material_muSpectre_base.hh
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material_muSpectre_base.hh
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	/**
	* @file material_muSpectre_base.hh
	*
	* @author Till Junge <till.junge@epfl.ch>
	*
	* @date 25 Oct 2017
	*
	* @brief Base class for materials written for µSpectre specifically. These
	* can take full advantage of the configuration-change utilities of
	* µSpectre. The user can inherit from them to define new constitutive
	* laws and is merely required to provide the methods for computing the
	* second Piola-Kirchhoff stress and Tangent. This class uses the
	* "curiously recurring template parameter" to avoid virtual calls.
	*
	* Copyright © 2017 Till Junge
	*
	* µSpectre is free software; you can redistribute it and/or
	* modify it under the terms of the GNU General Public License as
	* published by the Free Software Foundation, either version 3, or (at
	* your option) any later version.
	*
	* µSpectre 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
	* General Public License for more details.
	*
	* You should have received a copy of the GNU General Public License
	* along with GNU Emacs; see the file COPYING. If not, write to the
	* Free Software Foundation, Inc., 59 Temple Place - Suite 330,
	* Boston, MA 02111-1307, USA.
	*/

	#ifndef MATERIAL_MUSPECTRE_BASE_H
	#define MATERIAL_MUSPECTRE_BASE_H

	#include "common/common.hh"
	#include "materials/material_base.hh"
	#include "materials/materials_toolbox.hh"
	#include "common/field_collection.hh"
	#include "common/field.hh"
	#include "common//utilities.hh"

	#include <tuple>
	#include <type_traits>
	#include <iterator>
	#include <stdexcept>

	namespace muSpectre {

	// Forward declaration for factory function
	template <Dim_t DimS, Dim_t DimM>
	class CellBase;

	/**
	* material traits are used by `muSpectre::MaterialMuSpectre` to
	* break the circular dependence created by the curiously recurring
	* template parameter. These traits must define
	* - these `muSpectre::FieldMap`s:
	* - `StrainMap_t`: typically a `muSpectre::MatrixFieldMap` for a
	* constant second-order `muSpectre::TensorField`
	* - `StressMap_t`: typically a `muSpectre::MatrixFieldMap` for a
	* writable secord-order `muSpectre::TensorField`
	* - `TangentMap_t`: typically a `muSpectre::T4MatrixFieldMap` for a
	* writable fourth-order `muSpectre::TensorField`
	* - `strain_measure`: the expected strain type (will be replaced by the
	* small-strain tensor ε
	* `muspectre::StrainMeasure::Infinitesimal` in small
	* strain computations)
	* - `stress_measure`: the measure of the returned stress. Is used by
	* `muspectre::MaterialMuSpectre` to transform it into
	* Cauchy stress (`muspectre::StressMeasure::Cauchy`) in
	* small-strain computations and into first
	* Piola-Kirchhoff stress `muspectre::StressMeasure::PK1`
	* in finite-strain computations
	* - `InternalVariables`: a tuple of `muSpectre::FieldMap`s containing
	* internal variables
	*/
	template <class Material>
	struct MaterialMuSpectre_traits {

	};

	template <class Material, Dim_t DimS, Dim_t DimM>
	class MaterialMuSpectre;

	/**
	* Base class for most convenient implementation of materials
	*/
	template <class Material, Dim_t DimS, Dim_t DimM>
	class MaterialMuSpectre: public MaterialBase<DimS, DimM>
	{
	public:
	/**
	* type used to determine whether the
	* `muSpectre::MaterialMuSpectre::iterable_proxy` evaluate only
	* stresses or also tangent stiffnesses
	*/
	using NeedTangent = MatTB::NeedTangent;
	using Parent = MaterialBase<DimS, DimM>; //!< base class
	//! global field collection
	using GFieldCollection_t = typename Parent::GFieldCollection_t;
	//! expected type for stress fields
	using StressField_t = typename Parent::StressField_t;
	//! expected type for strain fields
	using StrainField_t = typename Parent::StrainField_t;
	//! expected type for tangent stiffness fields
	using TangentField_t = typename Parent::TangentField_t;

	//! traits for the CRTP subclass
	using traits = MaterialMuSpectre_traits<Material>;

	//! Default constructor
	MaterialMuSpectre() = delete;

	//! Construct by name
	MaterialMuSpectre(std::string name);

	//! Copy constructor
	MaterialMuSpectre(const MaterialMuSpectre &other) = delete;

