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solid_mechanics_model.hh
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			/**
			* @file solid_mechanics_model.hh
			*
			* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
			* @author Daniel Pino Muñoz <daniel.pinomunoz@epfl.ch>
			* @author Nicolas Richart <nicolas.richart@epfl.ch>
			*
			* @date creation: Tue Jul 27 2010
			* @date last modification: Tue Jan 19 2016
			*
			* @brief Model of Solid Mechanics
			*
			* @section LICENSE
			*
			* Copyright (©) 2010-2012, 2014, 2015 EPFL (Ecole Polytechnique Fédérale de
			* Lausanne) Laboratory (LSMS - Laboratoire de Simulation en Mécanique des
			* Solides)
			*
			* Akantu is free software: you can redistribute it and/or modify it under the
			* terms of the GNU Lesser General Public License as published by the Free
			* Software Foundation, either version 3 of the License, or (at your option) any
			* later version.
			*
			* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
			* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
			* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
			* details.
			*
			* You should have received a copy of the GNU Lesser General Public License
			* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
			*
			*/
			/* -------------------------------------------------------------------------- */
			#include "boundary_condition.hh"
			#include "data_accessor.hh"
			#include "model.hh"
			#include "non_local_manager.hh"
			#include "solid_mechanics_model_event_handler.hh"
			/* -------------------------------------------------------------------------- */
			#include "integrator_gauss.hh"
			#include "shape_lagrange.hh"
			/* -------------------------------------------------------------------------- */

			#ifndef __AKANTU_SOLID_MECHANICS_MODEL_HH__
			#define __AKANTU_SOLID_MECHANICS_MODEL_HH__

			namespace akantu {
			class Material;
			class MaterialSelector;
			class DumperIOHelper;
			class NonLocalManager;
			} // namespace akantu

			/* -------------------------------------------------------------------------- */
			namespace akantu {

			struct SolidMechanicsModelOptions : public ModelOptions {
			explicit SolidMechanicsModelOptions(
			AnalysisMethod analysis_method = _explicit_lumped_mass);

			template <typename... pack>
			SolidMechanicsModelOptions(use_named_args_t, pack &&... _pack);

			AnalysisMethod analysis_method;
			//bool no_init_materials;
			};

			/* -------------------------------------------------------------------------- */
			/* -------------------------------------------------------------------------- */
			class SolidMechanicsModel
			: public Model,
			public DataAccessor<Element>,
			public DataAccessor<UInt>,
			public BoundaryCondition<SolidMechanicsModel>,
			public NonLocalManagerCallback,
			public MeshEventHandler,
			public EventHandlerManager<SolidMechanicsModelEventHandler> {

			/* ------------------------------------------------------------------------ */
			/* Constructors/Destructors */
			/* ------------------------------------------------------------------------ */
			public:
			class NewMaterialElementsEvent : public NewElementsEvent {
			public:
			AKANTU_GET_MACRO_NOT_CONST(MaterialList, material, Array<UInt> &);
			AKANTU_GET_MACRO(MaterialList, material, const Array<UInt> &);

			protected:
			Array<UInt> material;
			};

			using MyFEEngineType = FEEngineTemplate<IntegratorGauss, ShapeLagrange>;

			protected:
			using EventManager = EventHandlerManager<SolidMechanicsModelEventHandler>;

			public:
			SolidMechanicsModel(Mesh & mesh, UInt spatial_dimension = _all_dimensions,
			const ID & id = "solid_mechanics_model",
			const MemoryID & memory_id = 0);

			virtual ~SolidMechanicsModel();

			/* ------------------------------------------------------------------------ */
			/* Methods */
			/* ------------------------------------------------------------------------ */
			public:
			template <typename P, typename T, typename... pack>
			void initFull(named_argument::param_t<P, T &&> && first, pack &&... _pack) {
			this->initFull(SolidMechanicsModelOptions{use_named_args, first, _pack...});
			}

			/// initialize completely the model
			void initFull(
			const ModelOptions & options = SolidMechanicsModelOptions()) override;

			/// initialize the fem object needed for boundary conditions
			void initFEEngineBoundary();

			/// register the tags associated with the parallel synchronizer
			// virtual void initParallel(MeshPartition * partition,
			// DataAccessor<Element> * data_accessor = NULL);

			/// allocate all vectors
			virtual void initArrays();

			/// allocate all vectors
			// void initArraysPreviousDisplacment();

