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			/**
			* Copyright (©) 2018-2023 EPFL (Ecole Polytechnique Fédérale de Lausanne)
			* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
			*
			* This file is part of Akantu
			*
			* 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_viscoelastic_maxwell.hh"
			#include "solid_mechanics_model.hh"

			namespace akantu {

			/* -------------------------------------------------------------------------- */
			template <Int dim>
			MaterialViscoelasticMaxwell<dim>::MaterialViscoelasticMaxwell(
			SolidMechanicsModel & model, const ID & id)
			: MaterialElastic<dim>(model, id),
			dissipated_energy(this->registerInternal("dissipated_energy", 1)),
			mechanical_work(this->registerInternal("mechanical_work", 1)) {
			this->registerParam("Einf", Einf, Real(1.), _pat_parsable \| _pat_modifiable,
			"Stiffness of the elastic element");
			this->registerParam("previous_dt", previous_dt, Real(0.), _pat_readable,
			"Time step of previous solveStep");
			this->registerParam("Eta", Eta, _pat_parsable \| _pat_modifiable,
			"Viscosity of a Maxwell element");
			this->registerParam("Ev", Ev, _pat_parsable \| _pat_modifiable,
			"Stiffness of a Maxwell element");
			}

			/* -------------------------------------------------------------------------- */
			template <Int dim> void MaterialViscoelasticMaxwell<dim>::initMaterial() {
			AKANTU_DEBUG_IN();

			this->E = Einf + Ev.lpNorm<1>();

			MaterialElastic<dim>::initMaterial();

			AKANTU_DEBUG_ASSERT(this->Eta.size() == this->Ev.size(),
			"Eta and Ev have different dimensions! Please correct.");

			AKANTU_DEBUG_ASSERT(
			!this->finite_deformation,
			"Current material works only in infinitesimal deformations.");

			auto stress_size = dim * dim;
			this->registerInternal("sigma_v", stress_size * this->Ev.size());
			this->registerInternal("epsilon_v", stress_size * this->Ev.size());

			this->sigma_v = this->getSharedPtrInternal("sigma_v");
			this->epsilon_v = this->getSharedPtrInternal("epsilon_v");

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			template <Int dim>
			void MaterialViscoelasticMaxwell<dim>::updateInternalParameters() {
			MaterialElastic<dim>::updateInternalParameters();

			[[maybe_unused]] auto pre_mult = 1 / (1 + this->nu) / (1 - 2 * this->nu);

			[[maybe_unused]] auto Miiii = pre_mult * (1 - this->nu);
			[[maybe_unused]] auto Miijj = pre_mult * this->nu;
			[[maybe_unused]] auto Mijij = pre_mult * 0.5 * (1 - 2 * this->nu);

			[[maybe_unused]] auto Diiii = 1;
			[[maybe_unused]] auto Diijj = -this->nu;
			[[maybe_unused]] auto Dijij = (2 + 2 * this->nu);

			C.zero();
			D.zero();

			if constexpr (dim == 1) {
			C(0, 0) = 1;
			D(0, 0) = 1;
			} else {
			C(0, 0) = Miiii;
			D(0, 0) = Diiii;
			}
			if constexpr (dim >= 2) {
			auto n = voigt_h::size;
			C(1, 1) = Miiii;
			C(0, 1) = Miijj;
			C(1, 0) = Miijj;
			C(n - 1, n - 1) = Mijij;

			D(1, 1) = Diiii;
			D(0, 1) = Diijj;
			D(1, 0) = Diijj;
			D(n - 1, n - 1) = Dijij;
			}

			if constexpr (dim == 3) {
			C(2, 2) = Miiii;
			C(0, 2) = Miijj;
			C(1, 2) = Miijj;
			C(2, 0) = Miijj;
			C(2, 1) = Miijj;
			C(3, 3) = Mijij;
			C(4, 4) = Mijij;

			D(2, 2) = Diiii;
			D(0, 2) = Diijj;
			D(1, 2) = Diijj;
			D(2, 0) = Diijj;
			D(2, 1) = Diijj;
			D(3, 3) = Dijij;
			D(4, 4) = Dijij;
			}
			}

			/* -------------------------------------------------------------------------- */
			template <Int dim>
			void MaterialViscoelasticMaxwell<dim>::computeStress(ElementType el_type,
			GhostType ghost_type) {
			// NOLINTNEXTLINE(bugprone-parent-virtual-call)
			Parent::computeStress(el_type, ghost_type);

			for (auto && args : getArguments(el_type, ghost_type)) {
			computeStressOnQuad(args);
			}
			}

