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material.cc
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			/**
			* @file material.cc
			*
			* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
			* @author Fabian Barras <fabian.barras@epfl.ch>
			* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
			* @author Lucas Frerot <lucas.frerot@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: Fri Apr 09 2021
			*
			* @brief Implementation of the common part of the material class
			*
			*
			* @section LICENSE
			*
			* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
			* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
			*
			* Akantu is free software: you can redistribute it and/or modify it under the
			* terms of the GNU Lesser General Public License as published by the Free
			* Software Foundation, either version 3 of the License, or (at your option) any
			* later version.
			*
			* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
			* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
			* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
			* details.
			*
			* You should have received a copy of the GNU Lesser General Public License
			* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
			*
			*/

			/* -------------------------------------------------------------------------- */
			#include "material.hh"
			#include "mesh_iterators.hh"
			#include "solid_mechanics_model.hh"
			/* -------------------------------------------------------------------------- */

			namespace akantu {

			/* -------------------------------------------------------------------------- */
			Material::Material(SolidMechanicsModel & model, const ID & id)
			: Parsable(ParserType::_material, id), id(id), fem(model.getFEEngine()),
			model(model), spatial_dimension(this->model.getSpatialDimension()),
			element_filter("element_filter", 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),
			interpolation_inverse_coordinates("interpolation inverse coordinates",
			*this),
			interpolation_points_matrices("interpolation points matrices", *this),
			eigen_grad_u(model.getSpatialDimension(), model.getSpatialDimension()) {
			eigen_grad_u.fill(0.);

			this->registerParam("eigen_grad_u", eigen_grad_u, _pat_parsable,
			"EigenGradU");

			/// 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();
			}

			/* -------------------------------------------------------------------------- */
			Material::Material(SolidMechanicsModel & model, Int dim, const Mesh & mesh,
			FEEngine & fe_engine, const ID & id)
			: Parsable(ParserType::_material, id), id(id), fem(fe_engine), model(model),
			spatial_dimension(dim), element_filter("element_filter", 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),
			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),
			eigen_grad_u(dim, dim) {
			eigen_grad_u.fill(0.);

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

			this->initialize();
			}

			/* -------------------------------------------------------------------------- */
			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);
			this->piola_kirchhoff_2.initializeHistory();
			this->green_strain.initialize(spatial_dimension * spatial_dimension);
			}

			this->stress.initializeHistory();
			this->gradu.initializeHistory();

			this->resizeInternals();

			auto dim = spatial_dimension;
			for (const auto & type :
			element_filter.elementTypes(_element_kind = _ek_regular)) {
			for (auto & eigen_gradu : make_view(eigengradu(type), dim, dim)) {
			eigen_gradu = eigen_grad_u;
			}
			}

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

			Int spatial_dimension = model.getSpatialDimension();

			if (!finite_deformation) {

			auto & internal_force = model.getInternalForce();

			// Mesh & mesh = fem.getMesh();
			for (auto && type :
			element_filter.elementTypes(spatial_dimension, ghost_type)) {
			auto && elem_filter = element_filter(type, ghost_type);
			auto 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$\mathbf{B}^t \mathbf{\sigma}_q@f$
			auto * 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$
			*/
			auto * 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] ghost_type compute the residual for _ghost or _not_ghost element
			*/
			void Material::computeAllStresses(GhostType ghost_type) {
			AKANTU_DEBUG_IN();

			auto spatial_dimension = model.getSpatialDimension();

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

			if (elem_filter.empty()) {
			continue;
			}
			auto & 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 <Int dim>
			void Material::StoCauchy(ElementType el_type, GhostType ghost_type) {
			AKANTU_DEBUG_IN();

			for (auto && data :
			zip(make_view<dim, dim>(this->gradu(el_type, ghost_type)),
			make_view<dim, dim>(this->piola_kirchhoff_2(el_type, ghost_type)),
			make_view<dim, dim>(this->stress(el_type, ghost_type)))) {
			auto && grad_u = std::get<0>(data);
			auto && piola = std::get<1>(data);
			auto && sigma = std::get<2>(data);

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

			AKANTU_DEBUG_OUT();
			}

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

			const auto & displacement = model.getDisplacement();

