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solid_mechanics_model_cohesive.cc
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			/**
			* @file solid_mechanics_model_cohesive.cc
			*
			* @author Marco Vocialta <marco.vocialta@epfl.ch>
			* @author Nicolas Richart <nicolas.richart@epfl.ch>
			*
			* @date creation: Tue May 08 2012
			* @date last modification: Fri Sep 05 2014
			*
			* @brief Solid mechanics model for cohesive elements
			*
			* @section LICENSE
			*
			* Copyright (©) 2014 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 <algorithm>
			#include "shape_cohesive.hh"
			#include "solid_mechanics_model_cohesive.hh"
			#include "dumpable_inline_impl.hh"
			#include "material_cohesive.hh"

			#ifdef AKANTU_USE_IOHELPER
			# include "dumper_paraview.hh"
			#endif

			/* -------------------------------------------------------------------------- */

			__BEGIN_AKANTU__

			const SolidMechanicsModelCohesiveOptions default_solid_mechanics_model_cohesive_options(_explicit_lumped_mass,
			false,
			false);

			/* -------------------------------------------------------------------------- */

			SolidMechanicsModelCohesive::SolidMechanicsModelCohesive(Mesh & mesh,
			UInt dim,
			const ID & id,
			const MemoryID & memory_id) :
			SolidMechanicsModel(mesh, dim, id, memory_id),
			tangents("tangents", id),
			facet_stress("facet_stress", id),
			facet_material("facet_material", id) {
			AKANTU_DEBUG_IN();

			inserter = NULL;

			#if defined(AKANTU_PARALLEL_COHESIVE_ELEMENT)
			facet_synchronizer = NULL;
			facet_stress_synchronizer = NULL;
			cohesive_distributed_synchronizer = NULL;
			global_connectivity = NULL;
			#endif

			delete material_selector;
			material_selector = new DefaultMaterialCohesiveSelector(*this);

			this->registerEventHandler(*this);

			#if defined(AKANTU_USE_IOHELPER)
			this->mesh.registerDumper<DumperParaview>("cohesive elements", id);
			this->mesh.addDumpMeshToDumper("cohesive elements",
			mesh, spatial_dimension, _not_ghost, _ek_cohesive);
			#endif

			AKANTU_DEBUG_OUT();
			}


			/* -------------------------------------------------------------------------- */
			SolidMechanicsModelCohesive::~SolidMechanicsModelCohesive() {
			AKANTU_DEBUG_IN();

			delete inserter;

			#if defined(AKANTU_PARALLEL_COHESIVE_ELEMENT)
			delete cohesive_distributed_synchronizer;
			delete facet_synchronizer;
			delete facet_stress_synchronizer;
			#endif

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void SolidMechanicsModelCohesive::setTimeStep(Real time_step) {
			SolidMechanicsModel::setTimeStep(time_step);

			#if defined(AKANTU_USE_IOHELPER)
			this->mesh.getDumper("cohesive elements").setTimeStep(time_step);
			#endif
			}

			/* -------------------------------------------------------------------------- */
			void SolidMechanicsModelCohesive::initFull(const ModelOptions & options) {
			AKANTU_DEBUG_IN();

			const SolidMechanicsModelCohesiveOptions & smmc_options =
			dynamic_cast<const SolidMechanicsModelCohesiveOptions &>(options);

			this->is_extrinsic = smmc_options.extrinsic;

			if (!inserter)
			inserter = new CohesiveElementInserter(mesh, is_extrinsic, synch_parallel,
			id+":cohesive_element_inserter");

			SolidMechanicsModel::initFull(options);

			#if defined(AKANTU_PARALLEL_COHESIVE_ELEMENT)
			if (facet_synchronizer != NULL)
			inserter->initParallel(facet_synchronizer);
			#endif

			if (is_extrinsic)
			initAutomaticInsertion();

			AKANTU_DEBUG_OUT();
			}


			/* -------------------------------------------------------------------------- */
			void SolidMechanicsModelCohesive::initMaterials() {
			AKANTU_DEBUG_IN();

			// make sure the material are instantiated
			if(!are_materials_instantiated) instantiateMaterials();

			/// find the first cohesive material
			UInt cohesive_index = 0;

			while ((dynamic_cast<MaterialCohesive *>(materials[cohesive_index]) == NULL)
			&& cohesive_index <= materials.size())
			++cohesive_index;