	//! Move constructor
	MaterialMuSpectre(MaterialMuSpectre &&other) = delete;

	//! Destructor
	virtual ~MaterialMuSpectre() = default;

	//! Factory
	template <class... ConstructorArgs>
	static Material & make(CellBase<DimS, DimM> & cell,
	ConstructorArgs &&... args);

	//! Copy assignment operator
	MaterialMuSpectre& operator=(const MaterialMuSpectre &other) = delete;

	//! Move assignment operator
	MaterialMuSpectre& operator=(MaterialMuSpectre &&other) = delete;


	//! allocate memory, etc
	virtual void initialise(bool stiffness = false) override;

	using Parent::compute_stresses;
	using Parent::compute_stresses_tangent;
	//! computes stress
	virtual void compute_stresses(const StrainField_t & F,
	StressField_t & P,
	Formulation form) override final;
	//! computes stress and tangent modulus
	virtual void compute_stresses_tangent(const StrainField_t & F,
	StressField_t & P,
	TangentField_t & K,
	Formulation form) override final;

	protected:
	//! computes stress with the formulation available at compile time
	//! __attribute__ required by g++-6 and g++-7 because of this bug:
	//! https://gcc.gnu.org/bugzilla/show_bug.cgi?id=80947
	template <Formulation Form>
	inline void compute_stresses_worker(const StrainField_t & F,
	StressField_t & P)
	__attribute__ ((visibility ("default")));

	//! computes stress with the formulation available at compile time
	//! __attribute__ required by g++-6 and g++-7 because of this bug:
	//! https://gcc.gnu.org/bugzilla/show_bug.cgi?id=80947
	template <Formulation Form>
	inline void compute_stresses_worker(const StrainField_t & F,
	StressField_t & P,
	TangentField_t & K)
	__attribute__ ((visibility ("default")));
	//! this iterable class is a default for simple laws that just take a strain
	//! the iterable is just a templated wrapper to provide a range to iterate over
	//! that does or does not include tangent moduli
	template<NeedTangent need_tgt = NeedTangent::no>
	class iterable_proxy;

	/**
	* inheriting classes with internal variables need to overload this function
	*/
	typename traits::InternalVariables& get_internals() {
	return static_cast<Material&>(*this).get_internals();}

	bool is_initialised{false}; //!< to handle double initialisation right

	private:
	};

	/* ---------------------------------------------------------------------- */
	template <class Material, Dim_t DimS, Dim_t DimM>
	MaterialMuSpectre<Material, DimS, DimM>::
	MaterialMuSpectre(std::string name)
	:Parent(name) {
	using stress_compatible = typename traits::StressMap_t::
	template is_compatible<StressField_t>;
	using strain_compatible = typename traits::StrainMap_t::
	template is_compatible<StrainField_t>;
	using tangent_compatible = typename traits::TangentMap_t::
	template is_compatible<TangentField_t>;

	static_assert((stress_compatible::value &&
	stress_compatible::explain()),
	"The material's declared stress map is not compatible "
	"with the stress field. More info in previously shown "
	"assert.");

	static_assert((strain_compatible::value &&
	strain_compatible::explain()),
	"The material's declared strain map is not compatible "
	"with the strain field. More info in previously shown "
	"assert.");

	static_assert((tangent_compatible::value &&
	tangent_compatible::explain()),
	"The material's declared tangent map is not compatible "
	"with the tangent field. More info in previously shown "
	"assert.");
	}


	/* ---------------------------------------------------------------------- */
	template <class Material, Dim_t DimS, Dim_t DimM>
	template <class... ConstructorArgs>
	Material & MaterialMuSpectre<Material, DimS, DimM>::
	make(CellBase<DimS, DimM> & cell,
	ConstructorArgs && ... args) {
	auto mat = std::make_unique<Material>(args...);
	auto & mat_ref = *mat;
	cell.add_material(std::move(mat));
	return mat_ref;
	}


	/* ---------------------------------------------------------------------- */
	template <class Material, Dim_t DimS, Dim_t DimM>
	void MaterialMuSpectre<Material, DimS, DimM>::
	initialise(bool /stiffness/) {
	if (!this->is_initialised) {
	this->internal_fields.initialise();
	this->is_initialised = true;
	}
	}

