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#material.hh#
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			/**
			* @file material.hh
			*
			* @author Daniel Pino Muñoz <daniel.pinomunoz@epfl.ch>
			* @author Nicolas Richart <nicolas.richart@epfl.ch>
			* @author Marco Vocialta <marco.vocialta@epfl.ch>
			*
			* @date creation: Fri Jun 18 2010
			* @date last modification: Wed Feb 21 2018
			*
			* @brief Mother class for all materials
			*
			* @section LICENSE
			*
			* Copyright (©) 2010-2018 EPFL (Ecole Polytechnique Fédérale de Lausanne)
			* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
			*
			* Akantu is free software: you can redistribute it and/or modify it under the
			* terms of the GNU Lesser General Public License as published by the Free
			* Software Foundation, either version 3 of the License, or (at your option) any
			* later version.
			*
			* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
			* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
			* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
			* details.
			*
			* You should have received a copy of the GNU Lesser General Public License
			* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
			*
			*/

			/* -------------------------------------------------------------------------- */
			#include "aka_factory.hh"
			#include "aka_voigthelper.hh"
			#include "data_accessor.hh"
			#include "integration_point.hh"
			#include "parsable.hh"
			#include "parser.hh"
			/* -------------------------------------------------------------------------- */
			#include "internal_field.hh"
			#include "random_internal_field.hh"
			/* -------------------------------------------------------------------------- */
			#include "mesh_events.hh"
			#include "solid_mechanics_model_event_handler.hh"
			/* -------------------------------------------------------------------------- */

			#ifndef __AKANTU_MATERIAL_HH__
			#define __AKANTU_MATERIAL_HH__

			/* -------------------------------------------------------------------------- */
			namespace akantu {
			class Model;
			class SolidMechanicsModel;
			} // namespace akantu

			namespace akantu {

			/**
			* Interface of all materials
			* Prerequisites for a new material
			* - inherit from this class
			* - implement the following methods:
			* \code
			* virtual Real getStableTimeStep(Real h, const Element & element =
			* ElementNull);
			*
			* virtual void computeStress(ElementType el_type,
			* GhostType ghost_type = _not_ghost);
			*
			* virtual void computeTangentStiffness(const ElementType & el_type,
			* Array<Real> & tangent_matrix,
			* GhostType ghost_type = _not_ghost);
			* \endcode
			*
			*/
			class Material : public Memory,
			public DataAccessor<Element>,
			public Parsable,
			public MeshEventHandler,
			protected SolidMechanicsModelEventHandler {
			/* ------------------------------------------------------------------------ */
			/* Constructors/Destructors */
			/* ------------------------------------------------------------------------ */
			public:
			#if __cplusplus > 199711L
			Material(const Material & mat) = delete;
			Material & operator=(const Material & mat) = delete;
			#endif

			/// Initialize material with defaults
			Material(SolidMechanicsModel & model, const ID & id = "");

			/// Initialize material with custom mesh & fe_engine
			Material(SolidMechanicsModel & model, UInt dim, const Mesh & mesh,
			FEEngine & fe_engine, const ID & id = "");

			/// Destructor
			~Material() override;

			protected:
			void initialize();

			/* ------------------------------------------------------------------------ */
			/* Function that materials can/should reimplement */
			/* ------------------------------------------------------------------------ */
			protected:
			/// constitutive law
			virtual void computeStress(__attribute__((unused)) ElementType el_type,
			__attribute__((unused))
			GhostType ghost_type = _not_ghost) {
			AKANTU_TO_IMPLEMENT();
			}

			/// compute the tangent stiffness matrix
			virtual void computeTangentModuli(__attribute__((unused))
			const ElementType & el_type,
			__attribute__((unused))
			Array<Real> & tangent_matrix,
			__attribute__((unused))
			GhostType ghost_type = _not_ghost) {
			AKANTU_TO_IMPLEMENT();
			}

			/// compute the potential energy
			virtual void computePotentialEnergy(ElementType el_type,
			GhostType ghost_type = _not_ghost);