			AKANTU_DEBUG_ASSERT(cohesive_index != materials.size(),
			"No cohesive materials in the material input file");

			material_selector->setFallback(cohesive_index);

			// set the facet information in the material in case of dynamic insertion
			if (is_extrinsic) {
			const Mesh & mesh_facets = inserter->getMeshFacets();
			mesh_facets.initElementTypeMapArray(facet_material, 1, spatial_dimension - 1);

			Element element;
			for (ghost_type_t::iterator gt = ghost_type_t::begin(); gt != ghost_type_t::end(); ++gt) {
			element.ghost_type = *gt;
			Mesh::type_iterator first = mesh_facets.firstType(spatial_dimension - 1, *gt);
			Mesh::type_iterator last = mesh_facets.lastType(spatial_dimension - 1, *gt);
			for(;first != last; ++first) {
			element.type = *first;
			Array<UInt> & f_material = facet_material(first, gt);
			UInt nb_element = mesh_facets.getNbElement(first, gt);
			f_material.resize(nb_element);
			f_material.set(cohesive_index);
			for (UInt el = 0; el < nb_element; ++el) {
			element.element = el;
			UInt mat_index = (*material_selector)(element);
			f_material(el) = mat_index;
			MaterialCohesive & mat = dynamic_cast<MaterialCohesive &>(*materials[mat_index]);
			mat.addFacet(element);
			}
			}
			}
			} else {
			for (ghost_type_t::iterator gt = ghost_type_t::begin(); gt != ghost_type_t::end(); ++gt) {
			Mesh::type_iterator first = mesh.firstType(spatial_dimension, *gt, _ek_cohesive);
			Mesh::type_iterator last = mesh.lastType(spatial_dimension, *gt, _ek_cohesive);

			for(;first != last; ++first) {
			Array<UInt> & mat_indexes = this->material_index(first, gt);
			Array<UInt> & mat_loc_num = this->material_local_numbering(first, gt);
			mat_indexes.set(cohesive_index);
			mat_loc_num.clear();
			}
			}
			}

			SolidMechanicsModel::initMaterials();

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			/**
			* Initialize the model,basically it pre-compute the shapes, shapes derivatives
			* and jacobian
			*
			*/
			void SolidMechanicsModelCohesive::initModel() {
			AKANTU_DEBUG_IN();

			SolidMechanicsModel::initModel();

			registerFEEngineObject<MyFEEngineCohesiveType>("CohesiveFEEngine", mesh, spatial_dimension);

			/// add cohesive type connectivity
			ElementType type = _not_defined;

			for (ghost_type_t::iterator gt = ghost_type_t::begin();
			gt != ghost_type_t::end(); ++gt) {

			GhostType type_ghost = *gt;

			Mesh::type_iterator it = mesh.firstType(spatial_dimension, type_ghost);
			Mesh::type_iterator last = mesh.lastType(spatial_dimension, type_ghost);

			for (; it != last; ++it) {
			const Array<UInt> & connectivity = mesh.getConnectivity(*it, type_ghost);
			if (connectivity.getSize() != 0) {
			type = *it;
			ElementType type_facet = Mesh::getFacetType(type);
			ElementType type_cohesive = FEEngine::getCohesiveElementType(type_facet);
			mesh.addConnectivityType(type_cohesive, type_ghost);
			}
			}
			}

			AKANTU_DEBUG_ASSERT(type != _not_defined, "No elements in the mesh");

			getFEEngine("CohesiveFEEngine").initShapeFunctions(_not_ghost);
			getFEEngine("CohesiveFEEngine").initShapeFunctions(_ghost);

			registerFEEngineObject<MyFEEngineType>("FacetsFEEngine",
			mesh.getMeshFacets(),
			spatial_dimension - 1);

			if (is_extrinsic) {
			getFEEngine("FacetsFEEngine").initShapeFunctions(_not_ghost);
			getFEEngine("FacetsFEEngine").initShapeFunctions(_ghost);
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void SolidMechanicsModelCohesive::limitInsertion(BC::Axis axis,
			Real first_limit,
			Real second_limit) {
			AKANTU_DEBUG_IN();
			inserter->setLimit(axis, first_limit, second_limit);
			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void SolidMechanicsModelCohesive::insertIntrinsicElements() {
			AKANTU_DEBUG_IN();
			inserter->insertIntrinsicElements();
			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void SolidMechanicsModelCohesive::initAutomaticInsertion() {
			AKANTU_DEBUG_IN();