			/* -------------------------------------------------------------------------- */
			template <Int dim>
			template <class Args>
			void MaterialViscoelasticMaxwell<dim>::computeStressOnQuad(Args && args) {
			Real dt = this->getModel().getTimeStep();
			// Wikipedia convention:
			// 2*eps_ij (i!=j) = voigt_eps_I
			// http://en.wikipedia.org/wiki/Voigt_notation
			auto voigt_current_strain = Material::strainToVoigt<dim>(
			Material::gradUToEpsilon<dim>(args["grad_u"_n]));
			auto voigt_previous_strain = Material::strainToVoigt<dim>(
			Material::gradUToEpsilon<dim>(args["previous_grad_u"_n]));

			Vector<Real, voigt_h::size> voigt_stress =
			this->Einf * this->C * voigt_current_strain;

			Vector<Real, voigt_h::size> stress =
			this->C * (voigt_current_strain - voigt_previous_strain);

			for (auto && [Eta, Ev, sigma] : zip(this->Eta, this->Ev, args["sigma_v"_n])) {
			auto lambda = Eta / Ev;
			auto exp_dt_lambda = exp(-dt / lambda);
			Real E_additional{0.};

			if (exp_dt_lambda == 1) {
			E_additional = Ev;
			} else {
			E_additional = (1 - exp_dt_lambda) * Ev * lambda / dt;
			}

			voigt_stress += E_additional * stress +
			exp_dt_lambda * Material::stressToVoigt<dim>(sigma);
			}

			auto && sigma = args["sigma"_n];
			for (Int I = 0; I < voigt_h::size; ++I) {
			auto && [i, j] = voigt_h::vec[I];
			sigma(i, j) = sigma(j, i) =
			voigt_stress(I) + Math::kronecker(i, j) * args["sigma_th"_n];
			}
			}

			/* -------------------------------------------------------------------------- */
			template <Int dim>
			void MaterialViscoelasticMaxwell<dim>::computePotentialEnergy(
			ElementType el_type) {
			for (auto && [args, epot, epsilon_v] :
			zip(getArguments(el_type), this->potential_energy(el_type),
			make_view((*this->epsilon_v)(el_type), dim, dim, Eta.size()))) {
			this->computePotentialEnergyOnQuad(args["grad_u"_n], epot,
			args["sigma_v"_n], epsilon_v);
			}
			}

			/* -------------------------------------------------------------------------- */
			template <Int dim>
			template <typename D1>
			void MaterialViscoelasticMaxwell<dim>::computePotentialEnergyOnQuad(
			const Eigen::MatrixBase<D1> & grad_u, Real & epot,
			Tensor3Proxy<Real> & sigma_v, Tensor3Proxy<Real> & epsilon_v) {
			auto voigt_strain =
			Material::strainToVoigt<dim>(Material::gradUToEpsilon<dim>(grad_u));
			Vector<Real, voigt_h::size> voigt_stress =
			this->Einf * this->C * voigt_strain;

			epot = 0.5 * voigt_stress.dot(voigt_strain);

			for (Int k = 0; k < this->Eta.size(); ++k) {
			epot += sigma_v(k).doubleDot(epsilon_v(k)) / 2.;
			}
			}

			/* -------------------------------------------------------------------------- */
			template <Int dim>
			void MaterialViscoelasticMaxwell<dim>::afterSolveStep(bool converged) {
			Material::afterSolveStep(converged);

			if (not converged) {
			return;
			}

			if (this->update_variable_flag) {
			updateIntVariables();
			}

			for (const auto & el_type : this->getElementFilter().elementTypes(
			_all_dimensions, _not_ghost, _ek_not_defined)) {
			this->updateDissipatedEnergy(el_type);
			}
			}
			/* -------------------------------------------------------------------------- */
			template <Int dim>
			template <typename D1, typename D2>
			void MaterialViscoelasticMaxwell<dim>::updateIntVarOnQuad(
			const Eigen::MatrixBase<D1> & grad_u,
			const Eigen::MatrixBase<D2> & previous_grad_u, Tensor3Proxy<Real> & sigma_v,
			Tensor3Proxy<Real> & epsilon_v) {
			Matrix<Real, dim, dim> grad_delta_u = grad_u - previous_grad_u;

			Real dt = this->getModel().getTimeStep();

			auto voigt_delta_strain =
			Material::strainToVoigt<dim>(Material::gradUToEpsilon<dim>(grad_delta_u));

			for (Idx k = 0; k < this->Eta.size(); ++k) {
			auto lambda = this->Eta(k) / this->Ev(k);
			auto exp_dt_lambda = exp(-dt / lambda);
			Real E_ef_v = this->Ev(k);

			if (exp_dt_lambda != 1) {
			E_ef_v = (1 - exp_dt_lambda) lambda / dt;
			}

			auto voigt_sigma_v = Material::stressToVoigt<dim>(sigma_v(k));