			// resizeInternalArray(gradu);

			auto spatial_dimension = model.getSpatialDimension();

			for (auto type : element_filter.elementTypes(spatial_dimension, ghost_type)) {
			auto & elem_filter = element_filter(type, ghost_type);
			auto & 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] ghost_type compute the residual for _ghost or _not_ghost element
			*/
			void Material::assembleStiffnessMatrix(GhostType ghost_type) {
			AKANTU_DEBUG_IN();

			auto 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 <Int dim>
			void Material::assembleStiffnessMatrix(ElementType type, GhostType ghost_type) {
			AKANTU_DEBUG_IN();

			const auto & elem_filter = element_filter(type, ghost_type);
			if (elem_filter.empty()) {
			AKANTU_DEBUG_OUT();
			return;
			}

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

			auto & gradu_vect = gradu(type, ghost_type);

			auto nb_element = elem_filter.size();
			auto nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
			auto 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);

			auto tangent_size = getTangentStiffnessVoigtSize(dim);

			auto tangent_stiffness_matrix = std::make_unique<Array<Real>>(
			nb_element * nb_quadrature_points, tangent_size * tangent_size,
			"tangent_stiffness_matrix");

			tangent_stiffness_matrix->zero();

			computeTangentModuli(type, *tangent_stiffness_matrix, ghost_type);

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

			auto bt_d_b = std::make_unique<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);

			/// compute @f$ k_e = \int_e \mathbf{B}^t * \mathbf{D} * \mathbf{B}@f$
			auto K_e = std::make_unique<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);

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

			AKANTU_DEBUG_OUT();
			}

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

			const auto & shapes_derivatives = fem.getShapesDerivatives(type, ghost_type);

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

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

			auto shapes_derivatives_filtered = std::make_unique<Array<Real>>(
			nb_element * nb_quadrature_points, dim * nb_nodes_per_element,
			"shapes derivatives filtered");

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

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

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

			auto piola_matrix_size = getCauchyStressMatrixSize(dim);

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

			for (auto && data :
			zip(make_view(*bt_s_b, bt_s_b_size, bt_s_b_size),
			make_view(piola_kirchhoff_2(type, ghost_type), dim, dim),
			make_view(*shapes_derivatives_filtered, spatial_dimension,
			nb_nodes_per_element))) {
			auto && Bt_S_B = std::get<0>(data);
			auto && Piola_kirchhoff_matrix = std::get<1>(data);
			auto && shapes_derivatives = std::get<2>(data);

			setCauchyStressMatrix<dim>(Piola_kirchhoff_matrix, S);
			VoigtHelper<dim>::transferBMatrixToBNL(shapes_derivatives, B,
			nb_nodes_per_element);
			Bt_S_B = B.transpose() * S * B;
			}

			/// compute @f$ k_e = \int_e \mathbf{B}^t * \mathbf{D} * \mathbf{B}@f$
			auto K_e = std::make_unique<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);

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

			AKANTU_DEBUG_OUT();
			}

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

			const auto & shapes_derivatives = fem.getShapesDerivatives(type, ghost_type);

			auto & elem_filter = element_filter(type, ghost_type);
			auto & gradu_vect = gradu(type, ghost_type);

			auto nb_element = elem_filter.size();
			auto nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
			auto 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);

			constexpr auto tangent_size = getTangentStiffnessVoigtSize(dim);

			auto tangent_stiffness_matrix = std::make_unique<Array<Real>>(
			nb_element * nb_quadrature_points, tangent_size * tangent_size,
			"tangent_stiffness_matrix");

			tangent_stiffness_matrix->zero();

			computeTangentModuli(type, *tangent_stiffness_matrix, ghost_type);

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

			/// compute @f$\mathbf{B}^t * \mathbf{D} * \mathbf{B}@f$
			auto bt_d_b_size = dim * nb_nodes_per_element;
			auto bt_d_b = std::make_unique<Array<Real>>(
			nb_element * nb_quadrature_points, bt_d_b_size * bt_d_b_size, "B^tDB");

			Matrix<Real, tangent_size> B(tangent_size, bt_d_b_size);
			Matrix<Real, tangent_size> B2(tangent_size, bt_d_b_size);

			for (auto && data :
			zip(make_view(*bt_d_b, bt_d_b_size, bt_d_b_size),
			make_view<dim, dim>(gradu_vect),
			make_view<tangent_size, tangent_size>(*tangent_stiffness_matrix),
			make_view<dim, Eigen::Dynamic>(*shapes_derivatives_filtered, dim,
			nb_nodes_per_element))) {
			auto && Bt_D_B = std::get<0>(data);
			auto && grad_u = std::get<1>(data);
			auto && D = std::get<2>(data);
			auto && shapes_derivative = std::get<3>(data);

