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material_cohesive.cc
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			/**
			* @file material_cohesive.cc
			*
			* @author Mauro Corrado <mauro.corrado@epfl.ch>
			* @author Nicolas Richart <nicolas.richart@epfl.ch>
			* @author Seyedeh Mohadeseh Taheri Mousavi <mohadeseh.taherimousavi@epfl.ch>
			* @author Marco Vocialta <marco.vocialta@epfl.ch>
			*
			* @date creation: Wed Feb 22 2012
			* @date last modification: Mon Feb 19 2018
			*
			* @brief Specialization of the material class for cohesive elements
			*
			*
			* 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 "material_cohesive.hh"
			#include "aka_random_generator.hh"
			#include "dof_synchronizer.hh"
			#include "fe_engine_template.hh"
			#include "integrator_gauss.hh"
			#include "shape_cohesive.hh"
			#include "solid_mechanics_model_cohesive.hh"
			#include "sparse_matrix.hh"
			/* -------------------------------------------------------------------------- */

			namespace akantu {

			/* -------------------------------------------------------------------------- */
			MaterialCohesive::MaterialCohesive(SolidMechanicsModel & model, const ID & id)
			: Material(model, id),
			facet_filter("facet_filter", id, this->getMemoryID()),
			fem_cohesive(
			model.getFEEngineClass<MyFEEngineCohesiveType>("CohesiveFEEngine")),
			reversible_energy("reversible_energy", *this),
			total_energy("total_energy", this), opening("opening", this),
			tractions("tractions", *this),
			contact_tractions("contact_tractions", *this),
			contact_opening("contact_opening", this), delta_max("delta max", this),
			use_previous_delta_max(false), use_previous_opening(false),
			damage("damage", this), sigma_c("sigma_c", this),
			normal(0, spatial_dimension, "normal") {

			AKANTU_DEBUG_IN();

			this->model = dynamic_cast<SolidMechanicsModelCohesive *>(&model);

			this->registerParam("sigma_c", sigma_c, _pat_parsable \| _pat_readable,
			"Critical stress");
			this->registerParam("delta_c", delta_c, Real(0.),
			_pat_parsable \| _pat_readable, "Critical displacement");

			this->element_filter.initialize(this->model->getMesh(),
			_spatial_dimension = spatial_dimension,
			_element_kind = _ek_cohesive);
			// this->model->getMesh().initElementTypeMapArray(
			// this->element_filter, 1, spatial_dimension, false, _ek_cohesive);

			if (this->model->getIsExtrinsic())
			this->facet_filter.initialize(this->model->getMeshFacets(),
			_spatial_dimension = spatial_dimension - 1,
			_element_kind = _ek_regular);
			// this->model->getMeshFacets().initElementTypeMapArray(facet_filter, 1,
			// spatial_dimension -
			// 1);

			this->reversible_energy.initialize(1);
			this->total_energy.initialize(1);

			this->tractions.initialize(spatial_dimension);
			this->tractions.initializeHistory();

			this->contact_tractions.initialize(spatial_dimension);
			this->contact_opening.initialize(spatial_dimension);

			this->opening.initialize(spatial_dimension);
			this->opening.initializeHistory();

			this->delta_max.initialize(1);
			this->damage.initialize(1);

			if (this->model->getIsExtrinsic())
			this->sigma_c.initialize(1);

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			MaterialCohesive::~MaterialCohesive() = default;

			/* -------------------------------------------------------------------------- */
			void MaterialCohesive::initMaterial() {
			AKANTU_DEBUG_IN();
			Material::initMaterial();
			if (this->use_previous_delta_max)
			this->delta_max.initializeHistory();
			if (this->use_previous_opening)
			this->opening.initializeHistory();
			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void MaterialCohesive::assembleInternalForces(GhostType ghost_type) {
			AKANTU_DEBUG_IN();

