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material.cc
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			/**
			* @file material.cc
			*
			* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
			* @author Marco Vocialta <marco.vocialta@epfl.ch>
			* @author Nicolas Richart <nicolas.richart@epfl.ch>
			* @author Daniel Pino Muñoz <daniel.pinomunoz@epfl.ch>
			*
			* @date creation: Tue Jul 27 2010
			* @date last modification: Tue Sep 16 2014
			*
			* @brief Implementation of the common part of the material class
			*
			* @section LICENSE
			*
			* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
			* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
			*
			* Akantu is free software: you can redistribute it and/or modify it under the
			* terms of the GNU Lesser General Public License as published by the Free
			* Software Foundation, either version 3 of the License, or (at your option) any
			* later version.
			*
			* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
			* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
			* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
			* details.
			*
			* You should have received a copy of the GNU Lesser General Public License
			* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
			*
			*/

			/* -------------------------------------------------------------------------- */
			#include "material.hh"
			#include "solid_mechanics_model.hh"
			#include "sparse_matrix.hh"
			#include "dof_synchronizer.hh"
			/* -------------------------------------------------------------------------- */


			__BEGIN_AKANTU__

			/* -------------------------------------------------------------------------- */
			Material::Material(SolidMechanicsModel & model, const ID & id) :
			Memory(id, model.getMemoryID()),
			Parsable(_st_material, id),
			is_init(false),
			finite_deformation(false),
			name(""),
			model(&model),
			spatial_dimension(this->model->getSpatialDimension()),
			element_filter("element_filter", id, this->memory_id),
			stress("stress", *this),
			eigenstrain("eigenstrain", *this),
			gradu("grad_u", *this),
			green_strain("green_strain",*this),
			piola_kirchhoff_2("piola_kirchhoff_2", *this),
			// potential_energy_vector(false),
			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
			model.getMesh().initElementTypeMapArray(element_filter,
			1,
			spatial_dimension,
			false,
			_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(_st_material, id),
			is_init(false),
			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),
			eigenstrain("eignestrain", *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("poila_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();
			mesh.initElementTypeMapArray(element_filter,
			1,
			spatial_dimension,
			false,
			_ek_regular);

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

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

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void Material::initialize() {
			registerParam("rho" , rho , 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
			eigenstrain.initialize(spatial_dimension * spatial_dimension);
			gradu.initialize(spatial_dimension * spatial_dimension);
			stress.initialize(spatial_dimension * spatial_dimension);

			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();

			for (std::map<ID, InternalField<Real> *>::iterator it = internal_vectors_real.begin();
			it != internal_vectors_real.end();
			++it) it->second->resize();

			for (std::map<ID, InternalField<UInt> *>::iterator it = internal_vectors_uint.begin();
			it != internal_vectors_uint.end();
			++it) it->second->resize();

			is_init = true;

			AKANTU_DEBUG_OUT();
			}

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

			for (std::map<ID, InternalField<Real> *>::iterator it = internal_vectors_real.begin();
			it != internal_vectors_real.end();
			++it) {
			if(it->second->hasHistory()) it->second->saveCurrentValues();
			}

			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::assembleResidual(GhostType ghost_type) {
			AKANTU_DEBUG_IN();

			UInt spatial_dimension = model->getSpatialDimension();

			if(!finite_deformation){

			Array<Real> & residual = const_cast<Array<Real> &>(model->getResidual());

			Mesh & mesh = model->getFEEngine().getMesh();
			Mesh::type_iterator it = element_filter.firstType(spatial_dimension, ghost_type);
			Mesh::type_iterator last_type = element_filter.lastType(spatial_dimension, ghost_type);
			for(; it != last_type; ++it) {
			const Array<Real> & shapes_derivatives = model->getFEEngine().getShapesDerivatives(*it, ghost_type);
			Array<UInt> & elem_filter = element_filter(*it, ghost_type);

			UInt size_of_shapes_derivatives = shapes_derivatives.getNbComponent();
			UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(*it);
			UInt nb_quadrature_points = model->getFEEngine().getNbQuadraturePoints(*it, ghost_type);

			UInt nb_element = elem_filter.getSize();
			/// 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");

			Array<Real> * shapesd_filtered =
			new Array<Real>(0, size_of_shapes_derivatives, "filtered shapesd");

			FEEngine::filterElementalData(mesh, shapes_derivatives, *shapesd_filtered,
			*it, ghost_type, elem_filter);

			Array<Real> & stress_vect = stress(*it, ghost_type);

			Array<Real>::matrix_iterator sigma =
			stress_vect.begin(spatial_dimension, spatial_dimension);
			Array<Real>::matrix_iterator B =
			shapesd_filtered->begin(spatial_dimension, nb_nodes_per_element);
			Array<Real>::matrix_iterator Bt_sigma_it =
			sigma_dphi_dx->begin(spatial_dimension, nb_nodes_per_element);

			for (UInt q = 0; q < nb_element*nb_quadrature_points; ++q, ++sigma, ++B, ++Bt_sigma_it)
			Bt_sigma_it->mul<false,false>(sigma, B);


			delete shapesd_filtered;

			/**
			* 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");

			model->getFEEngine().integrate(sigma_dphi_dx, int_sigma_dphi_dx,
			size_of_shapes_derivatives,
			*it, ghost_type,
			elem_filter);
			delete sigma_dphi_dx;


			/// assemble
			model->getFEEngine().assembleArray(*int_sigma_dphi_dx, residual,
			model->getDOFSynchronizer().getLocalDOFEquationNumbers(),
			residual.getNbComponent(),
			*it, ghost_type, elem_filter, -1);
			delete int_sigma_dphi_dx;
			}