			/// initialize all internal arrays for materials
			virtual void initMaterials();

			/// initialize the model
			void initModel() override;

			/// init PBC synchronizer
			// void initPBC();

			/// initialize a new solver and sets it as the default one to use
			void initNewSolver(const AnalysisMethod & method);

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

			protected:
			/// allocate an array if needed
			template <typename T>
			void allocNodalField(Array<T> *& array, const ID & name);

			/* ------------------------------------------------------------------------ */
			/* PBC */
			/* ------------------------------------------------------------------------ */
			public:
			/// change the equation number for proper assembly when using PBC
			// void changeEquationNumberforPBC(std::map <UInt, UInt> & pbc_pair);

			/// synchronize Residual for output
			// void synchronizeResidual();

			protected:
			/// register PBC synchronizer
			// void registerPBCSynchronizer();

			/* ------------------------------------------------------------------------ */
			/* Solver interface */
			/* ------------------------------------------------------------------------ */
			public:
			/// assembles the stiffness matrix,
			virtual void assembleStiffnessMatrix();
			/// assembles the internal forces in the array internal_forces
			virtual void assembleInternalForces();

			protected:
			/// callback for the solver, this adds f_{ext} - f_{int} to the residual
			void assembleResidual() override;

			/// callback for the solver, this assembles the stiffness matrix
			void assembleJacobian() override;

			/// callback for the solver, this is called at beginning of solve
			void predictor() override;
			/// callback for the solver, this is called at end of solve
			void corrector() override;

			/// Callback for the model to instantiate the matricees when needed
			void initSolver(TimeStepSolverType time_step_solver_type,
			NonLinearSolverType non_linear_solver_type) override;

			protected:
			/* ------------------------------------------------------------------------ */
			TimeStepSolverType getDefaultSolverType() const override;
			/* ------------------------------------------------------------------------ */
			ModelSolverOptions
			getDefaultSolverOptions(const TimeStepSolverType & type) const override;

			/* ------------------------------------------------------------------------ */
			/* Explicit */
			/* ------------------------------------------------------------------------ */
			// public:
			// /// initialize the stuff for the explicit scheme
			// void initExplicit(AnalysisMethod analysis_method =
			// _explicit_lumped_mass);

			public:
			bool isDefaultSolverExplicit() {
			return method == _explicit_lumped_mass \|\|
			method == _explicit_consistent_mass;
			}

			// /// initialize the array needed by updateResidual (residual,
			// current_position)
			// void initializeUpdateResidualData();

			protected:
			/// update the current position vector
			void updateCurrentPosition();

			// /// assemble the residual for the explicit scheme
			// virtual void updateResidual(bool need_initialize = true);

			// /**
			// * \brief compute the acceleration from the residual
			// * this function is the explicit equivalent to solveDynamic in implicit
			// * In the case of lumped mass just divide the residual by the mass
			// * In the case of not lumped mass call
			// solveDynamic<_acceleration_corrector>
			// */
			// void updateAcceleration();

			/// Update the increment of displacement
			// void updateIncrement();

			// /// Copy the actuel displacement into previous displacement
			// void updatePreviousDisplacement();

			// /// Save stress and strain through EventManager
			// void saveStressAndStrainBeforeDamage();
			// /// Update energies through EventManager
			// void updateEnergiesAfterDamage();

			// /// Solve the system @f[ A x = \alpha b @f] with A a lumped matrix
			// void solveLumped(Array<Real> & x, const Array<Real> & A,
			// const Array<Real> & b, const Array<bool> & blocked_dofs,
			// Real alpha);

			// /// explicit integration predictor
			// void explicitPred();

			// /// explicit integration corrector
			// void explicitCorr();

			// public:
			// void solveStep();

			// /*
			// ------------------------------------------------------------------------
			// */
			// /* Implicit */
			// /*
			// ------------------------------------------------------------------------
			// */
			// public:
			// /// initialize the solver and the jacobian_matrix (called by
			// initImplicit)
			// void initSolver();

			// /// initialize the stuff for the implicit solver
			// void initImplicit(bool dynamic = false);

			// /// solve Ma = f to get the initial acceleration
			// void initialAcceleration();

			// /// assemble the stiffness matrix
			// void assembleStiffnessMatrix();