	/* ---------------------------------------------------------------------- */
	template <class Material, Dim_t DimS, Dim_t DimM>
	void MaterialMuSpectre<Material, DimS, DimM>::
	compute_stresses(const StrainField_t &F, StressField_t &P,
	Formulation form) {
	switch (form) {
	case Formulation::finite_strain: {
	this->template compute_stresses_worker<Formulation::finite_strain>(F, P);
	break;
	}
	case Formulation::small_strain: {
	this->template compute_stresses_worker<Formulation::small_strain>(F, P);
	break;
	}
	default:
	throw std::runtime_error("Unknown formulation");
	break;
	}
	}

	/* ---------------------------------------------------------------------- */
	template <class Material, Dim_t DimS, Dim_t DimM>
	void MaterialMuSpectre<Material, DimS, DimM>::
	compute_stresses_tangent(const StrainField_t & F, StressField_t & P,
	TangentField_t & K,
	Formulation form) {
	switch (form) {
	case Formulation::finite_strain: {
	this->template compute_stresses_worker<Formulation::finite_strain>(F, P, K);
	break;
	}
	case Formulation::small_strain: {
	this->template compute_stresses_worker<Formulation::small_strain>(F, P, K);
	break;
	}
	default:
	throw std::runtime_error("Unknown formulation");
	break;
	}
	}

	/* ---------------------------------------------------------------------- */
	template <class Material, Dim_t DimS, Dim_t DimM>
	template <Formulation Form>
	void MaterialMuSpectre<Material, DimS, DimM>::
	compute_stresses_worker(const StrainField_t & F,
	StressField_t & P,
	TangentField_t & K){

	/* These lambdas are executed for every integration point.

	F contains the transformation gradient for finite strain calculations and
	the infinitesimal strain tensor in small strain problems

	The internal_variables tuple contains whatever internal variables
	Material declared (e.g., eigenstrain, strain rate, etc.)
	*/
	using Strains_t = std::tuple<typename traits::StrainMap_t::reference>;
	using Stresses_t = std::tuple<typename traits::StressMap_t::reference,
	typename traits::TangentMap_t::reference>;
	auto constitutive_law_small_strain = [this]
	(Strains_t Strains, Stresses_t Stresses, auto && internal_variables) {
	constexpr StrainMeasure stored_strain_m{get_stored_strain_type(Form)};
	constexpr StrainMeasure expected_strain_m{
	get_formulation_strain_type(Form, traits::strain_measure)};

	auto & this_mat = static_cast<Material&>(*this);

	// Transformation gradient is first in the strains tuple
	auto & F = std::get<0>(Strains);
	auto && strain = MatTB::convert_strain<stored_strain_m, expected_strain_m>(F);
	// return value contains a tuple of rvalue_refs to both stress and tangent moduli
	Stresses =
	apply([&strain, &this_mat] (auto && ... internals) {
	return
	this_mat.evaluate_stress_tangent(std::move(strain),
	internals...);},
	internal_variables);
	};

	auto constitutive_law_finite_strain = [this]
	(Strains_t Strains, Stresses_t Stresses, auto && internal_variables) {
	constexpr StrainMeasure stored_strain_m{get_stored_strain_type(Form)};
	constexpr StrainMeasure expected_strain_m{
	get_formulation_strain_type(Form, traits::strain_measure)};
	auto & this_mat = static_cast<Material&>(*this);

	// Transformation gradient is first in the strains tuple
	auto & grad = std::get<0>(Strains);
	auto && strain = MatTB::convert_strain<stored_strain_m, expected_strain_m>(grad);

	// TODO: Figure this out: I can't std::move(internals...),
	// because if there are no internals, compilation fails with "no
	// matching function for call to ‘move()’'. These are tuples of
	// lvalue references, so it shouldn't be too bad, but still
	// irksome.

	// return value contains a tuple of rvalue_refs to both stress
	// and tangent moduli
	auto stress_tgt =
	apply([&strain, &this_mat] (auto && ... internals) {
	return
	this_mat.evaluate_stress_tangent(std::move(strain),
	internals...);},
	internal_variables);
	auto & stress = std::get<0>(stress_tgt);
	auto & tangent = std::get<1>(stress_tgt);
	Stresses = MatTB::PK1_stress<traits::stress_measure, traits::strain_measure>
	(std::move(grad),
	std::move(stress),
	std::move(tangent));
	};

	iterable_proxy<NeedTangent::yes> fields{*this, F, P, K};
	for (auto && arglist: fields) {
	/**
	* arglist is a tuple of three tuples containing only Lvalue
	* references (see value_tye in the class definition of
	* iterable_proxy::iterator). Tuples contain strains, stresses
	* and internal variables, respectively,
	*/