			/// compute the potential energy for an element
			virtual void
			computePotentialEnergyByElement(__attribute__((unused)) ElementType type,
			__attribute__((unused)) UInt index,
			__attribute__((unused))
			Vector<Real> & epot_on_quad_points) {
			AKANTU_TO_IMPLEMENT();
			}

			virtual void updateEnergies(__attribute__((unused)) ElementType el_type,
			__attribute__((unused))
			GhostType ghost_type = _not_ghost) {}

			virtual void updateEnergiesAfterDamage(__attribute__((unused))
			ElementType el_type,
			__attribute__((unused))
			GhostType ghost_type = _not_ghost) {}

			/// set the material to steady state (to be implemented for materials that
			/// need it)
			virtual void setToSteadyState(__attribute__((unused)) ElementType el_type,
			__attribute__((unused))
			GhostType ghost_type = _not_ghost) {}

			/// function called to update the internal parameters when the modifiable
			/// parameters are modified
			virtual void updateInternalParameters() {}

			public:
			/// extrapolate internal values
			virtual void extrapolateInternal(const ID & id, const Element & element,
			const Matrix<Real> & points,
			Matrix<Real> & extrapolated);

			/// compute the p-wave speed in the material
			virtual Real getPushWaveSpeed(__attribute__((unused))
			const Element & element) const {
			AKANTU_TO_IMPLEMENT();
			}

			/// compute the s-wave speed in the material
			virtual Real getShearWaveSpeed(__attribute__((unused))
			const Element & element) const {
			AKANTU_TO_IMPLEMENT();
			}

			/// get a material celerity to compute the stable time step (default: is the
			/// push wave speed)
			virtual Real getCelerity(const Element & element) const {
			return getPushWaveSpeed(element);
			}

			/* ------------------------------------------------------------------------ */
			/* Methods */
			/* ------------------------------------------------------------------------ */
			public:
			template <typename T>
			void registerInternal(__attribute__((unused)) InternalField<T> & vect) {
			AKANTU_TO_IMPLEMENT();
			}

			template <typename T>
			void unregisterInternal(__attribute__((unused)) InternalField<T> & vect) {
			AKANTU_TO_IMPLEMENT();
			}

			/// initialize the material computed parameter
			virtual void initMaterial();

			/// compute the residual for this material
			// virtual void updateResidual(GhostType ghost_type = _not_ghost);

			/// assemble the residual for this material
			virtual void assembleInternalForces(GhostType ghost_type);

			/// save the stress in the previous_stress if needed
			virtual void savePreviousState();

			/// restore the stress from previous_stress if needed
			virtual void restorePreviousState();

			/// compute the stresses for this material
			virtual void computeAllStresses(GhostType ghost_type = _not_ghost);
			// virtual void
			// computeAllStressesFromTangentModuli(GhostType ghost_type = _not_ghost);
			virtual void computeAllCauchyStresses(GhostType ghost_type = _not_ghost);

			/// set material to steady state
			void setToSteadyState(GhostType ghost_type = _not_ghost);

			/// compute the stiffness matrix
			virtual void assembleStiffnessMatrix(GhostType ghost_type);

			/// add an element to the local mesh filter
			inline UInt addElement(const ElementType & type, UInt element,
			const GhostType & ghost_type);
			inline UInt addElement(const Element & element);

			/// add many elements at once
			void addElements(const Array<Element> & elements_to_add);

			/// remove many element at once
			void removeElements(const Array<Element> & elements_to_remove);

			/// function to print the contain of the class
			void printself(std::ostream & stream, int indent = 0) const override;

			/**
			* interpolate stress on given positions for each element by means
			* of a geometrical interpolation on quadrature points
			*/
			void interpolateStress(ElementTypeMapArray<Real> & result,
			const GhostType ghost_type = _not_ghost);

			/**
			* interpolate stress on given positions for each element by means
			* of a geometrical interpolation on quadrature points and store the
			* results per facet
			*/
			void interpolateStressOnFacets(ElementTypeMapArray<Real> & result,
			ElementTypeMapArray<Real> & by_elem_result,
			const GhostType ghost_type = _not_ghost);