			}
			else{
			switch (spatial_dimension){
			case 1:
			this->assembleResidual<1>(ghost_type);
			break;
			case 2:
			this->assembleResidual<2>(ghost_type);
			break;
			case 3:
			this->assembleResidual<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();

			Mesh::type_iterator it = model->getFEEngine().getMesh().firstType(spatial_dimension, ghost_type);
			Mesh::type_iterator last_type = model->getFEEngine().getMesh().lastType(spatial_dimension, ghost_type);

			for(; it != last_type; ++it) {
			Array<UInt> & elem_filter = element_filter(*it, ghost_type);
			Array<Real> & gradu_vect = gradu(*it, ghost_type);

			/// compute @f$\nabla u@f$
			model->getFEEngine().gradientOnQuadraturePoints(model->getDisplacement(), gradu_vect,
			spatial_dimension,
			*it, ghost_type, elem_filter);

			gradu_vect -= eigenstrain(*it, ghost_type);

			/// compute @f$\mathbf{\sigma}_q@f$ from @f$\nabla u@f$
			computeStress(*it, 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.");

			//resizeInternalArray(stress);

			Mesh::type_iterator it = model->getFEEngine().getMesh().firstType(spatial_dimension, ghost_type);
			Mesh::type_iterator last_type = model->getFEEngine().getMesh().lastType(spatial_dimension, ghost_type);

			for(; it != last_type; ++it)
			switch (spatial_dimension){
			case 1:
			this->computeCauchyStress<1>(*it, ghost_type);
			break;
			case 2:
			this->computeCauchyStress<2>(*it, ghost_type);
			break;
			case 3:
			this->computeCauchyStress<3>(*it, ghost_type);
			break;
			}

			AKANTU_DEBUG_OUT();
			}

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

			Array<Real>::matrix_iterator gradu_it =
			this->gradu(el_type, ghost_type).begin(dim, dim);

			Array<Real>::matrix_iterator gradu_end =
			this->gradu(el_type, ghost_type).end(dim, dim);

			Array<Real>::matrix_iterator piola_it =
			this->piola_kirchhoff_2(el_type, ghost_type).begin(dim, dim);

			Array<Real>::matrix_iterator stress_it =
			this->stress(el_type, ghost_type).begin(dim, dim);

			Matrix<Real> F_tensor(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;

			gradUToF<dim > (grad_u, F_tensor);
			this->computeCauchyStressOnQuad<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();

			Mesh::type_iterator it = model->getFEEngine().getMesh().firstType(spatial_dimension, ghost_type);
			Mesh::type_iterator last_type = model->getFEEngine().getMesh().lastType(spatial_dimension, ghost_type);

			for(; it != last_type; ++it) {
			Array<UInt> & elem_filter = element_filter(*it, ghost_type);
			Array<Real> & gradu_vect = gradu(*it, ghost_type);

			/// compute @f$\nabla u@f$
			model->getFEEngine().gradientOnQuadraturePoints(displacement, gradu_vect,
			spatial_dimension,
			*it, ghost_type, elem_filter);

			setToSteadyState(*it, 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();

			Mesh::type_iterator it = element_filter.firstType(spatial_dimension, ghost_type);
			Mesh::type_iterator last_type = element_filter.lastType(spatial_dimension, ghost_type);
			for(; it != last_type; ++it) {
			if(finite_deformation){
			switch (spatial_dimension) {
			case 1:
			{
			assembleStiffnessMatrixNL < 1 > (*it, ghost_type);
			assembleStiffnessMatrixL2 < 1 > (*it, ghost_type);
			break;
			}
			case 2:
			{
			assembleStiffnessMatrixNL < 2 > (*it, ghost_type);
			assembleStiffnessMatrixL2 < 2 > (*it, ghost_type);
			break;
			}
			case 3:
			{
			assembleStiffnessMatrixNL < 3 > (*it, ghost_type);
			assembleStiffnessMatrixL2 < 3 > (*it, ghost_type);
			break;
			}
			}
			} else {
			switch(spatial_dimension) {
			case 1: { assembleStiffnessMatrix<1>(*it, ghost_type); break; }
			case 2: { assembleStiffnessMatrix<2>(*it, ghost_type); break; }
			case 3: { assembleStiffnessMatrix<3>(*it, ghost_type); break; }
			}
			}
			}

			AKANTU_DEBUG_OUT();
			}

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

			SparseMatrix & K = const_cast<SparseMatrix &>(model->getStiffnessMatrix());

			const Array<Real> & shapes_derivatives = model->getFEEngine().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.getSize();
			UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
			UInt nb_quadrature_points = model->getFEEngine().getNbQuadraturePoints(type,
			ghost_type);

			gradu_vect.resize(nb_quadrature_points * nb_element);

			model->getFEEngine().gradientOnQuadraturePoints(model->getDisplacement(),
			gradu_vect, dim, type, ghost_type,
			elem_filter);

			UInt tangent_size = getTangentStiffnessVoigtSize(dim);

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

			tangent_stiffness_matrix->clear();

			computeTangentModuli(type, *tangent_stiffness_matrix, ghost_type);

			Array<Real> * shapesd_filtered =
			new Array<Real>(0, dim * nb_nodes_per_element, "filtered shapesd");

			FEEngine::filterElementalData(model->getFEEngine().getMesh(), shapes_derivatives,
			*shapesd_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> Bt_D(dim * nb_nodes_per_element, tangent_size);

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

			Array<Real>::matrix_iterator Bt_D_B_it
			= bt_d_b->begin(dimnb_nodes_per_element, dimnb_nodes_per_element);

			Array<Real>::matrix_iterator D_it
			= tangent_stiffness_matrix->begin(tangent_size, tangent_size);

