisplacement(), gradu_vect, dim,
			type, ghost_type, elem_filter);

			UInt tangent_size = getTangentStiffnessVoigtSize(dim);

			Array<Real> * tangent_stiffness_matrix =
			new Array<Real>(nb_element * nb_quadrature_points,
			tangent_size * tangent_size, "tangent_stiffness_matrix");

			tangent_stiffness_matrix->clear();

			computeTangentModuli(type, *tangent_stiffness_matrix, ghost_type);

			/// compute @f$\mathbf{B}^t * \mathbf{D} * \mathbf{B}@f$
			UInt bt_d_b_size = dim * nb_nodes_per_element;

			Array<Real> * bt_d_b = new Array<Real>(nb_element * nb_quadrature_points,
			bt_d_b_size * bt_d_b_size, "B^tDB");

			fem.computeBtDB(tangent_stiffness_matrix, bt_d_b, 4, type, ghost_type,
			elem_filter);

			delete tangent_stiffness_matrix;

			/// compute @f$ k_e = \int_e \mathbf{B}^t * \mathbf{D} * \mathbf{B}@f$
			Array<Real> * K_e =
			new Array<Real>(nb_element, bt_d_b_size * bt_d_b_size, "K_e");

			fem.integrate(bt_d_b, K_e, bt_d_b_size * bt_d_b_size, type, ghost_type,
			elem_filter);

			delete bt_d_b;

			model.getDOFManager().assembleElementalMatricesToMatrix(
			"K", "displacement", *K_e, type, ghost_type, _symmetric, elem_filter);
			delete K_e;

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			template <UInt dim>
			void Material::assembleStiffnessMatrixNL(const ElementType & type,
			GhostType ghost_type) {
			AKANTU_DEBUG_IN();

			const Array<Real> & shapes_derivatives =
			fem.getShapesDerivatives(type, ghost_type);

			Array<UInt> & elem_filter = element_filter(type, ghost_type);
			// Array<Real> & gradu_vect = delta_gradu(type, ghost_type);

			UInt nb_element = elem_filter.size();
			UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
			UInt nb_quadrature_points = fem.getNbIntegrationPoints(type, ghost_type);

			Array<Real> * shapes_derivatives_filtered = new Array<Real>(
			nb_element * nb_quadrature_points, dim * nb_nodes_per_element,
			"shapes derivatives filtered");

			fem.filterElementalData(fem.getMesh(), shapes_derivatives,
			*shapes_derivatives_filtered, type, ghost_type,
			elem_filter);

			/// compute @f$\mathbf{B}^t * \mathbf{D} * \mathbf{B}@f$
			UInt bt_s_b_size = dim * nb_nodes_per_element;

			Array<Real> * bt_s_b = new Array<Real>(nb_element * nb_quadrature_points,
			bt_s_b_size * bt_s_b_size, "B^tDB");

			UInt piola_matrix_size = getCauchyStressMatrixSize(dim);

			Matrix<Real> B(piola_matrix_size, bt_s_b_size);
			Matrix<Real> Bt_S(bt_s_b_size, piola_matrix_size);
			Matrix<Real> S(piola_matrix_size, piola_matrix_size);

			auto shapes_derivatives_filtered_it = shapes_derivatives_filtered->begin(
			spatial_dimension, nb_nodes_per_element);

			auto Bt_S_B_it = bt_s_b->begin(bt_s_b_size, bt_s_b_size);
			auto Bt_S_B_end = bt_s_b->end(bt_s_b_size, bt_s_b_size);
			auto piola_it = piola_kirchhoff_2(type, ghost_type).begin(dim, dim);

			for (; Bt_S_B_it != Bt_S_B_end;
			++Bt_S_B_it, ++shapes_derivatives_filtered_it, ++piola_it) {
			auto & Bt_S_B = *Bt_S_B_it;
			const auto & Piola_kirchhoff_matrix = *piola_it;

			setCauchyStressMatrix<dim>(Piola_kirchhoff_matrix, S);
			VoigtHelper<dim>::transferBMatrixToBNL(*shapes_derivatives_filtered_it, B,
			nb_nodes_per_element);
			Bt_S.template mul<true, false>(B, S);
			Bt_S_B.template mul<false, false>(Bt_S, B);
			}

			delete shapes_derivatives_filtered;