			#if defined(AKANTU_DEBUG_TOOLS)
			debug::element_manager.printData(debug::_dm_material_cohesive,
			"Cohesive Tractions", tractions);
			#endif

			auto & internal_force = const_cast<Array<Real> &>(model->getInternalForce());

			for (auto type : element_filter.elementTypes(spatial_dimension, ghost_type,
			_ek_cohesive)) {
			auto & elem_filter = element_filter(type, ghost_type);
			UInt nb_element = elem_filter.size();
			if (nb_element == 0)
			continue;

			const auto & shapes = fem_cohesive.getShapes(type, ghost_type);
			auto & traction = tractions(type, ghost_type);
			auto & contact_traction = contact_tractions(type, ghost_type);

			UInt size_of_shapes = shapes.getNbComponent();
			UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
			UInt nb_quadrature_points =
			fem_cohesive.getNbIntegrationPoints(type, ghost_type);

			/// compute @f$t_i N_a@f$

			Array<Real> * traction_cpy = new Array<Real>(
			nb_element * nb_quadrature_points, spatial_dimension * size_of_shapes);

			auto traction_it = traction.begin(spatial_dimension, 1);
			auto contact_traction_it = contact_traction.begin(spatial_dimension, 1);
			auto shapes_filtered_begin = shapes.begin(1, size_of_shapes);
			auto traction_cpy_it =
			traction_cpy->begin(spatial_dimension, size_of_shapes);

			Matrix<Real> traction_tmp(spatial_dimension, 1);

			for (UInt el = 0; el < nb_element; ++el) {

			UInt current_quad = elem_filter(el) * nb_quadrature_points;

			for (UInt q = 0; q < nb_quadrature_points; ++q, ++traction_it,
			++contact_traction_it, ++current_quad, ++traction_cpy_it) {

			const Matrix<Real> & shapes_filtered =
			shapes_filtered_begin[current_quad];

			traction_tmp.copy(*traction_it);
			traction_tmp += *contact_traction_it;

			traction_cpy_it->mul<false, false>(traction_tmp, shapes_filtered);
			}
			}

			/**
			* compute @f$\int t \cdot N\, dS@f$ by @f$ \sum_q \mathbf{N}^t
			* \mathbf{t}_q \overline w_q J_q@f$
			*/
			Array<Real> * partial_int_t_N = new Array<Real>(
			nb_element, spatial_dimension * size_of_shapes, "int_t_N");

			fem_cohesive.integrate(traction_cpy, partial_int_t_N,
			spatial_dimension * size_of_shapes, type, ghost_type,
			elem_filter);

			delete traction_cpy;

			Array<Real> * int_t_N = new Array<Real>(
			nb_element, 2 * spatial_dimension * size_of_shapes, "int_t_N");

			Real * int_t_N_val = int_t_N->storage();
			Real * partial_int_t_N_val = partial_int_t_N->storage();
			for (UInt el = 0; el < nb_element; ++el) {
			std::copy_n(partial_int_t_N_val, size_of_shapes * spatial_dimension,
			int_t_N_val);
			std::copy_n(partial_int_t_N_val, size_of_shapes * spatial_dimension,
			int_t_N_val + size_of_shapes * spatial_dimension);

			for (UInt n = 0; n < size_of_shapes * spatial_dimension; ++n)
			int_t_N_val[n] *= -1.;

			int_t_N_val += nb_nodes_per_element * spatial_dimension;
			partial_int_t_N_val += size_of_shapes * spatial_dimension;
			}

			delete partial_int_t_N;

			/// assemble
			model->getDOFManager().assembleElementalArrayLocalArray(
			*int_t_N, internal_force, type, ghost_type, 1, elem_filter);

			delete int_t_N;
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void MaterialCohesive::assembleStiffnessMatrix(GhostType ghost_type) {

			AKANTU_DEBUG_IN();

			for (auto type : element_filter.elementTypes(spatial_dimension, ghost_type,
			_ek_cohesive)) {
			UInt nb_quadrature_points =
			fem_cohesive.getNbIntegrationPoints(type, ghost_type);
			UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);

			const Array<Real> & shapes = fem_cohesive.getShapes(type, ghost_type);
			Array<UInt> & elem_filter = element_filter(type, ghost_type);

			UInt nb_element = elem_filter.size();

			if (!nb_element)
			continue;