			// public:
			// /**
			// * solve a step (predictor + convergence loop + corrector) using the
			// * the given convergence method (see akantu::SolveConvergenceMethod)
			// * and the given convergence criteria (see
			// * akantu::SolveConvergenceCriteria)
			// **/
			// template <SolveConvergenceMethod method, SolveConvergenceCriteria
			// criteria>
			// bool solveStep(Real tolerance, UInt max_iteration = 100);

			// template <SolveConvergenceMethod method, SolveConvergenceCriteria
			// criteria>
			// bool solveStep(Real tolerance, Real & error, UInt max_iteration = 100,
			// bool do_not_factorize = false);

			// public:
			// /**
			// * solve Ku = f using the the given convergence method (see
			// * akantu::SolveConvergenceMethod) and the given convergence
			// * criteria (see akantu::SolveConvergenceCriteria)
			// **/
			// template <SolveConvergenceMethod cmethod, SolveConvergenceCriteria
			// criteria>
			// bool solveStatic(Real tolerance, UInt max_iteration,
			// bool do_not_factorize = false);

			// /// create and return the velocity damping matrix
			// SparseMatrix & initVelocityDampingMatrix();

			// /// implicit time integration predictor
			// void implicitPred();

			// /// implicit time integration corrector
			// void implicitCorr();

			// /// compute the Cauchy stress on user demand.
			// void computeCauchyStresses();

			// // /// compute A and solve @f[ A\delta u = f_ext - f_int @f]
			// // template <NewmarkBeta::IntegrationSchemeCorrectorType type>
			// // void solve(Array<Real> &increment, Real block_val = 1.,
			// // bool need_factorize = true, bool has_profile_changed =
			// false);

			// protected:
			// /// finish the computation of residual to solve in increment
			// void updateResidualInternal();

			// /// compute the support reaction and store it in force
			// void updateSupportReaction();

			// private:
			// /// re-initialize the J matrix (to use if the profile of K changed)
			// void initJacobianMatrix();

			/* ------------------------------------------------------------------------ */
			// public:
			/// Update the stresses for the computation of the residual of the Stiffness
			/// matrix in the case of finite deformation
			// void computeStresses();

			/// synchronize the ghost element boundaries values
			// void synchronizeBoundaries();

			/* ------------------------------------------------------------------------ */
			/* Materials (solid_mechanics_model_material.cc) */
			/* ------------------------------------------------------------------------ */
			public:
			/// registers all the custom materials of a given type present in the input
			/// file
			// template <typename M> void registerNewCustomMaterials(const ID & mat_type);

			/// register an empty material of a given type
			Material & registerNewMaterial(const ID & mat_name, const ID & mat_type,
			const ID & opt_param);
			// /// Use a UIntData in the mesh to specify the material to use per
			// element void setMaterialIDsFromIntData(const std::string & data_name);

			/// reassigns materials depending on the material selector
			virtual void reassignMaterial();

			/// apply a constant eigen_grad_u on all quadrature points of a given material
			virtual void applyEigenGradU(const Matrix<Real> & prescribed_eigen_grad_u,
			const ID & material_name,
			const GhostType ghost_type = _not_ghost);

			protected:
			/// register a material in the dynamic database
			Material & registerNewMaterial(const ParserSection & mat_section);

			/// read the material files to instantiate all the materials
			void instantiateMaterials();

			/// set the element_id_by_material and add the elements to the good materials
			void
			assignMaterialToElements(const ElementTypeMapArray<UInt> * filter = NULL);

			/// reinitialize dof_synchronizer and solver (either in implicit or
			/// explicit) when cohesive elements are inserted
			// void reinitializeSolver();

			/* ------------------------------------------------------------------------ */
			/* Mass (solid_mechanics_model_mass.cc) */
			/* ------------------------------------------------------------------------ */
			public:
			/// assemble the lumped mass matrix
			void assembleMassLumped();

			/// assemble the mass matrix for consistent mass resolutions
			void assembleMass();

			protected:
			/// assemble the lumped mass matrix for local and ghost elements
			void assembleMassLumped(GhostType ghost_type);

			/// assemble the mass matrix for either _ghost or _not_ghost elements
			void assembleMass(GhostType ghost_type);

			/// assemble the lumped mass only for a given list of nodes
			void assembleMassLumped(const Array<UInt> & node_list);

			/// assemble the lumped mass only for a given list of nodes
			void assembleMass(const Array<UInt> & node_list);

			/// fill a vector of rho
			void computeRho(Array<Real> & rho, ElementType type, GhostType ghost_type);