	//auto && stress_tgt = std::get<0>(tuples);
	//auto && inputs = std::get<1>(tuples);TODO:clean this
	static_assert(std::is_same<typename traits::StrainMap_t::reference,
	std::remove_reference_t<
	decltype(std::get<0>(std::get<0>(arglist)))>>::value,
	"Type mismatch for strain reference, check iterator "
	"value_type");
	static_assert(std::is_same<typename traits::StressMap_t::reference,
	std::remove_reference_t<
	decltype(std::get<0>(std::get<1>(arglist)))>>::value,
	"Type mismatch for stress reference, check iterator"
	"value_type");
	static_assert(std::is_same<typename traits::TangentMap_t::reference,
	std::remove_reference_t<
	decltype(std::get<1>(std::get<1>(arglist)))>>::value,
	"Type mismatch for tangent reference, check iterator"
	"value_type");

	switch (Form) {
	case Formulation::small_strain: {
	apply(constitutive_law_small_strain, std::move(arglist));
	break;
	}
	case Formulation::finite_strain: {
	apply(constitutive_law_finite_strain, std::move(arglist));
	break;
	}
	}
	}
	}


	/* ---------------------------------------------------------------------- */
	template <class Material, Dim_t DimS, Dim_t DimM>
	template <Formulation Form>
	void MaterialMuSpectre<Material, DimS, DimM>::
	compute_stresses_worker(const StrainField_t & F,
	StressField_t & P){

	/* These lambdas are executed for every integration point.

	F contains the transformation gradient for finite strain calculations and
	the infinitesimal strain tensor in small strain problems

	The internal_variables tuple contains whatever internal variables
	Material declared (e.g., eigenstrain, strain rate, etc.)
	*/

	using Strains_t = std::tuple<typename traits::StrainMap_t::reference>;
	using Stresses_t = std::tuple<typename traits::StressMap_t::reference>;
	auto constitutive_law_small_strain = [this]
	(Strains_t Strains, Stresses_t Stresses, auto && internal_variables) {
	constexpr StrainMeasure stored_strain_m{get_stored_strain_type(Form)};
	constexpr StrainMeasure expected_strain_m{
	get_formulation_strain_type(Form, traits::strain_measure)};

	auto & this_mat = static_cast<Material&>(*this);

	// Transformation gradient is first in the strains tuple
	auto & F = std::get<0>(Strains);
	auto && strain = MatTB::convert_strain<stored_strain_m, expected_strain_m>(F);
	// return value contains a tuple of rvalue_refs to both stress and tangent moduli
	auto & sigma = std::get<0>(Stresses);
	sigma =
	apply([&strain, &this_mat] (auto && ... internals) {
	return
	this_mat.evaluate_stress(std::move(strain),
	internals...);},
	internal_variables);
	};

	auto constitutive_law_finite_strain = [this]
	(Strains_t Strains, Stresses_t && Stresses, auto && internal_variables) {
	constexpr StrainMeasure stored_strain_m{get_stored_strain_type(Form)};
	constexpr StrainMeasure expected_strain_m{
	get_formulation_strain_type(Form, traits::strain_measure)};
	auto & this_mat = static_cast<Material&>(*this);

	// Transformation gradient is first in the strains tuple
	auto & F = std::get<0>(Strains);
	auto && strain = MatTB::convert_strain<stored_strain_m, expected_strain_m>(F);

	// TODO: Figure this out: I can't std::move(internals...),
	// because if there are no internals, compilation fails with "no
	// matching function for call to ‘move()’'. These are tuples of
	// lvalue references, so it shouldn't be too bad, but still
	// irksome.

	// return value contains a tuple of rvalue_refs to both stress
	// and tangent moduli
	auto && stress =
	apply([&strain, &this_mat] (auto && ... internals) {
	return
	this_mat.evaluate_stress(std::move(strain),
	internals...);},
	internal_variables);
	auto & P = get<0>(Stresses);
	P = MatTB::PK1_stress<traits::stress_measure, traits::strain_measure>
	(F, stress);
	};

	iterable_proxy<NeedTangent::no> fields{*this, F, P};

	for (auto && arglist: fields) {
	/**
	* arglist is a tuple of three tuples containing only Lvalue
	* references (see value_tye in the class definition of
	* iterable_proxy::iterator). Tuples contain strains, stresses
	* and internal variables, respectively,
	*/