			UInt size_of_shapes = shapes.getNbComponent();

			Array<Real> * shapes_filtered = new Array<Real>(
			nb_element * nb_quadrature_points, size_of_shapes, "filtered shapes");

			Real * shapes_filtered_val = shapes_filtered->storage();
			UInt * elem_filter_val = elem_filter.storage();

			for (UInt el = 0; el < nb_element; ++el) {
			auto shapes_val = shapes.storage() + elem_filter_val[el] *
			size_of_shapes *
			nb_quadrature_points;
			memcpy(shapes_filtered_val, shapes_val,
			size_of_shapes * nb_quadrature_points * sizeof(Real));
			shapes_filtered_val += size_of_shapes * nb_quadrature_points;
			}

			Matrix<Real> A(spatial_dimension * size_of_shapes,
			spatial_dimension * nb_nodes_per_element);

			for (UInt i = 0; i < spatial_dimension * size_of_shapes; ++i) {
			A(i, i) = 1;
			A(i, i + spatial_dimension * size_of_shapes) = -1;
			}

			/// get the tangent matrix @f$\frac{\partial{(t/\delta)}}{\partial{\delta}}
			/// @f$
			Array<Real> * tangent_stiffness_matrix = new Array<Real>(
			nb_element * nb_quadrature_points,
			spatial_dimension * spatial_dimension, "tangent_stiffness_matrix");

			// Array<Real> * normal = new Array<Real>(nb_element *
			// nb_quadrature_points, spatial_dimension, "normal");
			normal.resize(nb_quadrature_points);

			computeNormal(model->getCurrentPosition(), normal, type, ghost_type);

			/// compute openings @f$\mathbf{\delta}@f$
			// computeOpening(model->getDisplacement(), opening(type, ghost_type), type,
			// ghost_type);

			tangent_stiffness_matrix->clear();

			computeTangentTraction(type, *tangent_stiffness_matrix, normal, ghost_type);

			// delete normal;

			UInt size_at_nt_d_n_a = spatial_dimension * nb_nodes_per_element *
			spatial_dimension * nb_nodes_per_element;
			Array<Real> * at_nt_d_n_a = new Array<Real>(
			nb_element * nb_quadrature_points, size_at_nt_d_n_a, "A^tN^tDNA");

			Array<Real>::iterator<Vector<Real>> shapes_filt_it =
			shapes_filtered->begin(size_of_shapes);

			Array<Real>::matrix_iterator D_it =
			tangent_stiffness_matrix->begin(spatial_dimension, spatial_dimension);

			Array<Real>::matrix_iterator At_Nt_D_N_A_it =
			at_nt_d_n_a->begin(spatial_dimension * nb_nodes_per_element,
			spatial_dimension * nb_nodes_per_element);

			Array<Real>::matrix_iterator At_Nt_D_N_A_end =
			at_nt_d_n_a->end(spatial_dimension * nb_nodes_per_element,
			spatial_dimension * nb_nodes_per_element);

			Matrix<Real> N(spatial_dimension, spatial_dimension * size_of_shapes);
			Matrix<Real> N_A(spatial_dimension,
			spatial_dimension * nb_nodes_per_element);
			Matrix<Real> D_N_A(spatial_dimension,
			spatial_dimension * nb_nodes_per_element);

			for (; At_Nt_D_N_A_it != At_Nt_D_N_A_end;
			++At_Nt_D_N_A_it, ++D_it, ++shapes_filt_it) {
			N.clear();
			/**
			* store the shapes in voigt notations matrix @f$\mathbf{N} =
			* \begin{array}{cccccc} N_0(\xi) & 0 & N_1(\xi) &0 & N_2(\xi) & 0 \\
			* 0 & * N_0(\xi)& 0 &N_1(\xi)& 0 & N_2(\xi) \end{array} @f$
			**/
			for (UInt i = 0; i < spatial_dimension; ++i)
			for (UInt n = 0; n < size_of_shapes; ++n)
			N(i, i + spatial_dimension * n) = (*shapes_filt_it)(n);