			/// compute the kinetic energy
			Real getKineticEnergy();
			Real getKineticEnergy(const ElementType & type, UInt index);

			/// compute the external work (for impose displacement, the velocity should be
			/// given too)
			Real getExternalWork();

			/* ------------------------------------------------------------------------ */
			/* NonLocalManager inherited members */
			/* ------------------------------------------------------------------------ */
			protected:
			void updateDataForNonLocalCriterion(ElementTypeMapReal & criterion) override;

			void computeNonLocalStresses(const GhostType & ghost_type) override;

			void
			insertIntegrationPointsInNeighborhoods(const GhostType & ghost_type) override;

			/// update the values of the non local internal
			void updateLocalInternal(ElementTypeMapReal & internal_flat,
			const GhostType & ghost_type,
			const ElementKind & kind) override;

			/// copy the results of the averaging in the materials
			void updateNonLocalInternal(ElementTypeMapReal & internal_flat,
			const GhostType & ghost_type,
			const ElementKind & kind) override;

			/* ------------------------------------------------------------------------ */
			/* Data Accessor 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;

			inline UInt getNbData(const Array<UInt> & dofs,
			const SynchronizationTag & tag) const override;

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

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

			protected:
			inline void splitElementByMaterial(const Array<Element> & elements,
			Array<Element> * elements_per_mat) const;

			/* ------------------------------------------------------------------------ */
			/* Mesh Event Handler inherited members */
			/* ------------------------------------------------------------------------ */
			protected:
			void onNodesAdded(const Array<UInt> & nodes_list,
			const NewNodesEvent & event) override;
			void onNodesRemoved(const Array<UInt> & element_list,
			const Array<UInt> & new_numbering,
			const RemovedNodesEvent & event) override;
			void onElementsAdded(const Array<Element> & nodes_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{};

			/* ------------------------------------------------------------------------ */
			/* Dumpable interface (kept for convenience) and dumper relative functions */
			/* ------------------------------------------------------------------------ */
			public:
			virtual void onDump();

			//! decide wether a field is a material internal or not
			bool isInternal(const std::string & field_name,
			const ElementKind & element_kind);
			#ifndef SWIG
			//! give the amount of data per element
			virtual ElementTypeMap<UInt>
			getInternalDataPerElem(const std::string & field_name,
			const ElementKind & kind);

			//! flatten a given material internal field
			ElementTypeMapArray<Real> &
			flattenInternal(const std::string & field_name, const ElementKind & kind,
			const GhostType ghost_type = _not_ghost);
			//! flatten all the registered material internals
			void flattenAllRegisteredInternals(const ElementKind & kind);
			#endif

			dumper::Field * createNodalFieldReal(const std::string & field_name,
			const std::string & group_name,
			bool padding_flag) override;

			dumper::Field * createNodalFieldBool(const std::string & field_name,
			const std::string & group_name,
			bool padding_flag) override;

			dumper::Field * createElementalField(const std::string & field_name,
			const std::string & group_name,
			bool padding_flag,
			const UInt & spatial_dimension,
			const ElementKind & kind) override;

			virtual void dump(const std::string & dumper_name);

			virtual void dump(const std::string & dumper_name, UInt step);

			virtual void dump(const std::string & dumper_name, Real time, UInt step);

			void dump() override;

			virtual void dump(UInt step);

			virtual void dump(Real time, UInt step);

			/* ------------------------------------------------------------------------ */
			/* Accessors */
			/* ------------------------------------------------------------------------ */
			public:
			/// return the dimension of the system space
			AKANTU_GET_MACRO(SpatialDimension, Model::spatial_dimension, UInt);

			/// get the current value of the time step
			// AKANTU_GET_MACRO(TimeStep, time_step, Real);

			/// set the value of the time step
			void setTimeStep(Real time_step, const ID & solver_id = "") override;
			/// void setTimeStep(Real time_step);

			/// return the of iterations done in the last solveStep
			// AKANTU_GET_MACRO(NumberIter, n_iter, UInt);

			/// get the value of the conversion from forces/ mass to acceleration
			AKANTU_GET_MACRO(F_M2A, f_m2a, Real);

			/// set the value of the conversion from forces/ mass to acceleration
			AKANTU_SET_MACRO(F_M2A, f_m2a, Real);

			/// get the SolidMechanicsModel::displacement vector
			AKANTU_GET_MACRO(Displacement, *displacement, Array<Real> &);