			/// compute @f$ k_e = \int_e \mathbf{B}^t * \mathbf{D} * \mathbf{B}@f$
			Array<Real> * K_e =
			new Array<Real>(nb_element, bt_s_b_size * bt_s_b_size, "K_e");

			fem.integrate(bt_s_b, K_e, bt_s_b_size * bt_s_b_size, type, ghost_type,
			elem_filter);

			delete bt_s_b;

			model.getDOFManager().assembleElementalMatricesToMatrix(
			"K", "displacement", *K_e, type, ghost_type, _symmetric, elem_filter);

			delete K_e;

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			template <UInt dim>
			void Material::assembleStiffnessMatrixL2(const ElementType & type,
			GhostType ghost_type) {
			AKANTU_DEBUG_IN();

			const Array<Real> & shapes_derivatives =
			fem.getShapesDerivatives(type, ghost_type);

			Array<UInt> & elem_filter = element_filter(type, ghost_type);
			Array<Real> & gradu_vect = gradu(type, ghost_type);

			UInt nb_element = elem_filter.size();
			UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
			UInt nb_quadrature_points = fem.getNbIntegrationPoints(type, ghost_type);

			gradu_vect.resize(nb_quadrature_points * nb_element);

			fem.gradientOnIntegrationPoints(model.getDisplacement(), gradu_vect, dim,
			type, ghost_type, elem_filter);

			UInt tangent_size = getTangentStiffnessVoigtSize(dim);

			Array<Real> * tangent_stiffness_matrix =
			new Array<Real>(nb_element * nb_quadrature_points,
			tangent_size * tangent_size, "tangent_stiffness_matrix");

			tangent_stiffness_matrix->clear();

			computeTangentModuli(type, *tangent_stiffness_matrix, ghost_type);

			Array<Real> * shapes_derivatives_filtered = new Array<Real>(
			nb_element * nb_quadrature_points, dim * nb_nodes_per_element,
			"shapes derivatives filtered");
			fem.filterElementalData(fem.getMesh(), shapes_derivatives,
			*shapes_derivatives_filtered, type, ghost_type,
			elem_filter);

			/// compute @f$\mathbf{B}^t * \mathbf{D} * \mathbf{B}@f$
			UInt bt_d_b_size = dim * nb_nodes_per_element;

			Array<Real> * bt_d_b = new Array<Real>(nb_element * nb_quadrature_points,
			bt_d_b_size * bt_d_b_size, "B^tDB");

			Matrix<Real> B(tangent_size, dim * nb_nodes_per_element);
			Matrix<Real> B2(tangent_size, dim * nb_nodes_per_element);
			Matrix<Real> Bt_D(dim * nb_nodes_per_element, tangent_size);

			auto shapes_derivatives_filtered_it = shapes_derivatives_filtered->begin(
			spatial_dimension, nb_nodes_per_element);

			auto Bt_D_B_it = bt_d_b->begin(bt_d_b_size, bt_d_b_size);
			auto grad_u_it = gradu_vect.begin(dim, dim);
			auto D_it = tangent_stiffness_matrix->begin(tangent_size, tangent_size);
			auto D_end = tangent_stiffness_matrix->end(tangent_size, tangent_size);

			for (; D_it != D_end;
			++D_it, ++Bt_D_B_it, ++shapes_derivatives_filtered_it, ++grad_u_it) {
			const auto & grad_u = *grad_u_it;
			const auto & D = *D_it;
			auto & Bt_D_B = *Bt_D_B_it;

			// transferBMatrixToBL1<dim > (*shapes_derivatives_filtered_it, B,
			// nb_nodes_per_element);
			VoigtHelper<dim>::transferBMatrixToSymVoigtBMatrix(
			*shapes_derivatives_filtered_it, B, nb_nodes_per_element);
			VoigtHelper<dim>::transferBMatrixToBL2(*shapes_derivatives_filtered_it,
			grad_u, B2, nb_nodes_per_element);
			B += B2;
			Bt_D.template mul<true, false>(B, D);
			Bt_D_B.template mul<false, false>(Bt_D, B);
			}

			delete tangent_stiffness_matrix;
			delete shapes_derivatives_filtered;