			Vector<Real, voigt_h::size> voigt_epsilon_v =
			exp_dt_lambda * voigt_sigma_v + E_ef_v * this->C * voigt_delta_strain;
			voigt_epsilon_v = 1 / Ev(k) * this->D * voigt_sigma_v;

			for (Int I = 0; I < voigt_h::size; ++I) {
			auto && [i, j] = voigt_h::vec[I];

			sigma_v(i, j, k) = sigma_v(j, i, k) = voigt_sigma_v(I);
			epsilon_v(i, j, k) = epsilon_v(j, i, k) = voigt_epsilon_v(I);
			}
			}
			}
			/* -------------------------------------------------------------------------- */
			template <Int dim>
			void MaterialViscoelasticMaxwell<dim>::computeTangentModuli(
			ElementType /el_type/, Array<Real> & tangent_matrix,
			GhostType /ghost_type/) {
			AKANTU_DEBUG_IN();

			Real dt = this->getModel().getTimeStep();
			Real E_ef = this->Einf;

			for (Int k = 0; k < Eta.size(); ++k) {
			Real lambda = this->Eta(k) / this->Ev(k);
			Real exp_dt_lambda = exp(-dt / lambda);
			if (exp_dt_lambda == 1) {
			E_ef += this->Ev(k);
			} else {
			E_ef += (1 - exp_dt_lambda) * this->Ev(k) * lambda / dt;
			}
			}

			this->previous_dt = dt;

			const auto tangent_size = Material::getTangentStiffnessVoigtSize(dim);
			for (auto && tangent :
			make_view<tangent_size, tangent_size>(tangent_matrix)) {
			this->computeTangentModuliOnQuad(tangent);
			}

			tangent_matrix *= E_ef;

			this->was_stiffness_assembled = true;

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			template <Int dim>
			template <typename D1>
			void MaterialViscoelasticMaxwell<dim>::computeTangentModuliOnQuad(
			Eigen::MatrixBase<D1> & tangent) {

			tangent = C;
			}

			/* -------------------------------------------------------------------------- */
			template <Int dim> void MaterialViscoelasticMaxwell<dim>::updateIntVariables() {

			for (const auto & el_type : this->getElementFilter().elementTypes()) {
			for (auto && [args, epsilon_v] :
			zip(getArguments(el_type),
			make_view((*this->epsilon_v)(el_type), dim, dim, Eta.size()))) {

			updateIntVarOnQuad(args["grad_u"_n], args["previous_grad_u"_n],
			args["sigma_v"_n], epsilon_v);
			}
			}
			}

			/* -------------------------------------------------------------------------- */
			template <Int dim>
			void MaterialViscoelasticMaxwell<dim>::updateDissipatedEnergy(
			ElementType el_type) {
			this->computePotentialEnergy(el_type);

			for (auto && [args, epot, edis, work] :
			zip(getArguments(el_type), this->potential_energy(el_type),
			this->dissipated_energy(el_type), this->mechanical_work(el_type))) {
			updateDissipatedEnergyOnQuad(args["grad_u"_n], args["previous_grad_u"_n],
			args["sigma"_n], args["previous_sigma"_n],
			edis, work, epot);
			}
			}

			/* -------------------------------------------------------------------------- */
			template <Int dim>
			template <typename D1, typename D2, typename D3, typename D4>
			void MaterialViscoelasticMaxwell<dim>::updateDissipatedEnergyOnQuad(
			const Eigen::MatrixBase<D1> & grad_u,
			const Eigen::MatrixBase<D2> & previous_grad_u,
			const Eigen::MatrixBase<D3> & sigma,
			const Eigen::MatrixBase<D4> & previous_sigma, Real & dis_energy,
			Real & mech_work, const Real & pot_energy) {
			Real dt = this->getModel().getTimeStep();

			auto && strain_rate = (grad_u - previous_grad_u) / dt;
			auto && av_stress = (sigma + previous_sigma) / 2.;

			mech_work += av_stress.doubleDot(strain_rate) * dt;

			dis_energy = mech_work - pot_energy;
			}

			/* -------------------------------------------------------------------------- */
			template <Int dim>
			Real MaterialViscoelasticMaxwell<dim>::getDissipatedEnergy() const {
			AKANTU_DEBUG_IN();

			auto & fem = this->getFEEngine();
			Real de = 0.;

			/// integrate the dissipated energy for each type of elements
			for (auto && type : this->getElementFilter().elementTypes(dim, _not_ghost)) {
			de += fem.integrate(this->dissipated_energy(type, _not_ghost), type,
			_not_ghost, this->getElementFilter(type, _not_ghost));
			}