			/**
			* function to initialize the elemental field interpolation
			* function by inverting the quadrature points' coordinates
			*/
			void initElementalFieldInterpolation(
			const ElementTypeMapArray<Real> & interpolation_points_coordinates);

			/* ------------------------------------------------------------------------ */
			/* Common part */
			/* ------------------------------------------------------------------------ */
			protected:
			/* ------------------------------------------------------------------------ */
			inline UInt getTangentStiffnessVoigtSize(UInt spatial_dimension) const;

			/// compute the potential energy by element
			void computePotentialEnergyByElements();

			/// resize the intenals arrays
			virtual void resizeInternals();

			/* ------------------------------------------------------------------------ */
			/* Finite deformation functions */
			/* This functions area implementing what is described in the paper of Bathe */
			/* et al, in IJNME, Finite Element Formulations For Large Deformation */
			/* Dynamic Analysis, Vol 9, 353-386, 1975 */
			/* ------------------------------------------------------------------------ */
			protected:
			/// assemble the residual
			template <UInt dim> void assembleInternalForces(GhostType ghost_type);

			/// Computation of Cauchy stress tensor in the case of finite deformation from
			/// the 2nd Piola-Kirchhoff for a given element type
			template <UInt dim>
			void computeCauchyStress(ElementType el_type,
			GhostType ghost_type = _not_ghost);

			/// Computation the Cauchy stress the 2nd Piola-Kirchhoff and the deformation
			/// gradient
			template <UInt dim>
			inline void computeCauchyStressOnQuad(const Matrix<Real> & F,
			const Matrix<Real> & S,
			Matrix<Real> & cauchy,
			const Real & C33 = 1.0) const;

			template <UInt dim>
			void computeAllStressesFromTangentModuli(const ElementType & type,
			GhostType ghost_type);

			template <UInt dim>
			void assembleStiffnessMatrix(const ElementType & type, GhostType ghost_type);

			/// assembling in finite deformation
			template <UInt dim>
			void assembleStiffnessMatrixNL(const ElementType & type,
			GhostType ghost_type);

			template <UInt dim>
			void assembleStiffnessMatrixL2(const ElementType & type,
			GhostType ghost_type);

			/// Size of the Stress matrix for the case of finite deformation see: Bathe et
			/// al, IJNME, Vol 9, 353-386, 1975
			inline UInt getCauchyStressMatrixSize(UInt spatial_dimension) const;

			/// Sets the stress matrix according to Bathe et al, IJNME, Vol 9, 353-386,
			/// 1975
			template <UInt dim>
			inline void setCauchyStressMatrix(const Matrix<Real> & S_t,
			Matrix<Real> & sigma);

			/// write the stress tensor in the Voigt notation.
			template <UInt dim>
			inline void setCauchyStressArray(const Matrix<Real> & S_t,
			Matrix<Real> & sigma_voight);

			/* ------------------------------------------------------------------------ */
			/* Conversion functions */
			/* ------------------------------------------------------------------------ */
			public:
			template <UInt dim>
			static inline void gradUToF(const Matrix<Real> & grad_u, Matrix<Real> & F);
			static inline void rightCauchy(const Matrix<Real> & F, Matrix<Real> & C);
			static inline void leftCauchy(const Matrix<Real> & F, Matrix<Real> & B);

			template <UInt dim>
			static inline void gradUToEpsilon(const Matrix<Real> & grad_u,
			Matrix<Real> & epsilon);
			template <UInt dim>
			static inline void gradUToGreenStrain(const Matrix<Real> & grad_u,
			Matrix<Real> & epsilon);

			static inline Real stressToVonMises(const Matrix<Real> & stress);

			protected:
			/// converts global element to local element
			inline Element convertToLocalElement(const Element & global_element) const;
			/// converts local element to global element
			inline Element convertToGlobalElement(const Element & local_element) const;

			/// converts global quadrature point to local quadrature point
			inline IntegrationPoint
			convertToLocalPoint(const IntegrationPoint & global_point) const;
			/// converts local quadrature point to global quadrature point
			inline IntegrationPoint
			convertToGlobalPoint(const IntegrationPoint & local_point) const;