			/// compute @f$ k_e = \int_e \mathbf{B}^t * \mathbf{D} * \mathbf{B}@f$
			Array<Real> * K_e =
			new Array<Real>(nb_element, bt_d_b_size * bt_d_b_size, "K_e");

			fem.integrate(bt_d_b, K_e, bt_d_b_size * bt_d_b_size, type, ghost_type,
			elem_filter);

			delete bt_d_b;

			model.getDOFManager().assembleElementalMatricesToMatrix(
			"K", "displacement", *K_e, type, ghost_type, _symmetric, elem_filter);
			delete K_e;

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			template <UInt dim>
			void Material::assembleInternalForces(GhostType ghost_type) {

			AKANTU_DEBUG_IN();

			Array<Real> & internal_force = model.getInternalForce();

			Mesh & mesh = fem.getMesh();
			for (auto type : element_filter.elementTypes(_ghost_type = ghost_type)) {
			const Array<Real> & shapes_derivatives =
			fem.getShapesDerivatives(type, ghost_type);

			Array<UInt> & elem_filter = element_filter(type, ghost_type);
			if (elem_filter.size() == 0)
			continue;
			UInt size_of_shapes_derivatives = shapes_derivatives.getNbComponent();
			UInt nb_element = elem_filter.size();
			UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
			UInt nb_quadrature_points = fem.getNbIntegrationPoints(type, ghost_type);

			Array<Real> * shapesd_filtered = new Array<Real>(
			nb_element, size_of_shapes_derivatives, "filtered shapesd");

			fem.filterElementalData(mesh, shapes_derivatives, *shapesd_filtered, type,
			ghost_type, elem_filter);

			Array<Real>::matrix_iterator shapes_derivatives_filtered_it =
			shapesd_filtered->begin(dim, nb_nodes_per_element);

			// Set stress vectors
			UInt stress_size = getTangentStiffnessVoigtSize(dim);

			// Set matrices B and BNL*
			UInt bt_s_size = dim * nb_nodes_per_element;

			auto * bt_s =
			new Array<Real>(nb_element * nb_quadrature_points, bt_s_size, "B^t*S");

			auto grad_u_it = this->gradu(type, ghost_type).begin(dim, dim);
			auto grad_u_end = this->gradu(type, ghost_type).end(dim, dim);
			auto stress_it = this->piola_kirchhoff_2(type, ghost_type).begin(dim, dim);
			shapes_derivatives_filtered_it =
			shapesd_filtered->begin(dim, nb_nodes_per_element);

			Array<Real>::matrix_iterator bt_s_it = bt_s->begin(bt_s_size, 1);

			Matrix<Real> B_tensor(stress_size, bt_s_size);
			Matrix<Real> B2_tensor(stress_size, bt_s_size);

			for (; grad_u_it != grad_u_end; ++grad_u_it, ++stress_it,
			++shapes_derivatives_filtered_it,
			++bt_s_it) {
			auto & grad_u = *grad_u_it;
			auto & r = *bt_s_it;
			auto & S = *stress_it;

			VoigtHelper<dim>::transferBMatrixToSymVoigtBMatrix(
			*shapes_derivatives_filtered_it, B_tensor, nb_nodes_per_element);

			VoigtHelper<dim>::transferBMatrixToBL2(*shapes_derivatives_filtered_it,
			grad_u, B2_tensor,
			nb_nodes_per_element);

			B_tensor += B2_tensor;

			auto S_vect = Material::stressToVoigt<dim>(S);
			Matrix<Real> S_voigt(S_vect.storage(), stress_size, 1);

			r.template mul<true, false>(B_tensor, S_voigt);
			}

			delete shapesd_filtered;

			/// compute @f$ k_e = \int_e \mathbf{B}^t * \mathbf{D} * \mathbf{B}@f$
			Array<Real> * r_e = new Array<Real>(nb_element, bt_s_size, "r_e");

			fem.integrate(bt_s, r_e, bt_s_size, type, ghost_type, elem_filter);

			delete bt_s;

			model.getDOFManager().assembleElementalArrayLocalArray(
			*r_e, internal_force, type, ghost_type, -1., elem_filter);
			delete r_e;
			}
			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void Material::computePotentialEnergyByElements() {
			AKANTU_DEBUG_IN();

			for (auto type : element_filter.elementTypes(spatial_dimension, _not_ghost)) {
			computePotentialEnergy(type);
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void Material::computePotentialEnergy(ElementType) {
			AKANTU_DEBUG_IN();
			AKANTU_TO_IMPLEMENT();
			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			Real Material::getPotentialEnergy() {
			AKANTU_DEBUG_IN();
			Real epot = 0.;

			computePotentialEnergyByElements();