			Array<Real>::matrix_iterator 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) {
			Matrix<Real> & D = *D_it;
			Matrix<Real> & Bt_D_B = *Bt_D_B_it;

			VoigtHelper<dim>::transferBMatrixToSymVoigtBMatrix(
			*shapes_derivatives_filtered_it, B, nb_nodes_per_element);
			Bt_D.mul<true, false>(B, D);
			Bt_D_B.mul<false, false>(Bt_D, B);
			}

			delete tangent_stiffness_matrix;
			delete shapesd_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");

			model->getFEEngine().integrate(bt_d_b, K_e,
			bt_d_b_size * bt_d_b_size,
			type, ghost_type,
			elem_filter);

			delete bt_d_b;

			model->getFEEngine().assembleMatrix(*K_e, K, spatial_dimension, type, ghost_type,
			elem_filter);
			delete K_e;

			AKANTU_DEBUG_OUT();
			}

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

			SparseMatrix & K = const_cast<SparseMatrix &> (model->getStiffnessMatrix());

			const Array<Real> & shapes_derivatives = model->getFEEngine().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.getSize();
			UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
			UInt nb_quadrature_points = model->getFEEngine().getNbQuadraturePoints(type, ghost_type);

			//gradu_vect.resize(nb_quadrature_points * nb_element);

			// model->getFEEngine().gradientOnQuadraturePoints(model->getIncrement(), gradu_vect,
			// dim, type, ghost_type, &elem_filter);

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


			Array<Real>::const_matrix_iterator shapes_derivatives_it = shapes_derivatives.begin(spatial_dimension,
			nb_nodes_per_element);

			Array<Real>::matrix_iterator shapes_derivatives_filtered_it = shapes_derivatives_filtered->begin(spatial_dimension,
			nb_nodes_per_element);
			UInt * elem_filter_val = elem_filter.storage();
			for (UInt e = 0; e < nb_element; ++e, ++elem_filter_val)
			for (UInt q = 0; q < nb_quadrature_points; ++q, ++shapes_derivatives_filtered_it)
			shapes_derivatives_filtered_it = shapes_derivatives_it[elem_filter_val * nb_quadrature_points + q];

			/// 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);

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

			Array<Real>::matrix_iterator Bt_S_B_it = bt_s_b->begin(bt_s_b_size,
			bt_s_b_size);
			Array<Real>::matrix_iterator Bt_S_B_end = bt_s_b->end(bt_s_b_size,
			bt_s_b_size);

			Array<Real>::matrix_iterator 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) {
			Matrix<Real> & Bt_S_B = *Bt_S_B_it;
			Matrix<Real> & 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.mul < true, false > (B, S);
			Bt_S_B.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");

			model->getFEEngine().integrate(bt_s_b, K_e,
			bt_s_b_size * bt_s_b_size,
			type, ghost_type,
			elem_filter);

			delete bt_s_b;

			model->getFEEngine().assembleMatrix(*K_e, K, spatial_dimension, type, ghost_type, elem_filter);
			delete K_e;

			AKANTU_DEBUG_OUT();
			}

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

			SparseMatrix & K = const_cast<SparseMatrix &> (model->getStiffnessMatrix());

			const Array<Real> & shapes_derivatives = model->getFEEngine().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.getSize();
			UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
			UInt nb_quadrature_points = model->getFEEngine().getNbQuadraturePoints(type, ghost_type);

			gradu_vect.resize(nb_quadrature_points * nb_element);

			model->getFEEngine().gradientOnQuadraturePoints(model->getDisplacement(), gradu_vect,
			dim, type, ghost_type, elem_filter);

			UInt tangent_size = getTangentStiffnessVoigtSize(dim);

			Array<Real> * tangent_stiffness_matrix =
			new Array<Real > (nb_elementnb_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");


			Array<Real>::const_matrix_iterator shapes_derivatives_it = shapes_derivatives.begin(spatial_dimension,
			nb_nodes_per_element);

			Array<Real>::matrix_iterator shapes_derivatives_filtered_it = shapes_derivatives_filtered->begin(spatial_dimension,
			nb_nodes_per_element);
			UInt * elem_filter_val = elem_filter.storage();
			for (UInt e = 0; e < nb_element; ++e, ++elem_filter_val)
			for (UInt q = 0; q < nb_quadrature_points; ++q, ++shapes_derivatives_filtered_it)
			shapes_derivatives_filtered_it = shapes_derivatives_it[elem_filter_val * nb_quadrature_points + q];

			/// 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);

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

			Array<Real>::matrix_iterator Bt_D_B_it = bt_d_b->begin(dim*nb_nodes_per_element,
			dim * nb_nodes_per_element);

			Array<Real>::matrix_iterator grad_u_it = gradu_vect.begin(dim, dim);

			Array<Real>::matrix_iterator D_it = tangent_stiffness_matrix->begin(tangent_size,
			tangent_size);
			Array<Real>::matrix_iterator 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) {
			Matrix<Real> & grad_u = *grad_u_it;
			Matrix<Real> & D = *D_it;
			Matrix<Real> & 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.mul < true, false > (B, D);
			Bt_D_B.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");

			model->getFEEngine().integrate(bt_d_b, K_e,
			bt_d_b_size * bt_d_b_size,
			type, ghost_type,
			elem_filter);

			delete bt_d_b;

			model->getFEEngine().assembleMatrix(*K_e, K, spatial_dimension, type, ghost_type, elem_filter);
			delete K_e;

			AKANTU_DEBUG_OUT();
			}

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

			AKANTU_DEBUG_IN();

			Array<Real> & residual = const_cast<Array<Real> &> (model->getResidual());