			/// get the SolidMechanicsModel::previous_displacement vector
			AKANTU_GET_MACRO(PreviousDisplacement, *previous_displacement, Array<Real> &);

			/// get the SolidMechanicsModel::current_position vector \warn only consistent
			/// after a call to SolidMechanicsModel::updateCurrentPosition
			const Array<Real> & getCurrentPosition();

			/// get the SolidMechanicsModel::increment vector \warn only consistent if
			/// SolidMechanicsModel::setIncrementFlagOn has been called before
			AKANTU_GET_MACRO(Increment, *displacement_increment, Array<Real> &);

			/// get the lumped SolidMechanicsModel::mass vector
			AKANTU_GET_MACRO(Mass, *mass, Array<Real> &);

			/// get the SolidMechanicsModel::velocity vector
			AKANTU_GET_MACRO(Velocity, *velocity, Array<Real> &);

			/// get the SolidMechanicsModel::acceleration vector, updated by
			/// SolidMechanicsModel::updateAcceleration
			AKANTU_GET_MACRO(Acceleration, *acceleration, Array<Real> &);

			/// get the SolidMechanicsModel::force vector (external forces)
			AKANTU_GET_MACRO(Force, *external_force, Array<Real> &);

			/// get the SolidMechanicsModel::internal_force vector (internal forces)
			AKANTU_GET_MACRO(InternalForce, *internal_force, Array<Real> &);

			/// get the SolidMechanicsModel::blocked_dofs vector
			AKANTU_GET_MACRO(BlockedDOFs, *blocked_dofs, Array<bool> &);

			/// get the SolidMechnicsModel::incrementAcceleration vector
			// AKANTU_GET_MACRO(IncrementAcceleration, *increment_acceleration,
			// Array<Real> &);

			/// get the value of the SolidMechanicsModel::increment_flag
			AKANTU_GET_MACRO(IncrementFlag, increment_flag, bool);

			/// get a particular material (by material index)
			inline Material & getMaterial(UInt mat_index);

			/// get a particular material (by material index)
			inline const Material & getMaterial(UInt mat_index) const;

			/// get a particular material (by material name)
			inline Material & getMaterial(const std::string & name);

			/// get a particular material (by material name)
			inline const Material & getMaterial(const std::string & name) const;

			/// get a particular material id from is name
			inline UInt getMaterialIndex(const std::string & name) const;

			/// give the number of materials
			inline UInt getNbMaterials() const { return materials.size(); }

			inline void setMaterialSelector(MaterialSelector & selector);

			/// give the material internal index from its id
			Int getInternalIndexFromID(const ID & id) const;

			/// compute the stable time step
			Real getStableTimeStep();

			/// get the energies
			Real getEnergy(const std::string & energy_id);

			/// compute the energy for energy
			Real getEnergy(const std::string & energy_id, const ElementType & type,
			UInt index);

			/**
			* @brief set the SolidMechanicsModel::increment_flag to on, the activate the
			* update of the SolidMechanicsModel::increment vector
			*/
			// void setIncrementFlagOn();

			// /// get the stiffness matrix
			// AKANTU_GET_MACRO(StiffnessMatrix, *stiffness_matrix, SparseMatrix &);

			// /// get the global jacobian matrix of the system
			// AKANTU_GET_MACRO(GlobalJacobianMatrix, *jacobian_matrix, const SparseMatrix
			// &);

			// /// get the mass matrix
			// AKANTU_GET_MACRO(MassMatrix, *mass_matrix, SparseMatrix &);

			// /// get the velocity damping matrix
			// AKANTU_GET_MACRO(VelocityDampingMatrix, *velocity_damping_matrix,
			// SparseMatrix &);

			/// get the FEEngine object to integrate or interpolate on the boundary
			inline FEEngine & getFEEngineBoundary(const ID & name = "");

			// /// get integrator
			// AKANTU_GET_MACRO(Integrator, *integrator, const IntegrationScheme2ndOrder
			// &);

			// /// get synchronizer
			// AKANTU_GET_MACRO(Synchronizer, *synch_parallel, const ElementSynchronizer
			// &);

			AKANTU_GET_MACRO(MaterialByElement, material_index,
			const ElementTypeMapArray<UInt> &);