			/// integrate the potential energy for each type of elements
			for (auto type : element_filter.elementTypes(spatial_dimension, _not_ghost)) {
			epot += fem.integrate(potential_energy(type, _not_ghost), type, _not_ghost,
			element_filter(type, _not_ghost));
			}

			AKANTU_DEBUG_OUT();
			return epot;
			}

			/* -------------------------------------------------------------------------- */
			Real Material::getPotentialEnergy(ElementType & type, UInt index) {
			AKANTU_DEBUG_IN();
			Real epot = 0.;

			Vector<Real> epot_on_quad_points(fem.getNbIntegrationPoints(type));

			computePotentialEnergyByElement(type, index, epot_on_quad_points);

			epot = fem.integrate(epot_on_quad_points, type, element_filter(type)(index));

			AKANTU_DEBUG_OUT();
			return epot;
			}

			/* -------------------------------------------------------------------------- */
			Real Material::getEnergy(const std::string & type) {
			AKANTU_DEBUG_IN();
			if (type == "potential")
			return getPotentialEnergy();
			AKANTU_DEBUG_OUT();
			return 0.;
			}

			/* -------------------------------------------------------------------------- */
			Real Material::getEnergy(const std::string & energy_id, ElementType type,
			UInt index) {
			AKANTU_DEBUG_IN();
			if (energy_id == "potential")
			return getPotentialEnergy(type, index);
			AKANTU_DEBUG_OUT();
			return 0.;
			}

			/* -------------------------------------------------------------------------- */
			void Material::initElementalFieldInterpolation(
			const ElementTypeMapArray<Real> & interpolation_points_coordinates) {
			AKANTU_DEBUG_IN();

			this->fem.initElementalFieldInterpolationFromIntegrationPoints(
			interpolation_points_coordinates, this->interpolation_points_matrices,
			this->interpolation_inverse_coordinates, &(this->element_filter));

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void Material::interpolateStress(ElementTypeMapArray<Real> & result,
			const GhostType ghost_type) {

			this->fem.interpolateElementalFieldFromIntegrationPoints(
			this->stress, this->interpolation_points_matrices,
			this->interpolation_inverse_coordinates, result, ghost_type,
			&(this->element_filter));
			}

			/* -------------------------------------------------------------------------- */
			void Material::interpolateStressOnFacets(
			ElementTypeMapArray<Real> & result,
			ElementTypeMapArray<Real> & by_elem_result, const GhostType ghost_type) {

			interpolateStress(by_elem_result, ghost_type);

			UInt stress_size = this->stress.getNbComponent();

			const Mesh & mesh = this->model.getMesh();
			const Mesh & mesh_facets = mesh.getMeshFacets();

			for (auto type : element_filter.elementTypes(spatial_dimension, ghost_type)) {
			Array<UInt> & elem_fil = element_filter(type, ghost_type);
			Array<Real> & by_elem_res = by_elem_result(type, ghost_type);
			UInt nb_element = elem_fil.size();
			UInt nb_element_full = this->model.getMesh().getNbElement(type, ghost_type);
			UInt nb_interpolation_points_per_elem =
			by_elem_res.size() / nb_element_full;

			const Array<Element> & facet_to_element =
			mesh_facets.getSubelementToElement(type, ghost_type);
			ElementType type_facet = Mesh::getFacetType(type);
			UInt nb_facet_per_elem = facet_to_element.getNbComponent();
			UInt nb_quad_per_facet =
			nb_interpolation_points_per_elem / nb_facet_per_elem;
			Element element_for_comparison{type, 0, ghost_type};
			const Array<std::vector<Element>> * element_to_facet = nullptr;
			GhostType current_ghost_type = _casper;
			Array<Real> * result_vec = nullptr;

			Array<Real>::const_matrix_iterator result_it =
			by_elem_res.begin_reinterpret(
			stress_size, nb_interpolation_points_per_elem, nb_element_full);

			for (UInt el = 0; el < nb_element; ++el) {
			UInt global_el = elem_fil(el);
			element_for_comparison.element = global_el;
			for (UInt f = 0; f < nb_facet_per_elem; ++f) {