			Mesh & mesh = model->getFEEngine().getMesh();
			Mesh::type_iterator it = element_filter.firstType(dim, ghost_type);
			Mesh::type_iterator last_type = element_filter.lastType(dim, ghost_type);
			for (; it != last_type; ++it) {
			const Array<Real> & shapes_derivatives = model->getFEEngine().getShapesDerivatives(*it, ghost_type);

			Array<UInt> & elem_filter = element_filter(*it, ghost_type);

			UInt size_of_shapes_derivatives = shapes_derivatives.getNbComponent();
			UInt nb_element = elem_filter.getSize();
			UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(*it);
			UInt nb_quadrature_points = model->getFEEngine().getNbQuadraturePoints(*it, ghost_type);

			Array<Real> * shapesd_filtered =
			new Array<Real>(0, size_of_shapes_derivatives, "filtered shapesd");

			FEEngine::filterElementalData(mesh, shapes_derivatives, *shapesd_filtered,
			*it, 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;

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

			Array<Real>::matrix_iterator grad_u_it = this->gradu(*it, ghost_type).begin(dim, dim);

			Array<Real>::matrix_iterator grad_u_end = this->gradu(*it, ghost_type).end(dim, dim);

			Array<Real>::matrix_iterator stress_it = this->piola_kirchhoff_2(*it, 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> S_vect(stress_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) {
			Matrix<Real> & grad_u = *grad_u_it;
			Matrix<Real> & r_it = *bt_s_it;
			Matrix<Real> & S_it = *stress_it;

			SetCauchyStressArray <dim> (S_it, S_vect);
			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;

			r_it.mul < true, false > (B_tensor, S_vect);
			}

			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");

			model->getFEEngine().integrate(bt_s, r_e,
			bt_s_size,
			*it, ghost_type,
			elem_filter);

			delete bt_s;

			model->getFEEngine().assembleArray(*r_e, residual,
			model->getDOFSynchronizer().getLocalDOFEquationNumbers(),
			residual.getNbComponent(),
			*it, ghost_type, elem_filter, -1);

			delete r_e;

			}
			AKANTU_DEBUG_OUT();

			}

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

			UInt spatial_dimension = model->getSpatialDimension();

			Mesh::type_iterator it = element_filter.firstType(spatial_dimension, ghost_type);
			Mesh::type_iterator last_type = element_filter.lastType(spatial_dimension, ghost_type);
			for(; it != last_type; ++it) {
			switch(spatial_dimension) {
			case 1: { computeAllStressesFromTangentModuli<1>(*it, ghost_type); break; }
			case 2: { computeAllStressesFromTangentModuli<2>(*it, ghost_type); break; }
			case 3: { computeAllStressesFromTangentModuli<3>(*it, ghost_type); break; }
			}
			}

			AKANTU_DEBUG_OUT();
			}

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

			const Array<Real> & shapes_derivatives = model->getFEEngine().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.getSize();
			UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
			UInt nb_quadrature_points = model->getFEEngine().getNbQuadraturePoints(type, ghost_type);


			gradu_vect.resize(nb_quadrature_points * nb_element);

			Array<Real> & disp = model->getDisplacement();

			model->getFEEngine().gradientOnQuadraturePoints(disp, gradu_vect,
			dim, type, ghost_type, elem_filter);

			UInt tangent_moduli_size = getTangentStiffnessVoigtSize(dim);

			Array<Real> * tangent_moduli_tensors =
			new Array<Real>(nb_elementnb_quadrature_points, tangent_moduli_size tangent_moduli_size,
			"tangent_moduli_tensors");

			tangent_moduli_tensors->clear();
			computeTangentModuli(type, *tangent_moduli_tensors, ghost_type);

			Array<Real> * shapesd_filtered =
			new Array<Real>(0, dim* nb_nodes_per_element, "filtered shapesd");

			FEEngine::filterElementalData(model->getFEEngine().getMesh(), shapes_derivatives, *shapesd_filtered,
			type, ghost_type, elem_filter);

			Array<Real> filtered_u(nb_element, nb_nodes_per_element * spatial_dimension);

			FEEngine::extractNodalToElementField(model->getFEEngine().getMesh(), disp, filtered_u,
			type, ghost_type, elem_filter);

			/// compute @f$\mathbf{D} \mathbf{B} \mathbf{u}@f$
			Array<Real>::matrix_iterator shapes_derivatives_filtered_it =
			shapesd_filtered->begin(dim, nb_nodes_per_element);

			Array<Real>::matrix_iterator D_it = tangent_moduli_tensors->begin(tangent_moduli_size,
			tangent_moduli_size);
			Array<Real>::matrix_iterator sigma_it = stress(type, ghost_type).begin(spatial_dimension,
			spatial_dimension);
			Array<Real>::vector_iterator u_it = filtered_u.begin(spatial_dimension * nb_nodes_per_element);

			Matrix<Real> B(tangent_moduli_size, spatial_dimension * nb_nodes_per_element);
			Vector<Real> Bu(tangent_moduli_size);
			Vector<Real> DBu(tangent_moduli_size);

			for (UInt e = 0; e < nb_element; ++e, ++u_it) {
			for (UInt q = 0; q < nb_quadrature_points; ++q, ++D_it, ++shapes_derivatives_filtered_it, ++sigma_it) {
			Vector<Real> & u = *u_it;
			Matrix<Real> & sigma = *sigma_it;
			Matrix<Real> & D = *D_it;

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

			Bu.mul<false>(B, u);
			DBu.mul<false>(D, Bu);

			// Voigt notation to full symmetric tensor
			for (UInt i = 0; i < dim; ++i) sigma(i, i) = DBu(i);
			if(dim == 2) {
			sigma(0,1) = sigma(1,0) = DBu(2);
			} else if(dim == 3) {
			sigma(1,2) = sigma(2,1) = DBu(3);
			sigma(0,2) = sigma(2,0) = DBu(4);
			sigma(0,1) = sigma(1,0) = DBu(5);
			}
			}
			}