			/**
			* compute stiffness matrix @f$ \mathbf{K} = \delta \mathbf{U}^T
			* \int_{\Gamma_c} {\mathbf{P}^t \frac{\partial{\mathbf{t}}}
			*{\partial{\delta}}
			* \mathbf{P} d\Gamma \Delta \mathbf{U}} @f$
			**/
			N_A.mul<false, false>(N, A);
			D_N_A.mul<false, false>(*D_it, N_A);
			(*At_Nt_D_N_A_it).mul<true, false>(D_N_A, N_A);
			}

			delete tangent_stiffness_matrix;
			delete shapes_filtered;

			Array<Real> * K_e = new Array<Real>(nb_element, size_at_nt_d_n_a, "K_e");

			fem_cohesive.integrate(at_nt_d_n_a, K_e, size_at_nt_d_n_a, type,
			ghost_type, elem_filter);

			delete at_nt_d_n_a;

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

			delete K_e;
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- *
			* Compute traction from displacements
			*
			* @param[in] ghost_type compute the residual for _ghost or _not_ghost element
			*/
			void MaterialCohesive::computeTraction(GhostType ghost_type) {
			AKANTU_DEBUG_IN();

			#if defined(AKANTU_DEBUG_TOOLS)
			debug::element_manager.printData(debug::_dm_material_cohesive,
			"Cohesive Openings", opening);
			#endif

			for (auto & type : element_filter.elementTypes(spatial_dimension, ghost_type,
			_ek_cohesive)) {
			Array<UInt> & elem_filter = element_filter(type, ghost_type);

			UInt nb_element = elem_filter.size();
			if (nb_element == 0)
			continue;

			UInt nb_quadrature_points =
			nb_element * fem_cohesive.getNbIntegrationPoints(type, ghost_type);

			normal.resize(nb_quadrature_points);

			/// compute normals @f$\mathbf{n}@f$
			computeNormal(model->getCurrentPosition(), normal, type, ghost_type);

			/// compute openings @f$\mathbf{\delta}@f$
			computeOpening(model->getDisplacement(), opening(type, ghost_type), type,
			ghost_type);

			/// compute traction @f$\mathbf{t}@f$
			computeTraction(normal, type, ghost_type);
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void MaterialCohesive::computeNormal(const Array<Real> & position,
			Array<Real> & normal, ElementType type,
			GhostType ghost_type) {
			AKANTU_DEBUG_IN();

			auto & fem_cohesive =
			this->model->getFEEngineClass<MyFEEngineCohesiveType>("CohesiveFEEngine");

			normal.clear();

			#define COMPUTE_NORMAL(type) \
			fem_cohesive.getShapeFunctions() \
			.computeNormalsOnIntegrationPoints<type, CohesiveReduceFunctionMean>( \
			position, normal, ghost_type, element_filter(type, ghost_type));

			AKANTU_BOOST_COHESIVE_ELEMENT_SWITCH(COMPUTE_NORMAL);
			#undef COMPUTE_NORMAL

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void MaterialCohesive::computeOpening(const Array<Real> & displacement,
			Array<Real> & opening, ElementType type,
			GhostType ghost_type) {
			AKANTU_DEBUG_IN();

			auto & fem_cohesive =
			this->model->getFEEngineClass<MyFEEngineCohesiveType>("CohesiveFEEngine");

			#define COMPUTE_OPENING(type) \
			fem_cohesive.getShapeFunctions() \
			.interpolateOnIntegrationPoints<type, CohesiveReduceFunctionOpening>( \
			displacement, opening, spatial_dimension, ghost_type, \
			element_filter(type, ghost_type));

			AKANTU_BOOST_COHESIVE_ELEMENT_SWITCH(COMPUTE_OPENING);
			#undef COMPUTE_OPENING

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void MaterialCohesive::updateEnergies(ElementType type) {
			AKANTU_DEBUG_IN();

			if (Mesh::getKind(type) != _ek_cohesive)
			return;