			Element facet_elem = facet_to_element(global_el, f);
			UInt global_facet = facet_elem.element;
			if (facet_elem.ghost_type != current_ghost_type) {
			current_ghost_type = facet_elem.ghost_type;
			element_to_facet = &mesh_facets.getElementToSubelement(
			type_facet, current_ghost_type);
			result_vec = &result(type_facet, current_ghost_type);
			}

			bool is_second_element =
			(*element_to_facet)(global_facet)[0] != element_for_comparison;

			for (UInt q = 0; q < nb_quad_per_facet; ++q) {
			Vector<Real> result_local(result_vec->storage() +
			(global_facet * nb_quad_per_facet + q) *
			result_vec->getNbComponent() +
			is_second_element * stress_size,
			stress_size);

			const Matrix<Real> & result_tmp(result_it[global_el]);
			result_local = result_tmp(f * nb_quad_per_facet + q);
			}
			}
			}
			}
			}

			/* -------------------------------------------------------------------------- */
			template <typename T>
			const Array<T> & Material::getArray(const ID & /vect_id/,
			const ElementType & /type/,
			const GhostType & /ghost_type/) const {
			AKANTU_TO_IMPLEMENT();
			return NULL;
			}

			/* -------------------------------------------------------------------------- */
			template <typename T>
			Array<T> & Material::getArray(const ID & /vect_id/,
			const ElementType & /type/,
			const GhostType & /ghost_type/) {
			AKANTU_TO_IMPLEMENT();
			}

			/* -------------------------------------------------------------------------- */
			template <>
			const Array<Real> & Material::getArray(const ID & vect_id,
			const ElementType & type,
			const GhostType & ghost_type) const {
			std::stringstream sstr;
			std::string ghost_id = "";
			if (ghost_type == _ghost)
			ghost_id = ":ghost";
			sstr << getID() << ":" << vect_id << ":" << type << ghost_id;

			ID fvect_id = sstr.str();
			try {
			return Memory::getArray<Real>(fvect_id);
			} catch (debug::Exception & e) {
			AKANTU_SILENT_EXCEPTION("The material " << name << "(" << getID()
			<< ") does not contain a vector "
			<< vect_id << " (" << fvect_id
			<< ") [" << e << "]");
			}
			}

			/* -------------------------------------------------------------------------- */
			template <>
			Array<Real> & Material::getArray(const ID & vect_id, const ElementType & type,
			const GhostType & ghost_type) {
			std::stringstream sstr;
			std::string ghost_id = "";
			if (ghost_type == _ghost)
			ghost_id = ":ghost";
			sstr << getID() << ":" << vect_id << ":" << type << ghost_id;

			ID fvect_id = sstr.str();
			try {
			return Memory::getArray<Real>(fvect_id);
			} catch (debug::Exception & e) {
			AKANTU_SILENT_EXCEPTION("The material " << name << "(" << getID()
			<< ") does not contain a vector "
			<< vect_id << " (" << fvect_id
			<< ") [" << e << "]");
			}
			}

			/* -------------------------------------------------------------------------- */
			template <>
			const Array<UInt> & Material::getArray(const ID & vect_id,
			const ElementType & type,
			const GhostType & ghost_type) const {
			std::stringstream sstr;
			std::string ghost_id = "";
			if (ghost_type == _ghost)
			ghost_id = ":ghost";
			sstr << getID() << ":" << vect_id << ":" << type << ghost_id;

			ID fvect_id = sstr.str();
			try {
			return Memory::getArray<UInt>(fvect_id);
			} catch (debug::Exception & e) {
			AKANTU_SILENT_EXCEPTION("The material " << name << "(" << getID()
			<< ") does not contain a vector "
			<< vect_id << " (" << fvect_id
			<< ") [" << e << "]");
			}
			}

			/* -------------------------------------------------------------------------- */
			template <>
			Array<UInt> & Material::getArray(const ID & vect_id, const ElementType & type,
			const GhostType & ghost_type) {
			std::stringstream sstr;
			std::string ghost_id = "";
			if (ghost_type == _ghost)
			ghost_id = ":ghost";
			sstr << getID() << ":" << vect_id << ":" << type << ghost_id;

			ID fvect_id = sstr.str();
			try {
			return Memory::getArray<UInt>(fvect_id);
			} catch (debug::Exception & e) {
			AKANTU_SILENT_EXCEPTION("The material " << name << "(" << getID()
			<< ") does not contain a vector "
			<< vect_id << "(" << fvect_id
			<< ") [" << e << "]");
			}
			}