			AKANTU_DEBUG_OUT();
			}


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

			Mesh::type_iterator it = element_filter.firstType(spatial_dimension);
			Mesh::type_iterator last_type = element_filter.lastType(spatial_dimension);
			for(; it != last_type; ++it) {
			computePotentialEnergy(*it);
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void Material::computePotentialEnergy(ElementType el_type, GhostType ghost_type) {
			AKANTU_DEBUG_IN();

			if(!potential_energy.exists(el_type, ghost_type)) {
			UInt nb_element = element_filter(el_type, ghost_type).getSize();
			UInt nb_quadrature_points = model->getFEEngine().getNbQuadraturePoints(el_type, _not_ghost);

			potential_energy.alloc(nb_element * nb_quadrature_points, 1,
			el_type, ghost_type);
			}

			AKANTU_DEBUG_OUT();
			}


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

			computePotentialEnergyByElements();

			/// integrate the potential energy for each type of elements
			Mesh::type_iterator it = element_filter.firstType(spatial_dimension);
			Mesh::type_iterator last_type = element_filter.lastType(spatial_dimension);
			for(; it != last_type; ++it) {

			epot += model->getFEEngine().integrate(potential_energy(it, _not_ghost), it,
			_not_ghost, element_filter(*it, _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(model->getFEEngine().getNbQuadraturePoints(type));

			computePotentialEnergyByElement(type, index, epot_on_quad_points);

			epot = model->getFEEngine().integrate(epot_on_quad_points, type, element_filter(type)(index));

			AKANTU_DEBUG_OUT();
			return epot;
			}

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

			/* -------------------------------------------------------------------------- */
			Real Material::getEnergy(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::computeQuadraturePointsCoordinates(ElementTypeMapArray<Real> & quadrature_points_coordinates,
			const GhostType & ghost_type) const {
			AKANTU_DEBUG_IN();

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

			Array<Real> nodes_coordinates(mesh.getNodes(), true);
			nodes_coordinates += this->model->getDisplacement();

			Mesh::type_iterator it = this->element_filter.firstType(spatial_dimension, ghost_type);
			Mesh::type_iterator last_type = this->element_filter.lastType(spatial_dimension, ghost_type);
			for(; it != last_type; ++it) {
			const Array<UInt> & elem_filter = this->element_filter(*it, ghost_type);

			UInt nb_element = elem_filter.getSize();
			UInt nb_tot_quad = this->model->getFEEngine().getNbQuadraturePoints(it, ghost_type) nb_element;

			Array<Real> & quads = quadrature_points_coordinates(*it, ghost_type);
			quads.resize(nb_tot_quad);

			this->model->getFEEngine().interpolateOnQuadraturePoints(nodes_coordinates,
			quads, spatial_dimension,
			*it, ghost_type, elem_filter);
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void Material::initElementalFieldInterpolation(const ElementTypeMapArray<Real> & interpolation_points_coordinates) {
			AKANTU_DEBUG_IN();
			const Mesh & mesh = model->getFEEngine().getMesh();

			ElementTypeMapArray<Real> quadrature_points_coordinates("quadrature_points_coordinates_for_interpolation", getID());
			mesh.initElementTypeMapArray(quadrature_points_coordinates, spatial_dimension, spatial_dimension);

			for (ghost_type_t::iterator gt = ghost_type_t::begin();
			gt != ghost_type_t::end(); ++gt) {

			GhostType ghost_type = *gt;

			computeQuadraturePointsCoordinates(quadrature_points_coordinates, ghost_type);

			Mesh::type_iterator it = element_filter.firstType(spatial_dimension, ghost_type);
			Mesh::type_iterator last = element_filter.lastType(spatial_dimension, ghost_type);
			for (; it != last; ++it) {
			ElementType type = *it;
			UInt nb_element = mesh.getNbElement(type, ghost_type);
			if (nb_element == 0) continue;

			const Array<Real> & interp_points_coord = interpolation_points_coordinates(type, ghost_type);
			UInt nb_interpolation_points_per_elem = interp_points_coord.getSize() / nb_element;

			AKANTU_DEBUG_ASSERT(interp_points_coord.getSize() % nb_element == 0,
			"Number of interpolation points is wrong");

			#define AKANTU_INIT_INTERPOLATE_ELEMENTAL_FIELD(type) \
			initElementalFieldInterpolation<type>(quadrature_points_coordinates(type, ghost_type), \
			interp_points_coord, \
			nb_interpolation_points_per_elem, \
			ghost_type) \

			AKANTU_BOOST_REGULAR_ELEMENT_SWITCH(AKANTU_INIT_INTERPOLATE_ELEMENTAL_FIELD);
			#undef AKANTU_INIT_INTERPOLATE_ELEMENTAL_FIELD
			}
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			template <ElementType type>
			void Material::initElementalFieldInterpolation(const Array<Real> & quad_coordinates,
			const Array<Real> & interpolation_points_coordinates,
			const UInt nb_interpolation_points_per_elem,
			const GhostType ghost_type) {
			AKANTU_DEBUG_IN();
			Array<UInt> & elem_fil = element_filter(type, ghost_type);
			UInt nb_element = elem_fil.getSize();
			UInt nb_quad_per_element = model->getFEEngine().getNbQuadraturePoints(type, ghost_type);

			if(!interpolation_inverse_coordinates.exists(type, ghost_type))
			interpolation_inverse_coordinates.alloc(nb_element,
			nb_quad_per_element*nb_quad_per_element,
			type, ghost_type);
			else
			interpolation_inverse_coordinates(type, ghost_type).resize(nb_element);

			if(!interpolation_points_matrices.exists(type, ghost_type))
			interpolation_points_matrices.alloc(nb_element,
			nb_interpolation_points_per_elem * nb_quad_per_element,
			type, ghost_type);
			else
			interpolation_points_matrices(type, ghost_type).resize(nb_element);