	//auto && stress_tgt = std::get<0>(tuples);
	//auto && inputs = std::get<1>(tuples);TODO:clean this
	static_assert(std::is_same<typename traits::StrainMap_t::reference,
	std::remove_reference_t<
	decltype(std::get<0>(std::get<0>(arglist)))>>::value,
	"Type mismatch for strain reference, check iterator "
	"value_type");
	static_assert(std::is_same<typename traits::StressMap_t::reference,
	std::remove_reference_t<
	decltype(std::get<0>(std::get<1>(arglist)))>>::value,
	"Type mismatch for stress reference, check iterator"
	"value_type");

	switch (Form) {
	case Formulation::small_strain: {
	apply(constitutive_law_small_strain, std::move(arglist));
	break;
	}
	case Formulation::finite_strain: {
	apply(constitutive_law_finite_strain, std::move(arglist));
	break;
	}
	}
	}
	}


	/* ---------------------------------------------------------------------- */
	//! this iterator class is a default for simple laws that just take a strain
	template <class Material, Dim_t DimS, Dim_t DimM>
	template <MatTB::NeedTangent NeedTgt>
	class MaterialMuSpectre<Material, DimS, DimM>::iterable_proxy {
	public:
	//! Default constructor
	iterable_proxy() = delete;
	/**
	* type used to determine whether the
	* `muSpectre::MaterialMuSpectre::iterable_proxy` evaluate only
	* stresses or also tangent stiffnesses
	*/
	using NeedTangent =
	typename MaterialMuSpectre<Material, DimS, DimM>::NeedTangent;
	/** Iterator uses the material's internal variables field
	collection to iterate selectively over the global fields
	(such as the transformation gradient F and first
	Piola-Kirchhoff stress P.
	**/
	template<bool DoNeedTgt=(NeedTgt == NeedTangent::yes)>
	iterable_proxy(MaterialMuSpectre & mat,
	const StrainField_t & F,
	StressField_t & P,
	std::enable_if_t<DoNeedTgt, TangentField_t> & K)
	:material{mat}, strain_field{F}, stress_tup{P,K},
	internals{material.get_internals()}{};

	/** Iterator uses the material's internal variables field
	collection to iterate selectively over the global fields
	(such as the transformation gradient F and first
	Piola-Kirchhoff stress P.
	**/
	template<bool DontNeedTgt=(NeedTgt == NeedTangent::no)>
	iterable_proxy(MaterialMuSpectre & mat,
	const StrainField_t & F,
	std::enable_if_t<DontNeedTgt, StressField_t> & P)
	:material{mat}, strain_field{F}, stress_tup{P},
	internals{material.get_internals()}{};

	//! Expected type for strain fields
	using StrainMap_t = typename traits::StrainMap_t;
	//! Expected type for stress fields
	using StressMap_t = typename traits::StressMap_t;
	//! Expected type for tangent stiffness fields
	using TangentMap_t = typename traits::TangentMap_t;
	//! expected type for strain values
	using Strain_t = typename traits::StrainMap_t::reference;
	//! expected type for stress values
	using Stress_t = typename traits::StressMap_t::reference;
	//! expected type for tangent stiffness values
	using Tangent_t = typename traits::TangentMap_t::reference;

	//! tuple of intervnal variables, depends on the material
	using InternalVariables = typename traits::InternalVariables;
	//! tuple containing a stress and possibly a tangent stiffness field
	using StressFieldTup = std::conditional_t
	<(NeedTgt == NeedTangent::yes),
	std::tuple<StressField_t&, TangentField_t&>,
	std::tuple<StressField_t&>>;
	//! tuple containing a stress and possibly a tangent stiffness field map
	using StressMapTup = std::conditional_t
	<(NeedTgt == NeedTangent::yes),
	std::tuple<StressMap_t, TangentMap_t>,
	std::tuple<StressMap_t>>;
	//! tuple containing a stress and possibly a tangent stiffness value ref
	using Stress_tTup = std::conditional_t<(NeedTgt == NeedTangent::yes),
	std::tuple<Stress_t, Tangent_t>,
	std::tuple<Stress_t>>;


	//! Copy constructor
	iterable_proxy(const iterable_proxy &other) = default;

	//! Move constructor
	iterable_proxy(iterable_proxy &&other) = default;

	//! Destructor
	virtual ~iterable_proxy() = default;

	//! Copy assignment operator
	iterable_proxy& operator=(const iterable_proxy &other) = default;