			/// vectors containing local material element index for each global element
			/// index
			AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(MaterialByElement, material_index,
			UInt);
			AKANTU_GET_MACRO_BY_ELEMENT_TYPE(MaterialByElement, material_index, UInt);
			AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(MaterialLocalNumbering,
			material_local_numbering, UInt);
			AKANTU_GET_MACRO_BY_ELEMENT_TYPE(MaterialLocalNumbering,
			material_local_numbering, UInt);

			/// Get the type of analysis method used
			AKANTU_GET_MACRO(AnalysisMethod, method, AnalysisMethod);

			/// Access the non_local_manager interface
			AKANTU_GET_MACRO(NonLocalManager, *non_local_manager, NonLocalManager &);
			protected:
			friend class Material;

			protected:
			/// compute the stable time step
			Real getStableTimeStep(const GhostType & ghost_type);

			/* ------------------------------------------------------------------------ */
			/* Class Members */
			/* ------------------------------------------------------------------------ */
			protected:
			/// number of iterations
			// UInt n_iter;

			/// time step
			// Real time_step;

			/// conversion coefficient form force/mass to acceleration
			Real f_m2a;

			/// displacements array
			Array<Real> * displacement;
			UInt displacement_release{0};

			/// displacements array at the previous time step (used in finite deformation)
			Array<Real> * previous_displacement;

			/// increment of displacement
			Array<Real> * displacement_increment;

			/// lumped mass array
			Array<Real> * mass;

			/// velocities array
			Array<Real> * velocity;

			/// accelerations array
			Array<Real> * acceleration;

			/// accelerations array
			// Array<Real> * increment_acceleration;

			/// external forces array
			Array<Real> * external_force;

			/// internal forces array
			Array<Real> * internal_force;

			/// array specifing if a degree of freedom is blocked or not
			Array<bool> * blocked_dofs;

			/// array of current position used during update residual
			Array<Real> * current_position;
			UInt current_position_release{0};

			/// mass matrix
			SparseMatrix * mass_matrix;

			/// velocity damping matrix
			SparseMatrix * velocity_damping_matrix;

			/// stiffness matrix
			SparseMatrix * stiffness_matrix;

			/// jacobian matrix @f[A = cM + dD + K@f] with @f[c = \frac{1}{\beta \Delta
			/// t^2}, d = \frac{\gamma}{\beta \Delta t} @f]
			SparseMatrix * jacobian_matrix;

			/// Arrays containing the material index for each element
			ElementTypeMapArray<UInt> material_index;

			/// Arrays containing the position in the element filter of the material
			/// (material's local numbering)
			ElementTypeMapArray<UInt> material_local_numbering;

			#ifdef SWIGPYTHON
			public:
			#endif
			/// list of used materials
			std::vector<std::unique_ptr<Material>> materials;

			/// mapping between material name and material internal id
			std::map<std::string, UInt> materials_names_to_id;
			#ifdef SWIGPYTHON
			protected:
			#endif

			/// class defining of to choose a material
			MaterialSelector * material_selector;

			/// define if it is the default selector or not
			bool is_default_material_selector;

			// /// integration scheme of second order used
			// IntegrationScheme2ndOrder *integrator;

			/// flag defining if the increment must be computed or not
			bool increment_flag;

			/// analysis method check the list in akantu::AnalysisMethod
			AnalysisMethod method;

			/// tells if the material are instantiated
			bool are_materials_instantiated;

			typedef std::map<std::pair<std::string, ElementKind>,
			ElementTypeMapArray<Real> *>
			flatten_internal_map;

			/// map a registered internals to be flattened for dump purposes
			flatten_internal_map registered_internals;

			/// non local manager
			std::unique_ptr<NonLocalManager> non_local_manager;

			/// pointer to the pbc synchronizer
			// PBCSynchronizer * pbc_synch;
			};

			/* -------------------------------------------------------------------------- */
			namespace BC {
			namespace Neumann {
			typedef FromHigherDim FromStress;
			typedef FromSameDim FromTraction;
			} // namespace Neumann
			} // namespace BC

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

			} // namespace akantu

			/* -------------------------------------------------------------------------- */
			/* inline functions */
			/* -------------------------------------------------------------------------- */
			#include "material.hh"
			#include "parser.hh"

			#include "solid_mechanics_model_inline_impl.cc"
			#include "solid_mechanics_model_tmpl.hh"

			#include "material_selector_tmpl.hh"

			#endif /* __AKANTU_SOLID_MECHANICS_MODEL_HH__ */

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rAKA/src/model/solid_mechanics/solid_mechanics_model.hh
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