			Array<Real> & interp_inv_coord = interpolation_inverse_coordinates(type, ghost_type);
			Array<Real> & interp_points_mat = interpolation_points_matrices(type, ghost_type);

			Matrix<Real> quad_coord_matrix(nb_quad_per_element, nb_quad_per_element);

			Array<Real>::const_matrix_iterator quad_coords_it =
			quad_coordinates.begin_reinterpret(spatial_dimension,
			nb_quad_per_element,
			nb_element);

			Array<Real>::const_matrix_iterator points_coords_begin =
			interpolation_points_coordinates.begin_reinterpret(spatial_dimension,
			nb_interpolation_points_per_elem,
			interpolation_points_coordinates.getSize() / nb_interpolation_points_per_elem);

			Array<Real>::matrix_iterator inv_quad_coord_it =
			interp_inv_coord.begin(nb_quad_per_element, nb_quad_per_element);

			Array<Real>::matrix_iterator inv_points_mat_it =
			interp_points_mat.begin(nb_interpolation_points_per_elem, nb_quad_per_element);

			/// loop over the elements of the current material and element type
			for (UInt el = 0; el < nb_element; ++el, ++inv_quad_coord_it,
			++inv_points_mat_it, ++quad_coords_it) {
			/// matrix containing the quadrature points coordinates
			const Matrix<Real> & quad_coords = *quad_coords_it;
			/// matrix to store the matrix inversion result
			Matrix<Real> & inv_quad_coord_matrix = *inv_quad_coord_it;

			/// insert the quad coordinates in a matrix compatible with the interpolation
			buildElementalFieldInterpolationCoodinates<type>(quad_coords,
			quad_coord_matrix);

			/// invert the interpolation matrix
			inv_quad_coord_matrix.inverse(quad_coord_matrix);


			/// matrix containing the interpolation points coordinates
			const Matrix<Real> & points_coords = points_coords_begin[elem_fil(el)];
			/// matrix to store the interpolation points coordinates
			/// compatible with these functions
			Matrix<Real> & inv_points_coord_matrix = *inv_points_mat_it;

			/// insert the quad coordinates in a matrix compatible with the interpolation
			buildElementalFieldInterpolationCoodinates<type>(points_coords,
			inv_points_coord_matrix);
			}

			AKANTU_DEBUG_OUT();
			}

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

			/* -------------------------------------------------------------------------- */
			void Material::interpolateElementalField(const ElementTypeMapArray<Real> & field,
			ElementTypeMapArray<Real> & result,
			const GhostType ghost_type) {
			AKANTU_DEBUG_IN();

			Mesh::type_iterator it = element_filter.firstType(spatial_dimension, ghost_type);
			Mesh::type_iterator last = element_filter.lastType(spatial_dimension, ghost_type);
			for (; it != last; ++it) {
			ElementType type = *it;

			Array<UInt> & elem_fil = element_filter(type, ghost_type);
			UInt nb_element = elem_fil.getSize();
			UInt nb_quad_per_element = model->getFEEngine().getNbQuadraturePoints(type, ghost_type);

			const Array<Real> & field_vec = field(type, ghost_type);
			Array<Real> & result_vec = result(type, ghost_type);

			Matrix<Real> coefficients(nb_quad_per_element, field_vec.getNbComponent());

			const Array<Real> & interp_inv_coord = interpolation_inverse_coordinates(type, ghost_type);
			const Array<Real> & interp_points_coord = interpolation_points_matrices(type, ghost_type);

			UInt nb_interpolation_points_per_elem
			= interp_points_coord.getNbComponent() / nb_quad_per_element;

			Array<Real>::const_matrix_iterator field_it
			= field_vec.begin_reinterpret(field_vec.getNbComponent(),
			nb_quad_per_element,
			nb_element);

			Array<Real>::const_matrix_iterator interpolation_points_coordinates_it =
			interp_points_coord.begin(nb_interpolation_points_per_elem, nb_quad_per_element);

			Array<Real>::matrix_iterator result_begin
			= result_vec.begin_reinterpret(field_vec.getNbComponent(),
			nb_interpolation_points_per_elem,
			result_vec.getSize() / nb_interpolation_points_per_elem);

			Array<Real>::const_matrix_iterator inv_quad_coord_it =
			interp_inv_coord.begin(nb_quad_per_element, nb_quad_per_element);

			/// loop over the elements of the current material and element type
			for (UInt el = 0; el < nb_element;
			++el, ++field_it, ++inv_quad_coord_it, ++interpolation_points_coordinates_it) {
			/**
			* matrix containing the inversion of the quadrature points'
			* coordinates
			*/
			const Matrix<Real> & inv_quad_coord_matrix = *inv_quad_coord_it;

			/**
			* multiply it by the field values over quadrature points to get
			* the interpolation coefficients
			*/
			coefficients.mul<false, true>(inv_quad_coord_matrix, *field_it);

			/// matrix containing the points' coordinates
			const Matrix<Real> & coord = *interpolation_points_coordinates_it;

			/// multiply the coordinates matrix by the coefficients matrix and store the result
			Matrix<Real> res(result_begin[elem_fil(el)]);
			res.mul<true, true>(coefficients, coord);
			}
			}

			AKANTU_DEBUG_OUT();
			}

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

			/* -------------------------------------------------------------------------- */
			void Material::interpolateElementalFieldOnFacets(const ElementTypeMapArray<Real> & field,
			ElementTypeMapArray<Real> & result,
			const GhostType ghost_type) {
			AKANTU_DEBUG_IN();