			AKANTU_DEBUG_OUT();
			return de;
			}

			/* -------------------------------------------------------------------------- */
			template <Int dim>
			Real MaterialViscoelasticMaxwell<dim>::getDissipatedEnergy(
			const Element & element) const {
			auto & fem = this->getFEEngine();
			auto nb_quadrature_points = fem.getNbIntegrationPoints(element.type);
			auto it =
			make_view(this->dissipated_energy(element.type), nb_quadrature_points)
			.begin();
			auto mat_element = element;
			mat_element.element = this->getElementFilter()(element);

			return fem.integrate(it[element.element], mat_element);
			}

			/* -------------------------------------------------------------------------- */
			template <Int dim>
			Real MaterialViscoelasticMaxwell<dim>::getMechanicalWork() const {
			auto & fem = this->getFEEngine();
			Real mw = 0.;

			/// integrate the dissipated energy for each type of elements
			for (auto && type : this->getElementFilter().elementTypes(dim)) {
			mw += fem.integrate(this->mechanical_work(type), type, _not_ghost,
			this->getElementFilter(type, _not_ghost));
			}

			return mw;
			}

			/* -------------------------------------------------------------------------- */
			template <Int dim>
			Real MaterialViscoelasticMaxwell<dim>::getMechanicalWork(
			const Element & element) const {
			auto & fem = this->getFEEngine();
			auto nb_quadrature_points = fem.getNbIntegrationPoints(element.type);
			auto it = make_view(this->mechanical_work(element.type), nb_quadrature_points)
			.begin();

			auto mat_element = element;
			mat_element.element = this->getElementFilter()(element);

			return fem.integrate(it[element.element], mat_element);
			}

			/* -------------------------------------------------------------------------- */
			template <Int dim>
			Real MaterialViscoelasticMaxwell<dim>::getPotentialEnergy() const {
			AKANTU_DEBUG_IN();

			auto & fem = this->getFEEngine();
			Real epot = 0.;

			/// integrate the dissipated energy for each type of elements
			for (auto && type : this->getElementFilter().elementTypes(dim, _not_ghost)) {
			epot += fem.integrate(this->potential_energy(type, _not_ghost), type,
			_not_ghost, this->getElementFilter(type, _not_ghost));
			}

			AKANTU_DEBUG_OUT();
			return epot;
			}

			/* -------------------------------------------------------------------------- */
			template <Int dim>
			Real MaterialViscoelasticMaxwell<dim>::getPotentialEnergy(
			const Element & element) const {
			AKANTU_DEBUG_IN();

			auto & fem = this->getFEEngine();
			auto nb_quadrature_points = fem.getNbIntegrationPoints(element.type);
			auto it =
			make_view(this->potential_energy(element.type), nb_quadrature_points)
			.begin();
			auto mat_element = element;
			mat_element.element = this->getElementFilter()(element);

			AKANTU_DEBUG_OUT();
			return fem.integrate(it[element.element], mat_element);
			}

			/* -------------------------------------------------------------------------- */
			template <Int dim>
			Real MaterialViscoelasticMaxwell<dim>::getEnergy(const std::string & type) {
			if (type == "dissipated") {
			return getDissipatedEnergy();
			}
			if (type == "potential") {
			return getPotentialEnergy();
			}
			if (type == "work") {
			return getMechanicalWork();
			}
			return MaterialElastic<dim>::getEnergy(type);
			}

			/* -------------------------------------------------------------------------- */
			template <Int dim>
			Real MaterialViscoelasticMaxwell<dim>::getEnergy(const std::string & energy_id,
			const Element & element) {
			if (energy_id == "dissipated") {
			return getDissipatedEnergy(element);
			}
			if (energy_id == "potential") {
			return getPotentialEnergy(element);
			}
			if (energy_id == "work") {
			return getMechanicalWork(element);
			}
			return MaterialElastic<dim>::getEnergy(energy_id, element);
			}

			/* -------------------------------------------------------------------------- */
			template <Int dim>
			void MaterialViscoelasticMaxwell<dim>::forceUpdateVariable() {
			update_variable_flag = true;
			}

			/* -------------------------------------------------------------------------- */
			template <Int dim>
			void MaterialViscoelasticMaxwell<dim>::forceNotUpdateVariable() {
			update_variable_flag = false;
			}

			/* -------------------------------------------------------------------------- */
			const bool material_is_allocated_viscoelastic_maxwell [[maybe_unused]] =
			instantiateMaterial<MaterialViscoelasticMaxwell>("viscoelastic_maxwell");

			} // namespace akantu

rAKA/src/model/solid_mechanics/materials/material_viscoelastic/material_viscoelastic_maxwell.cc1f632f71ba75bugfixes/documentation

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rAKA/src/model/solid_mechanics/materials/material_viscoelastic/material_viscoelastic_maxwell.cc
1f632f71ba75bugfixes/documentation

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