			Vector<Real> b(spatial_dimension);
			Vector<Real> h(spatial_dimension);
			auto erev = reversible_energy(type).begin();
			auto etot = total_energy(type).begin();
			auto traction_it = tractions(type).begin(spatial_dimension);
			auto traction_old_it = tractions.previous(type).begin(spatial_dimension);
			auto opening_it = opening(type).begin(spatial_dimension);
			auto opening_old_it = opening.previous(type).begin(spatial_dimension);

			auto traction_end = tractions(type).end(spatial_dimension);

			/// loop on each quadrature point
			for (; traction_it != traction_end; ++traction_it, ++traction_old_it,
			++opening_it, ++opening_old_it, ++erev,
			++etot) {
			/// trapezoidal integration
			b = *opening_it;
			b -= *opening_old_it;

			h = *traction_old_it;
			h += *traction_it;

			etot += .5 b.dot(h);
			erev = .5 traction_it->dot(*opening_it);
			}

			/// update old values

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			Real MaterialCohesive::getReversibleEnergy() {
			AKANTU_DEBUG_IN();
			Real erev = 0.;

			/// integrate reversible energy for each type of elements
			for (auto & type : element_filter.elementTypes(spatial_dimension, _not_ghost,
			_ek_cohesive)) {
			erev +=
			fem_cohesive.integrate(reversible_energy(type, _not_ghost), type,
			_not_ghost, element_filter(type, _not_ghost));
			}

			AKANTU_DEBUG_OUT();
			return erev;
			}

			/* -------------------------------------------------------------------------- */
			Real MaterialCohesive::getDissipatedEnergy() {
			AKANTU_DEBUG_IN();
			Real edis = 0.;

			/// integrate dissipated energy for each type of elements
			for (auto & type : element_filter.elementTypes(spatial_dimension, _not_ghost,
			_ek_cohesive)) {
			Array<Real> dissipated_energy(total_energy(type, _not_ghost));
			dissipated_energy -= reversible_energy(type, _not_ghost);
			edis += fem_cohesive.integrate(dissipated_energy, type, _not_ghost,
			element_filter(type, _not_ghost));
			}

			AKANTU_DEBUG_OUT();
			return edis;
			}

			/* -------------------------------------------------------------------------- */
			Real MaterialCohesive::getContactEnergy() {
			AKANTU_DEBUG_IN();
			Real econ = 0.;

			/// integrate contact energy for each type of elements
			for (auto & type : element_filter.elementTypes(spatial_dimension, _not_ghost,
			_ek_cohesive)) {

			auto & el_filter = element_filter(type, _not_ghost);
			UInt nb_quad_per_el = fem_cohesive.getNbIntegrationPoints(type, _not_ghost);
			UInt nb_quad_points = el_filter.size() * nb_quad_per_el;
			Array<Real> contact_energy(nb_quad_points);

			auto contact_traction_it =
			contact_tractions(type, _not_ghost).begin(spatial_dimension);
			auto contact_opening_it =
			contact_opening(type, _not_ghost).begin(spatial_dimension);

			/// loop on each quadrature point
			for (UInt q = 0; q < nb_quad_points;
			++contact_traction_it, ++contact_opening_it, ++q) {

			contact_energy(q) = .5 * contact_traction_it->dot(*contact_opening_it);
			}

			econ += fem_cohesive.integrate(contact_energy, type, _not_ghost, el_filter);
			}

			AKANTU_DEBUG_OUT();
			return econ;
			}

			/* -------------------------------------------------------------------------- */
			Real MaterialCohesive::getEnergy(const std::string & type) {
			AKANTU_DEBUG_IN();

			if (type == "reversible")
			return getReversibleEnergy();
			else if (type == "dissipated")
			return getDissipatedEnergy();
			else if (type == "cohesive contact")
			return getContactEnergy();

			AKANTU_DEBUG_OUT();
			return 0.;
			}

			/* -------------------------------------------------------------------------- */
			} // namespace akantu

rAKA/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/material_cohesive.ccf2b54f6e0331features/cohesive_clust…

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rAKA/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/material_cohesive.cc
f2b54f6e0331features/cohesive_clust…

material_cohesive.cc
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