			UInt sp2 = spatial_dimension * spatial_dimension;

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

			Mesh::type_iterator it = element_filter.firstType(spatial_dimension, ghost_type);
			Mesh::type_iterator last = element_filter.lastType(spatial_dimension, ghost_type);
			for (; it != last; ++it) {
			ElementType type = *it;

			Array<UInt> & elem_fil = element_filter(type, ghost_type);
			UInt nb_element = elem_fil.getSize();
			UInt nb_quad_per_element = model->getFEEngine().getNbQuadraturePoints(type, ghost_type);

			const Array<Real> & field_vec = field(type, ghost_type);

			Matrix<Real> coefficients(nb_quad_per_element, field_vec.getNbComponent());

			const Array<Real> & interp_inv_coord = interpolation_inverse_coordinates(type, ghost_type);
			const Array<Real> & interp_points_coord = interpolation_points_matrices(type, ghost_type);

			UInt nb_interpolation_points_per_elem
			= interp_points_coord.getNbComponent() / nb_quad_per_element;

			Array<Real>::const_matrix_iterator field_it
			= field_vec.begin_reinterpret(field_vec.getNbComponent(),
			nb_quad_per_element,
			nb_element);

			Array<Real>::const_matrix_iterator interpolation_points_coordinates_it =
			interp_points_coord.begin(nb_interpolation_points_per_elem, nb_quad_per_element);

			Array<Real>::const_matrix_iterator inv_quad_coord_it =
			interp_inv_coord.begin(nb_quad_per_element, nb_quad_per_element);

			Matrix<Real> result_tmp(sp2, nb_interpolation_points_per_elem);

			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 = NULL;
			GhostType current_ghost_type = _casper;
			Array<Real> * result_vec = NULL;

			/// loop over the elements of the current material and element type
			for (UInt el = 0; el < nb_element;
			++el, ++field_it, ++inv_quad_coord_it, ++interpolation_points_coordinates_it) {
			/**
			* matrix containing the inversion of the quadrature points'
			* coordinates
			*/
			const Matrix<Real> & inv_quad_coord_matrix = *inv_quad_coord_it;

			/**
			* multiply it by the field values over quadrature points to get
			* the interpolation coefficients
			*/
			coefficients.mul<false, true>(inv_quad_coord_matrix, *field_it);

			/// matrix containing the points' coordinates
			const Matrix<Real> & coord = *interpolation_points_coordinates_it;

			/// multiply the coordinates matrix by the coefficients matrix and store the result
			result_tmp.mul<true, true>(coefficients, coord);

			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 * sp2,
			sp2);

			result_local = result_tmp(f * nb_quad_per_facet + q);
			}
			}
			}
			}

			AKANTU_DEBUG_OUT();
			}

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

			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_EXCEPTION("The material " << name << "(" <<getID() << ") does not contain a vector " << vect_id << "(" << fvect_id << ") [" << e << "]");
			}
			}

			/* -------------------------------------------------------------------------- */
			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_EXCEPTION("The material " << name << "(" << getID() << ") does not contain a vector " << vect_id << "(" << fvect_id << ") [" << e << "]");
			}
			}

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

			/* -------------------------------------------------------------------------- */
			InternalField<Real> & Material::getInternal(const ID & int_id) {
			std::map<ID, InternalField<Real> *>::iterator it = internal_vectors_real.find(getID() + ":" + int_id);
			if(it == internal_vectors_real.end()) {
			AKANTU_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());

			Element element;
			for (ghost_type_t::iterator gt = ghost_type_t::begin(); gt != ghost_type_t::end(); ++gt) {
			GhostType ghost_type = *gt;
			element.ghost_type = ghost_type;

			ElementTypeMapArray<UInt>::type_iterator it = element_filter.firstType(_all_dimensions, ghost_type, _ek_not_defined);
			ElementTypeMapArray<UInt>::type_iterator end = element_filter.lastType(_all_dimensions, ghost_type, _ek_not_defined);

			for(; it != end; ++it) {
			ElementType type = *it;
			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.getSize(), 1, type, ghost_type);
			Array<UInt> & mat_renumbering = material_local_new_numbering(type, ghost_type);

			UInt nb_element = elem_filter.getSize();
			element.kind=(*el_begin).kind;
			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.getSize());
			elem_filter.copy(elem_filter_tmp);
			}
			}

			for (std::map<ID, InternalField<Real> *>::iterator it = internal_vectors_real.begin();
			it != internal_vectors_real.end();
			++it) it->second->removeQuadraturePoints(material_local_new_numbering);

			for (std::map<ID, InternalField<UInt> *>::iterator it = internal_vectors_uint.begin();
			it != internal_vectors_uint.end();
			++it) it->second->removeQuadraturePoints(material_local_new_numbering);

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void Material::resizeInternals() {
			AKANTU_DEBUG_IN();
			for (std::map<ID, InternalField<Real> *>::iterator it = internal_vectors_real.begin();
			it != internal_vectors_real.end();
			++it) it->second->resize();

			for (std::map<ID, InternalField<UInt> *>::iterator it = internal_vectors_uint.begin();
			it != internal_vectors_uint.end();
			++it) it->second->resize();
			AKANTU_DEBUG_OUT();
			}

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

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

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

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

			for (ghost_type_t::iterator g = ghost_type_t::begin(); g != ghost_type_t::end(); ++g) {
			GhostType gt = *g;