	//! Move assignment operator
	iterable_proxy& operator=(iterable_proxy &&other) = default;

	/**
	* dereferences into a tuple containing strains, and internal
	* variables, as well as maps to the stress and potentially
	* stiffness maps where to write the response of a pixel
	*/
	class iterator
	{
	public:
	//! type to refer to internal variables owned by a CRTP material
	using InternalReferences = MatTB::ReferenceTuple_t<InternalVariables>;
	//! return type to be unpacked per pixel my the constitutive law
	using value_type =
	std::tuple<std::tuple<Strain_t>, Stress_tTup, InternalReferences>;
	using iterator_category = std::forward_iterator_tag; //!< stl conformance

	//! Default constructor
	iterator() = delete;

	/** Iterator uses the material's internal variables field
	collection to iterate selectively over the global fields
	(such as the transformation gradient F and first
	Piola-Kirchhoff stress P.
	**/
	iterator(const iterable_proxy & it, bool begin = true)
	: it{it}, strain_map{it.strain_field},
	stress_map {it.stress_tup},
	index{begin ? 0:it.material.internal_fields.size()}{}


	//! Copy constructor
	iterator(const iterator &other) = default;

	//! Move constructor
	iterator(iterator &&other) = default;

	//! Destructor
	virtual ~iterator() = default;

	//! Copy assignment operator
	iterator& operator=(const iterator &other) = default;

	//! Move assignment operator
	iterator& operator=(iterator &&other) = default;

	//! pre-increment
	inline iterator & operator++();
	//! dereference
	inline value_type operator*();
	//! inequality
	inline bool operator!=(const iterator & other) const;


	protected:
	const iterable_proxy & it; //!< ref to the proxy
	StrainMap_t strain_map; //!< map onto the global strain field
	//! map onto the global stress field and possibly tangent stiffness
	StressMapTup stress_map;
	size_t index; //!< index or pixel currently referred to
	private:
	};

	//! returns iterator to first pixel if this material
	iterator begin() {return std::move(iterator(*this));}
	//! returns iterator past the last pixel in this material
	iterator end() {return std::move(iterator(*this, false));}

	protected:
	MaterialMuSpectre & material; //!< reference to the proxied material
	const StrainField_t & strain_field; //!< cell's global strain field
	//! references to the global stress field and perhaps tangent stiffness
	StressFieldTup stress_tup;
	//! references to the internal variables
	InternalVariables & internals;

	private:
	};

	/* ---------------------------------------------------------------------- */
	template <class Material, Dim_t DimS, Dim_t DimM>
	template <MatTB::NeedTangent NeedTgt>
	bool
	MaterialMuSpectre<Material, DimS, DimM>::iterable_proxy<NeedTgt>::iterator::
	operator!=(const iterator & other) const {
	return (this->index != other.index);
	}

	/* ---------------------------------------------------------------------- */
	template <class Material, Dim_t DimS, Dim_t DimM>
	template <MatTB::NeedTangent NeedTgt>
	typename MaterialMuSpectre<Material, DimS, DimM>::
	template iterable_proxy<NeedTgt>::
	iterator &
	MaterialMuSpectre<Material, DimS, DimM>::iterable_proxy<NeedTgt>::iterator::
	operator++() {
	this->index++;
	return *this;
	}

	/* ---------------------------------------------------------------------- */
	template <class Material, Dim_t DimS, Dim_t DimM>
	template <MatTB::NeedTangent NeedTgT>
	typename MaterialMuSpectre<Material, DimS, DimM>::
	template iterable_proxy<NeedTgT>::iterator::
	value_type
	MaterialMuSpectre<Material, DimS, DimM>::iterable_proxy<NeedTgT>::iterator::
	operator*() {

	const Ccoord_t<DimS> pixel{
	this->it.material.internal_fields.get_ccoord(this->index)};
	auto && strain = std::make_tuple(this->strain_map[pixel]);

	auto && stresses =
	apply([&pixel] (auto && ... stress_tgt) {
	return std::make_tuple(stress_tgt[pixel]...);},
	this->stress_map);
	auto && internal = this->it.material.get_internals();
	const auto id{this->index};
	auto && internals =
	apply([id] (auto && ... internals_) {
	return InternalReferences{internals_[id]...};},
	internal);
	return std::make_tuple(std::move(strain),
	std::move(stresses),
	std::move(internals));
	}

	} // muSpectre


	#endif /* MATERIAL_MUSPECTRE_BASE_H */

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