			// transferBMatrixToBL1<dim > (*shapes_derivatives_filtered_it, B,
			// nb_nodes_per_element);
			VoigtHelper<dim>::transferBMatrixToSymVoigtBMatrix(shapes_derivative, B,
			nb_nodes_per_element);
			VoigtHelper<dim>::transferBMatrixToBL2(shapes_derivative, grad_u, B2,
			nb_nodes_per_element);
			B += B2;
			Bt_D_B = B.transpose() * D * B;
			}

			/// compute @f$ k_e = \int_e \mathbf{B}^t * \mathbf{D} * \mathbf{B}@f$
			auto K_e = std::make_unique<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);

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

			AKANTU_DEBUG_OUT();
			}

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

			auto & internal_force = model.getInternalForce();
			auto & mesh = fem.getMesh();
			for (auto type : element_filter.elementTypes(_ghost_type = ghost_type)) {
			const auto & shapes_derivatives =
			fem.getShapesDerivatives(type, ghost_type);

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

			auto shapesd_filtered = std::make_unique<Array<Real>>(
			nb_element, size_of_shapes_derivatives, "filtered shapesd");

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

			// Set stress vectors
			auto stress_size = getTangentStiffnessVoigtSize(dim);
			auto bt_s_size = dim * nb_nodes_per_element;

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

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

			for (auto && data :
			zip(make_view<dim, dim>(this->gradu(type, ghost_type)),
			make_view<dim, dim>(this->piola_kirchhoff_2(type, ghost_type)),
			make_view(*bt_s, bt_s_size),
			make_view<dim, Eigen::Dynamic>(*shapesd_filtered, dim,
			nb_nodes_per_element))) {
			auto && grad_u = std::get<0>(data);
			auto && S = std::get<1>(data);
			auto && r = std::get<2>(data);
			auto && shapes_derivative = std::get<3>(data);

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

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

			B_tensor += B2_tensor;
			r = B_tensor.transpose() * Material::stressToVoigt<dim>(S);
			}

			/// compute @f$ k_e = \int_e \mathbf{B}^t * \mathbf{D} * \mathbf{B}@f$
			auto r_e = std::make_unique<Array<Real>>(nb_element, bt_s_size, "r_e");
			fem.integrate(bt_s, r_e, bt_s_size, type, ghost_type, elem_filter);

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

			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_TO_IMPLEMENT(); }

			/* -------------------------------------------------------------------------- */
			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, Int index) {
			return getPotentialEnergy({type, index, _not_ghost});
			}

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

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

			epot = fem.integrate(epot_on_quad_points,
			{element.type,
			element_filter(element.type)(element.element),
			_not_ghost});

			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,
			const Element & element) {
			AKANTU_DEBUG_IN();
			if (energy_id == "potential") {
			return getPotentialEnergy(element);
			}
			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);

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

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

			for (auto type : element_filter.elementTypes(spatial_dimension, ghost_type)) {
			auto & elem_fil = element_filter(type, ghost_type);
			auto & by_elem_res = by_elem_result(type, ghost_type);
			auto nb_element_full = mesh.getNbElement(type, ghost_type);
			auto nb_interpolation_points_per_elem =
			by_elem_res.size() / nb_element_full;

			const auto & facet_to_element =
			mesh_facets.getSubelementToElement(type, ghost_type);
			auto type_facet = Mesh::getFacetType(type);
			auto nb_facet_per_elem = facet_to_element.getNbComponent();
			auto 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;
			auto current_ghost_type = _casper;
			Array<Real>::matrix_iterator result_vec_it;

			auto result_it =
			make_view(by_elem_res, stress_size, nb_interpolation_points_per_elem)
			.begin();

			for (auto global_el : elem_fil) {
			element_for_comparison.element = global_el;

			for (Int f = 0; f < nb_facet_per_elem; ++f) {
			auto facet_elem = facet_to_element(global_el, f);
			auto 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_it =
			make_view(result(type_facet, current_ghost_type), stress_size, 2)
			.begin();
			}

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

			for (Int q = 0; q < nb_quad_per_facet; ++q) {
			auto && result_local =
			result_vec_it[global_facet * nb_quad_per_facet + q](
			is_second_element);
			result_local = result_it[global_el](f * nb_quad_per_facet + q);
			}
			}
			}
			}
			}

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

			UInt mat_id = model.getMaterialIndex(name);
			for (const auto & element : elements_to_add) {
			auto index = this->addElement(element);
			model.material_index(element) = mat_id;
			model.material_local_numbering(element) = index;
			}

			this->resizeInternals();