			ElementTypeMapArray<UInt>::type_iterator it = new_numbering.firstType(_all_dimensions, gt, _ek_not_defined);
			ElementTypeMapArray<UInt>::type_iterator end = new_numbering.lastType (_all_dimensions, gt, _ek_not_defined);
			for (; it != end; ++it) {
			ElementType type = *it;
			if(element_filter.exists(type, gt)){
			Array<UInt> & elem_filter = element_filter(type, gt);

			Array<UInt> & mat_indexes = this->model->getMaterialByElement (*it, gt);
			Array<UInt> & mat_loc_num = this->model->getMaterialLocalNumbering(*it, gt);
			UInt 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.getSize(), 1, type, gt);

			Array<UInt> & mat_renumbering = material_local_new_numbering(type, gt);
			const Array<UInt> & renumbering = new_numbering(type, gt);
			Array<UInt> elem_filter_tmp;
			UInt ni = 0;
			Element el;
			el.type = type;
			el.ghost_type = gt;
			for (UInt i = 0; i < elem_filter.getSize(); ++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.getSize());
			elem_filter.copy(elem_filter);
			}
			}
			}

			for (std::map<ID, InternalField<Real> *>::iterator it = internal_vectors_real.begin();
			it != internal_vectors_real.end();
			++it) it->second->removeQuadraturePoints(material_local_new_numbering);

			for (std::map<ID, InternalField<UInt> *>::iterator it = internal_vectors_uint.begin();
			it != internal_vectors_uint.end();
			++it) it->second->removeQuadraturePoints(material_local_new_numbering);
			}

			/* -------------------------------------------------------------------------- */
			void Material::onBeginningSolveStep(const AnalysisMethod & method) {
			this->savePreviousState();
			}

			/* -------------------------------------------------------------------------- */
			void Material::onEndSolveStep(const AnalysisMethod & method) {
			ElementTypeMapArray<UInt>::type_iterator it
			= this->element_filter.firstType(_all_dimensions, _not_ghost, _ek_not_defined);
			ElementTypeMapArray<UInt>::type_iterator end
			= element_filter.lastType(_all_dimensions, _not_ghost, _ek_not_defined);

			for(; it != end; ++it) {
			this->updateEnergies(*it, _not_ghost);
			}
			}
			/* -------------------------------------------------------------------------- */
			void Material::onDamageIteration() {
			this->savePreviousState();
			}

			/* -------------------------------------------------------------------------- */
			void Material::onDamageUpdate() {
			ElementTypeMapArray<UInt>::type_iterator it
			= this->element_filter.firstType(_all_dimensions, _not_ghost, _ek_not_defined);
			ElementTypeMapArray<UInt>::type_iterator end
			= element_filter.lastType(_all_dimensions, _not_ghost, _ek_not_defined);

			for(; it != end; ++it) {

			if(!this->potential_energy.exists(*it, _not_ghost)) {
			UInt nb_element = this->element_filter(*it, _not_ghost).getSize();
			UInt nb_quadrature_points = this->model->getFEEngine().getNbQuadraturePoints(*it, _not_ghost);

			this->potential_energy.alloc(nb_element * nb_quadrature_points, 1,
			*it, _not_ghost);
			}
			this->updateEnergiesAfterDamage(*it, _not_ghost);
			}
			}

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

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

			/* -------------------------------------------------------------------------- */
			void Material::flattenInternal(const std::string & field_id,
			ElementTypeMapArray<Real> & internal_flat,
			const GhostType ghost_type,
			ElementKind element_kind){

			typedef ElementTypeMapArray<UInt>::type_iterator iterator;
			iterator tit = this->element_filter.firstType(this->spatial_dimension,
			ghost_type, element_kind);
			iterator end = this->element_filter.lastType(this->spatial_dimension,
			ghost_type, element_kind);


			for (; tit != end; ++tit) {

			ElementType type = *tit;

			try {
			__attribute__((unused)) const Array<Real> & src_vect
			= this->getArray(field_id,type,ghost_type);

			} catch(debug::Exception & e) {
			continue;
			}

			const Array<Real> & src_vect = this->getArray(field_id,type,ghost_type);
			const Array<UInt> & filter = this->element_filter(type,ghost_type);

			// total number of elements for a given type
			UInt nb_element = this->model->mesh.getNbElement(type,ghost_type);
			// number of filtered elements
			UInt nb_element_src = filter.getSize();
			// number of quadrature points per elem
			UInt nb_quad_per_elem = 0;
			// number of data per quadrature point
			UInt nb_data_per_quad = src_vect.getNbComponent();

			if (!internal_flat.exists(type,ghost_type)) {
			internal_flat.alloc(nb_element*nb_quad_per_elem,nb_data_per_quad,type,ghost_type);
			}

			if (nb_element_src == 0) continue;
			nb_quad_per_elem = (src_vect.getSize()/nb_element_src);

			// number of data per element
			UInt nb_data = nb_quad_per_elem * src_vect.getNbComponent();

			Array<Real> & dst_vect = internal_flat(type,ghost_type);
			dst_vect.resize(nb_element*nb_quad_per_elem);

			Array<UInt>::const_scalar_iterator it = filter.begin();
			Array<UInt>::const_scalar_iterator end = filter.end();
			Array<Real>::const_vector_iterator it_src =
			src_vect.begin_reinterpret(nb_data,nb_element_src);

			Array<Real>::vector_iterator it_dst =
			dst_vect.begin_reinterpret(nb_data,nb_element);

			for (; it != end ; ++it,++it_src) {
			it_dst[it] = it_src;
			}
			}
			};
			/* -------------------------------------------------------------------------- */


			__END_AKANTU__

rAKA/src/model/solid_mechanics/material.ccc3c539faffaafeatures/joss-2023

material.ccView Options

rAKA/src/model/solid_mechanics/material.cc
c3c539faffaafeatures/joss-2023

material.cc
View Options