			/* -------------------------------------------------------------------------- */
			template <typename T>
			const InternalField<T> &
			Material::getInternal([[gnu::unused]] const ID & int_id) const {
			AKANTU_TO_IMPLEMENT();
			return NULL;
			}

			/* -------------------------------------------------------------------------- */
			template <typename T>
			InternalField<T> & Material::getInternal([[gnu::unused]] const ID & int_id) {
			AKANTU_TO_IMPLEMENT();
			return NULL;
			}

			/* -------------------------------------------------------------------------- */
			template <>
			const InternalField<Real> & Material::getInternal(const ID & int_id) const {
			auto it = internal_vectors_real.find(getID() + ":" + int_id);
			if (it == internal_vectors_real.end()) {
			AKANTU_SILENT_EXCEPTION("The material " << name << "(" << getID()
			<< ") does not contain an internal "
			<< int_id << " ("
			<< (getID() + ":" + int_id) << ")");
			}
			return *it->second;
			}

			/* -------------------------------------------------------------------------- */
			template <> InternalField<Real> & Material::getInternal(const ID & int_id) {
			auto it = internal_vectors_real.find(getID() + ":" + int_id);
			if (it == internal_vectors_real.end()) {
			AKANTU_SILENT_EXCEPTION("The material " << name << "(" << getID()
			<< ") does not contain an internal "
			<< int_id << " ("
			<< (getID() + ":" + int_id) << ")");
			}
			return *it->second;
			}

			/* -------------------------------------------------------------------------- */
			template <>
			const InternalField<UInt> & Material::getInternal(const ID & int_id) const {
			auto it = internal_vectors_uint.find(getID() + ":" + int_id);
			if (it == internal_vectors_uint.end()) {
			AKANTU_SILENT_EXCEPTION("The material " << name << "(" << getID()
			<< ") does not contain an internal "
			<< int_id << " ("
			<< (getID() + ":" + int_id) << ")");
			}
			return *it->second;
			}

			/* -------------------------------------------------------------------------- */
			template <> InternalField<UInt> & Material::getInternal(const ID & int_id) {
			auto it = internal_vectors_uint.find(getID() + ":" + int_id);
			if (it == internal_vectors_uint.end()) {
			AKANTU_SILENT_EXCEPTION("The material " << name << "(" << getID()
			<< ") does not contain an internal "
			<< int_id << " ("
			<< (getID() + ":" + int_id) << ")");
			}
			return *it->second;
			}

			/* -------------------------------------------------------------------------- */
			void Material::addElements(const Array<Element> & elements_to_add) {
			AKANTU_DEBUG_IN();
			UInt mat_id = model.getInternalIndexFromID(getID());
			Array<Element>::const_iterator<Element> el_begin = elements_to_add.begin();
			Array<Element>::const_iterator<Element> el_end = elements_to_add.end();
			for (; el_begin != el_end; ++el_begin) {
			const Element & element = *el_begin;
			Array<UInt> & mat_indexes =
			model.getMaterialByElement(element.type, element.ghost_type);
			Array<UInt> & mat_loc_num =
			model.getMaterialLocalNumbering(element.type, element.ghost_type);

			UInt index =
			this->addElement(element.type, element.element, element.ghost_type);
			mat_indexes(element.element) = mat_id;
			mat_loc_num(element.element) = index;
			}

			this->resizeInternals();

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void Material::removeElements(const Array<Element> & elements_to_remove) {
			AKANTU_DEBUG_IN();

			Array<Element>::const_iterator<Element> el_begin = elements_to_remove.begin();
			Array<Element>::const_iterator<Element> el_end = elements_to_remove.end();

			if (el_begin == el_end)
			return;

			ElementTypeMapArray<UInt> material_local_new_numbering(
			"remove mat filter elem", getID(), getMemoryID());

			Element element;
			for (auto ghost_type : ghost_types) {
			element.ghost_type = ghost_type;

			for (auto & type : element_filter.elementTypes(_ghost_type = ghost_type,
			_element_kind = _ek_not_defined)) {
			element.type = type;

			Array<UInt> & elem_filter = this->element_filter(type, ghost_type);
			Array<UInt> & mat_loc_num =
			this->model.getMaterialLocalNumbering(type, ghost_type);

			if (!material_local_new_numbering.exists(type, ghost_type))
			material_local_new_numbering.alloc(elem_filter.size(), 1, type,
			ghost_type);
			Array<UInt> & mat_renumbering =
			material_local_new_numbering(type, ghost_type);