			/* ------------------------------------------------------------------------ */
			/* DataAccessor inherited members */
			/* ------------------------------------------------------------------------ */
			public:
			inline UInt getNbData(const Array<Element> & elements,
			const SynchronizationTag & tag) const override;

			inline void packData(CommunicationBuffer & buffer,
			const Array<Element> & elements,
			const SynchronizationTag & tag) const override;

			inline void unpackData(CommunicationBuffer & buffer,
			const Array<Element> & elements,
			const SynchronizationTag & tag) override;

			template <typename T>
			inline void packElementDataHelper(const ElementTypeMapArray<T> & data_to_pack,
			CommunicationBuffer & buffer,
			const Array<Element> & elements,
			const ID & fem_id = ID()) const;

			template <typename T>
			inline void unpackElementDataHelper(ElementTypeMapArray<T> & data_to_unpack,
			CommunicationBuffer & buffer,
			const Array<Element> & elements,
			const ID & fem_id = ID());

			/* ------------------------------------------------------------------------ */
			/* MeshEventHandler inherited members */
			/* ------------------------------------------------------------------------ */
			public:
			/* ------------------------------------------------------------------------ */
			void onNodesAdded(const Array<UInt> &, const NewNodesEvent &) override{};
			void onNodesRemoved(const Array<UInt> &, const Array<UInt> &,
			const RemovedNodesEvent &) override{};
			void onElementsAdded(const Array<Element> & element_list,
			const NewElementsEvent & event) override;
			void onElementsRemoved(const Array<Element> & element_list,
			const ElementTypeMapArray<UInt> & new_numbering,
			const RemovedElementsEvent & event) override;
			void onElementsChanged(const Array<Element> &, const Array<Element> &,
			const ElementTypeMapArray<UInt> &,
			const ChangedElementsEvent &) override{};

			/* ------------------------------------------------------------------------ */
			/* SolidMechanicsModelEventHandler inherited members */
			/* ------------------------------------------------------------------------ */
			public:
			virtual void beforeSolveStep();
			virtual void afterSolveStep();

			void onDamageIteration() override;
			void onDamageUpdate() override;
			void onDump() override;

			/* ------------------------------------------------------------------------ */
			/* Accessors */
			/* ------------------------------------------------------------------------ */
			public:
			AKANTU_GET_MACRO(Name, name, const std::string &);

			AKANTU_GET_MACRO(Model, model, const SolidMechanicsModel &)

			AKANTU_GET_MACRO(ID, Memory::getID(), const ID &);
			AKANTU_GET_MACRO(Rho, rho, Real);
			AKANTU_SET_MACRO(Rho, rho, Real);

			AKANTU_GET_MACRO(SpatialDimension, spatial_dimension, UInt);

			/// return the potential energy for the subset of elements contained by the
			/// material
			Real getPotentialEnergy();
			/// return the potential energy for the provided element
			Real getPotentialEnergy(ElementType & type, UInt index);

			/// return the energy (identified by id) for the subset of elements contained
			/// by the material
			virtual Real getEnergy(const std::string & energy_id);
			/// return the energy (identified by id) for the provided element
			virtual Real getEnergy(const std::string & energy_id, ElementType type,
			UInt index);

			AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(ElementFilter, element_filter, UInt);
			AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(GradU, gradu, Real);
			AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(Stress, stress, Real);
			AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(PotentialEnergy, potential_energy,
			Real);
			AKANTU_GET_MACRO(GradU, gradu, const ElementTypeMapArray<Real> &);
			AKANTU_GET_MACRO(Stress, stress, const ElementTypeMapArray<Real> &);
			AKANTU_GET_MACRO(ElementFilter, element_filter,
			const ElementTypeMapArray<UInt> &);
			AKANTU_GET_MACRO(FEEngine, fem, FEEngine &);

			bool isNonLocal() const { return is_non_local; }

			template <typename T>
			const Array<T> & getArray(const ID & id, const ElementType & type,
			const GhostType & ghost_type = _not_ghost) const;
			template <typename T>
			Array<T> & getArray(const ID & id, const ElementType & type,
			const GhostType & ghost_type = _not_ghost);

			template <typename T>
			const InternalField<T> & getInternal(const ID & id) const;
			template <typename T> InternalField<T> & getInternal(const ID & id);