			AKANTU_DEBUG_OUT();
			}

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

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

			if (elements_to_remove.empty()) {
			return;
			}

			auto & mesh = this->model.getMesh();

			ElementTypeMapArray<Idx> material_local_new_numbering(
			"remove mat filter elem", id);

			material_local_new_numbering.initialize(
			mesh, _element_filter = &element_filter, _element_kind = _ek_not_defined,
			_with_nb_element = true);

			ElementTypeMapArray<Idx> element_filter_tmp("element_filter_tmp", id);

			element_filter_tmp.initialize(mesh, _element_filter = &element_filter,
			_element_kind = _ek_not_defined);

			ElementTypeMap<Idx> new_ids, element_ids;

			for_each_element(
			mesh,
			[&](auto && el) {
			if (not new_ids(el.type, el.ghost_type)) {
			element_ids(el.type, el.ghost_type) = 0;
			}

			auto & element_id = element_ids(el.type, el.ghost_type);
			auto l_el = Element{el.type, element_id, el.ghost_type};
			if (std::find(el_begin, el_end, el) != el_end) {
			material_local_new_numbering(l_el) = UInt(-1);
			return;
			}

			element_filter_tmp(el.type, el.ghost_type).push_back(el.element);
			if (not new_ids(el.type, el.ghost_type)) {
			new_ids(el.type, el.ghost_type) = 0;
			}

			auto & new_id = new_ids(el.type, el.ghost_type);

			material_local_new_numbering(l_el) = new_id;
			model.material_local_numbering(el) = new_id;

			++new_id;
			++element_id;
			},
			_element_filter = &element_filter, _element_kind = _ek_not_defined);

			for (auto ghost_type : ghost_types) {
			for (const auto & type : element_filter.elementTypes(
			_ghost_type = ghost_type, _element_kind = _ek_not_defined)) {
			element_filter(type, ghost_type)
			.copy(element_filter_tmp(type, ghost_type));
			}
			}

			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> & /unused/,
			const NewElementsEvent & /unused/) {
			this->resizeInternals();
			}

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

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

			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).empty()) {
			continue;
			}

			auto & elem_filter = element_filter(type, gt);
			auto & mat_indexes = this->model.material_index(type, gt);
			auto & mat_loc_num = this->model.material_local_numbering(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<Idx> elem_filter_tmp;
			UInt ni = 0;
			Element el{type, 0, gt};

			for (auto && data : enumerate(elem_filter)) {
			el.element = std::get<1>(data);
			if (std::find(el_begin, el_end, el) == el_end) {
			auto new_el = renumbering(el.element);
			AKANTU_DEBUG_ASSERT(new_el != -1,
			"A not removed element as been badly renumbered");
			elem_filter_tmp.push_back(new_el);
			mat_renumbering(std::get<0>(data)) = ni;

			mat_indexes(new_el) = my_num;
			mat_loc_num(new_el) = ni;
			++ni;
			} else {
			mat_renumbering(std::get<0>(data)) = -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(bool converged) {
			if (not converged) {
			this->restorePreviousState();
			return;
			}

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

			/* -------------------------------------------------------------------------- */
			void Material::onDamageUpdate() {
			for (const 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,
			const Matrix<Real> & /point/,
			Matrix<Real> & extrapolated) {
			if (this->isInternal<Real>(id, element.kind())) {
			auto name = this->getID() + ":" + id;
			auto nb_quads =
			this->internal_vectors_real[name]->getFEEngine().getNbIntegrationPoints(
			element.type, element.ghost_type);
			const auto & internal =
			this->getArray<Real>(id, element.type, element.ghost_type);
			auto nb_component = internal.getNbComponent();
			auto internal_it = make_view(internal, nb_component, nb_quads).begin();
			auto 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");

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

			for (Int i = 0; i < extrapolated.size(); ++i) {
			extrapolated(i) = values(index);
			}
			} else {
			extrapolated.fill(0.);
			}
			}

			/* -------------------------------------------------------------------------- */
			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).empty()) {
			continue;
			}

			for (auto & eigengradu : make_view(this->eigengradu(type, ghost_type),
			spatial_dimension, spatial_dimension)) {
			eigengradu = prescribed_eigen_grad_u;
			}
			}
			}

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

			} // namespace akantu

rAKA/src/model/solid_mechanics/material.cccb6de5f8a3bcfeatures/eigen

material.ccView Options

rAKA/src/model/solid_mechanics/material.cc
cb6de5f8a3bcfeatures/eigen

material.cc
View Options