			UInt nb_element = elem_filter.size();
			Array<UInt> elem_filter_tmp;

			UInt new_id = 0;
			for (UInt el = 0; el < nb_element; ++el) {
			element.element = elem_filter(el);

			if (std::find(el_begin, el_end, element) == el_end) {
			elem_filter_tmp.push_back(element.element);

			mat_renumbering(el) = new_id;
			mat_loc_num(element.element) = new_id;
			++new_id;
			} else {
			mat_renumbering(el) = UInt(-1);
			}
			}

			elem_filter.resize(elem_filter_tmp.size());
			elem_filter.copy(elem_filter_tmp);
			}
			}

			for (auto it = internal_vectors_real.begin();
			it != internal_vectors_real.end(); ++it)
			it->second->removeIntegrationPoints(material_local_new_numbering);

			for (auto it = internal_vectors_uint.begin();
			it != internal_vectors_uint.end(); ++it)
			it->second->removeIntegrationPoints(material_local_new_numbering);

			for (auto it = internal_vectors_bool.begin();
			it != internal_vectors_bool.end(); ++it)
			it->second->removeIntegrationPoints(material_local_new_numbering);

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void Material::resizeInternals() {
			AKANTU_DEBUG_IN();
			for (auto it = internal_vectors_real.begin();
			it != internal_vectors_real.end(); ++it)
			it->second->resize();

			for (auto it = internal_vectors_uint.begin();
			it != internal_vectors_uint.end(); ++it)
			it->second->resize();

			for (auto it = internal_vectors_bool.begin();
			it != internal_vectors_bool.end(); ++it)
			it->second->resize();
			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void Material::onElementsAdded(const Array<Element> &,
			const NewElementsEvent &) {
			this->resizeInternals();
			}

			/* -------------------------------------------------------------------------- */
			void Material::onElementsRemoved(
			const Array<Element> & element_list,
			const ElementTypeMapArray<UInt> & new_numbering,
			[[gnu::unused]] const RemovedElementsEvent & event) {
			UInt my_num = model.getInternalIndexFromID(getID());

			ElementTypeMapArray<UInt> material_local_new_numbering(
			"remove mat filter elem", getID(), getMemoryID());

			auto el_begin = element_list.begin();
			auto el_end = element_list.end();

			for (auto && gt : ghost_types) {
			for (auto && type :
			new_numbering.elementTypes(_all_dimensions, gt, _ek_not_defined)) {

			if (not element_filter.exists(type, gt) \|\|
			element_filter(type, gt).size() == 0)
			continue;

			auto & elem_filter = element_filter(type, gt);
			auto & mat_indexes = this->model.getMaterialByElement(type, gt);
			auto & mat_loc_num = this->model.getMaterialLocalNumbering(type, gt);
			auto nb_element = this->model.getMesh().getNbElement(type, gt);

			// all materials will resize of the same size...
			mat_indexes.resize(nb_element);
			mat_loc_num.resize(nb_element);

			if (!material_local_new_numbering.exists(type, gt))
			material_local_new_numbering.alloc(elem_filter.size(), 1, type, gt);

			auto & mat_renumbering = material_local_new_numbering(type, gt);
			const auto & renumbering = new_numbering(type, gt);
			Array<UInt> elem_filter_tmp;
			UInt ni = 0;
			Element el{type, 0, gt};

			for (UInt i = 0; i < elem_filter.size(); ++i) {
			el.element = elem_filter(i);
			if (std::find(el_begin, el_end, el) == el_end) {
			UInt new_el = renumbering(el.element);
			AKANTU_DEBUG_ASSERT(new_el != UInt(-1),
			"A not removed element as been badly renumbered");
			elem_filter_tmp.push_back(new_el);
			mat_renumbering(i) = ni;

			mat_indexes(new_el) = my_num;
			mat_loc_num(new_el) = ni;
			++ni;
			} else {
			mat_renumbering(i) = UInt(-1);
			}
			}

			elem_filter.resize(elem_filter_tmp.size());
			elem_filter.copy(elem_filter_tmp);
			}
			}

			for (auto it = internal_vectors_real.begin();
			it != internal_vectors_real.end(); ++it)
			it->second->removeIntegrationPoints(material_local_new_numbering);

			for (auto it = internal_vectors_uint.begin();
			it != internal_vectors_uint.end(); ++it)
			it->second->removeIntegrationPoints(material_local_new_numbering);

			for (auto it = internal_vectors_bool.begin();
			it != internal_vectors_bool.end(); ++it)
			it->second->removeIntegrationPoints(material_local_new_numbering);
			}