			template <typename T>
			inline bool isInternal(const ID & id, const ElementKind & element_kind) const;

			template <typename T>
			ElementTypeMap<UInt>
			getInternalDataPerElem(const ID & id, const ElementKind & element_kind) const;

			bool isFiniteDeformation() const { return finite_deformation; }
			bool isInelasticDeformation() const { return inelastic_deformation; }

			template <typename T> inline void setParam(const ID & param, T value);
			inline const Parameter & getParam(const ID & param) const;

			template <typename T>
			void flattenInternal(const std::string & field_id,
			ElementTypeMapArray<T> & internal_flat,
			const GhostType ghost_type = _not_ghost,
			ElementKind element_kind = _ek_not_defined) const;

			/// apply a constant eigengrad_u everywhere in the material
			virtual void applyEigenGradU(const Matrix<Real> & prescribed_eigen_grad_u,
			const GhostType = _not_ghost);

			/// specify if the matrix need to be recomputed for this material
			virtual bool hasStiffnessMatrixChanged() { return true; }

			protected:
			bool isInit() const { return is_init; }

			/* ------------------------------------------------------------------------ */
			/* Class Members */
			/* ------------------------------------------------------------------------ */
			protected:
			/// boolean to know if the material has been initialized
			bool is_init;

			std::map<ID, InternalField<Real> *> internal_vectors_real;
			std::map<ID, InternalField<UInt> *> internal_vectors_uint;
			std::map<ID, InternalField<bool> *> internal_vectors_bool;

			protected:
			/// Link to the fem object in the model
			FEEngine & fem;

			/// Finite deformation
			bool finite_deformation;

			/// Finite deformation
			bool inelastic_deformation;

			/// material name
			std::string name;

			/// The model to witch the material belong
			SolidMechanicsModel & model;

			/// density : rho
			Real rho;

			/// spatial dimension
			UInt spatial_dimension;

			/// list of element handled by the material
			ElementTypeMapArray<UInt> element_filter;

			/// stresses arrays ordered by element types
			InternalField<Real> stress;

			/// eigengrad_u arrays ordered by element types
			InternalField<Real> eigengradu;

			/// grad_u arrays ordered by element types
			InternalField<Real> gradu;

			/// Green Lagrange strain (Finite deformation)
			InternalField<Real> green_strain;

			/// Second Piola-Kirchhoff stress tensor arrays ordered by element types
			/// (Finite deformation)
			InternalField<Real> piola_kirchhoff_2;

			/// potential energy by element
			InternalField<Real> potential_energy;

			/// tell if using in non local mode or not
			bool is_non_local;

			/// tell if the material need the previous stress state
			bool use_previous_stress;

			/// tell if the material need the previous strain state
			bool use_previous_gradu;

			/// elemental field interpolation coordinates
			InternalField<Real> interpolation_inverse_coordinates;

			/// elemental field interpolation points
			InternalField<Real> interpolation_points_matrices;

			/// vector that contains the names of all the internals that need to
			/// be transferred when material interfaces move
			std::vector<ID> internals_to_transfer;
			};

			/// standard output stream operator
			inline std::ostream & operator<<(std::ostream & stream,
			const Material & _this) {
			_this.printself(stream);
			return stream;
			}

			} // namespace akantu

			#include "material_inline_impl.cc"

			#include "internal_field_tmpl.hh"
			#include "random_internal_field_tmpl.hh"