			/* -------------------------------------------------------------------------- */
			void Material::beforeSolveStep() { this->savePreviousState(); }

			/* -------------------------------------------------------------------------- */
			void Material::afterSolveStep() {
			for (auto & type : element_filter.elementTypes(_all_dimensions, _not_ghost,
			_ek_not_defined)) {
			this->updateEnergies(type);
			}
			}
			/* -------------------------------------------------------------------------- */
			void Material::onDamageIteration() { this->savePreviousState(); }

			/* -------------------------------------------------------------------------- */
			void Material::onDamageUpdate() {
			for (auto & type : element_filter.elementTypes(_all_dimensions, _not_ghost,
			_ek_not_defined)) {
			this->updateEnergiesAfterDamage(type);
			}
			}

			/* -------------------------------------------------------------------------- */
			void Material::onDump() {
			if (this->isFiniteDeformation())
			this->computeAllCauchyStresses(_not_ghost);
			}

			/* -------------------------------------------------------------------------- */
			void Material::printself(std::ostream & stream, int indent) const {
			std::string space(indent, AKANTU_INDENT);
			std::string type = getID().substr(getID().find_last_of(':') + 1);

			stream << space << "Material " << type << " [" << std::endl;
			Parsable::printself(stream, indent);
			stream << space << "]" << std::endl;
			}

			/* -------------------------------------------------------------------------- */
			/// extrapolate internal values
			void Material::extrapolateInternal(const ID & id, const Element & element,
			[[gnu::unused]] const Matrix<Real> & point,
			Matrix<Real> & extrapolated) {
			if (this->isInternal<Real>(id, element.kind())) {
			UInt nb_element =
			this->element_filter(element.type, element.ghost_type).size();
			const ID name = this->getID() + ":" + id;
			UInt nb_quads =
			this->internal_vectors_real[name]->getFEEngine().getNbIntegrationPoints(
			element.type, element.ghost_type);
			const Array<Real> & internal =
			this->getArray<Real>(id, element.type, element.ghost_type);
			UInt nb_component = internal.getNbComponent();
			Array<Real>::const_matrix_iterator internal_it =
			internal.begin_reinterpret(nb_component, nb_quads, nb_element);
			Element local_element = this->convertToLocalElement(element);

			/// instead of really extrapolating, here the value of the first GP
			/// is copied into the result vector. This works only for linear
			/// elements
			/// @todo extrapolate!!!!
			AKANTU_DEBUG_WARNING("This is a fix, values are not truly extrapolated");

			const Matrix<Real> & values = internal_it[local_element.element];
			UInt index = 0;
			Vector<Real> tmp(nb_component);
			for (UInt j = 0; j < values.cols(); ++j) {
			tmp = values(j);
			if (tmp.norm() > 0) {
			index = j;
			break;
			}
			}

			for (UInt i = 0; i < extrapolated.size(); ++i) {
			extrapolated(i) = values(index);
			}
			} else {
			Matrix<Real> default_values(extrapolated.rows(), extrapolated.cols(), 0.);
			extrapolated = default_values;
			}
			}

			/* -------------------------------------------------------------------------- */
			void Material::applyEigenGradU(const Matrix<Real> & prescribed_eigen_grad_u,
			const GhostType ghost_type) {

			for (auto && type : element_filter.elementTypes(_all_dimensions, _not_ghost,
			_ek_not_defined)) {
			if (!element_filter(type, ghost_type).size())
			continue;
			auto eigen_it = this->eigengradu(type, ghost_type)
			.begin(spatial_dimension, spatial_dimension);
			auto eigen_end = this->eigengradu(type, ghost_type)
			.end(spatial_dimension, spatial_dimension);
			for (; eigen_it != eigen_end; ++eigen_it) {
			auto & current_eigengradu = *eigen_it;
			current_eigengradu = prescribed_eigen_grad_u;
			}
			}
			}

			/* -------------------------------------------------------------------------- */
			MaterialFactory & Material::getFactory() {
			return MaterialFactory::getInstance();
			}

			} // namespace akantu

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material.cc
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