			/* -------------------------------------------------------------------------- */
			/* Auto loop */
			/* -------------------------------------------------------------------------- */
			/// This can be used to automatically write the loop on quadrature points in
			/// functions such as computeStress. This macro in addition to write the loop
			/// provides two tensors (matrices) sigma and grad_u
			#define MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type) \
			Array<Real>::matrix_iterator gradu_it = \
			this->gradu(el_type, ghost_type) \
			.begin(this->spatial_dimension, this->spatial_dimension); \
			Array<Real>::matrix_iterator gradu_end = \
			this->gradu(el_type, ghost_type) \
			.end(this->spatial_dimension, this->spatial_dimension); \
			\
			this->stress(el_type, ghost_type) \
			.resize(this->gradu(el_type, ghost_type).size()); \
			\
			Array<Real>::iterator<Matrix<Real>> stress_it = \
			this->stress(el_type, ghost_type) \
			.begin(this->spatial_dimension, this->spatial_dimension); \
			\
			if (this->isFiniteDeformation()) { \
			this->piola_kirchhoff_2(el_type, ghost_type) \
			.resize(this->gradu(el_type, ghost_type).size()); \
			stress_it = this->piola_kirchhoff_2(el_type, ghost_type) \
			.begin(this->spatial_dimension, this->spatial_dimension); \
			} \
			\
			for (; gradu_it != gradu_end; ++gradu_it, ++stress_it) { \
			Matrix<Real> & __attribute__((unused)) grad_u = *gradu_it; \
			Matrix<Real> & __attribute__((unused)) sigma = *stress_it

			#define MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END }

			/// This can be used to automatically write the loop on quadrature points in
			/// functions such as computeTangentModuli. This macro in addition to write the
			/// loop provides two tensors (matrices) sigma_tensor, grad_u, and a matrix
			/// where the elemental tangent moduli should be stored in Voigt Notation
			#define MATERIAL_TANGENT_QUADRATURE_POINT_LOOP_BEGIN(tangent_mat) \
			Array<Real>::matrix_iterator gradu_it = \
			this->gradu(el_type, ghost_type) \
			.begin(this->spatial_dimension, this->spatial_dimension); \
			Array<Real>::matrix_iterator gradu_end = \
			this->gradu(el_type, ghost_type) \
			.end(this->spatial_dimension, this->spatial_dimension); \
			Array<Real>::matrix_iterator sigma_it = \
			this->stress(el_type, ghost_type) \
			.begin(this->spatial_dimension, this->spatial_dimension); \
			\
			tangent_mat.resize(this->gradu(el_type, ghost_type).size()); \
			\
			UInt tangent_size = \
			this->getTangentStiffnessVoigtSize(this->spatial_dimension); \
			Array<Real>::matrix_iterator tangent_it = \
			tangent_mat.begin(tangent_size, tangent_size); \
			\
			for (; gradu_it != gradu_end; ++gradu_it, ++sigma_it, ++tangent_it) { \
			Matrix<Real> & __attribute__((unused)) grad_u = *gradu_it; \
			Matrix<Real> & __attribute__((unused)) sigma_tensor = *sigma_it; \
			Matrix<Real> & tangent = *tangent_it

			#define MATERIAL_TANGENT_QUADRATURE_POINT_LOOP_END }

			/* -------------------------------------------------------------------------- */
			namespace akantu {
			using MaterialFactory =
			Factory<Material, ID, UInt, const ID &, SolidMechanicsModel &, const ID &>;
			} // namespace akantu

			#define INSTANTIATE_MATERIAL_ONLY(mat_name) \
			template class mat_name<1>; \
			template class mat_name<2>; \
			template class mat_name<3>

			#define MATERIAL_DEFAULT_PER_DIM_ALLOCATOR(id, mat_name) \
			[](UInt dim, const ID &, SolidMechanicsModel & model, \
			const ID & id) -> std::unique_ptr<Material> { \
			switch (dim) { \
			case 1: \
			return std::make_unique<mat_name<1>>(model, id); \
			case 2: \
			return std::make_unique<mat_name<2>>(model, id); \
			case 3: \
			return std::make_unique<mat_name<3>>(model, id); \
			default: \
			AKANTU_EXCEPTION("The dimension " \
			<< dim << "is not a valid dimension for the material " \
			<< #id); \
			} \
			}

			#define INSTANTIATE_MATERIAL(id, mat_name) \
			INSTANTIATE_MATERIAL_ONLY(mat_name); \
			static bool material_is_alocated_##id[[gnu::unused]] = \
			MaterialFactory::getInstance().registerAllocator( \
			#id, MATERIAL_DEFAULT_PER_DIM_ALLOCATOR(id, mat_name))

			#endif /* __AKANTU_MATERIAL_HH__ */

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#material.hh#
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