			#if defined(AKANTU_PARALLEL_COHESIVE_ELEMENT)
			if (facet_stress_synchronizer != NULL) {
			DataAccessor * data_accessor = this;
			const ElementTypeMapArray<UInt> & rank_to_element = synch_parallel->getPrankToElement();

			facet_stress_synchronizer->updateFacetStressSynchronizer(*inserter,
			rank_to_element,
			*data_accessor);
			}
			#endif

			inserter->getMeshFacets().initElementTypeMapArray(facet_stress,
			2 * spatial_dimension * spatial_dimension,
			spatial_dimension - 1);

			resizeFacetStress();

			/// compute normals on facets
			computeNormals();

			initStressInterpolation();
			}

			/* -------------------------------------------------------------------------- */
			void SolidMechanicsModelCohesive::updateAutomaticInsertion() {
			AKANTU_DEBUG_IN();

			inserter->limitCheckFacets();

			#if defined(AKANTU_PARALLEL_COHESIVE_ELEMENT)
			if (facet_stress_synchronizer != NULL) {
			DataAccessor * data_accessor = this;
			const ElementTypeMapArray<UInt> & rank_to_element = synch_parallel->getPrankToElement();

			facet_stress_synchronizer->updateFacetStressSynchronizer(*inserter,
			rank_to_element,
			*data_accessor);
			}
			#endif

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void SolidMechanicsModelCohesive::initStressInterpolation() {
			Mesh & mesh_facets = inserter->getMeshFacets();

			/// compute quadrature points coordinates on facets
			Array<Real> & position = mesh.getNodes();

			ElementTypeMapArray<Real> quad_facets("quad_facets", id);
			mesh_facets.initElementTypeMapArray(quad_facets,
			spatial_dimension, spatial_dimension - 1);

			getFEEngine("FacetsFEEngine").interpolateOnQuadraturePoints(position, quad_facets);

			/// compute elements quadrature point positions and build
			/// element-facet quadrature points data structure
			ElementTypeMapArray<Real> elements_quad_facets("elements_quad_facets", id);

			mesh.initElementTypeMapArray(elements_quad_facets,
			spatial_dimension,
			spatial_dimension);

			for (ghost_type_t::iterator gt = ghost_type_t::begin();
			gt != ghost_type_t::end(); ++gt) {

			GhostType elem_gt = *gt;

			Mesh::type_iterator it = mesh.firstType(spatial_dimension, elem_gt);
			Mesh::type_iterator last = mesh.lastType(spatial_dimension, elem_gt);

			for (; it != last; ++it) {
			ElementType type = *it;
			UInt nb_element = mesh.getNbElement(type, elem_gt);
			if (nb_element == 0) continue;

			/// compute elements' quadrature points and list of facet
			/// quadrature points positions by element
			Array<Element> & facet_to_element = mesh_facets.getSubelementToElement(type,
			elem_gt);
			UInt nb_facet_per_elem = facet_to_element.getNbComponent();

			Array<Real> & el_q_facet = elements_quad_facets(type, elem_gt);

			ElementType facet_type = Mesh::getFacetType(type);

			UInt nb_quad_per_facet =
			getFEEngine("FacetsFEEngine").getNbQuadraturePoints(facet_type);

			el_q_facet.resize(nb_element * nb_facet_per_elem * nb_quad_per_facet);

			for (UInt el = 0; el < nb_element; ++el) {
			for (UInt f = 0; f < nb_facet_per_elem; ++f) {
			Element global_facet_elem = facet_to_element(el, f);
			UInt global_facet = global_facet_elem.element;
			GhostType facet_gt = global_facet_elem.ghost_type;
			const Array<Real> & quad_f = quad_facets(facet_type, facet_gt);

			for (UInt q = 0; q < nb_quad_per_facet; ++q) {
			for (UInt s = 0; s < spatial_dimension; ++s) {
			el_q_facet(el * nb_facet_per_elem * nb_quad_per_facet
			+ f * nb_quad_per_facet + q, s)
			= quad_f(global_facet * nb_quad_per_facet + q, s);
			}
			}
			}
			}
			}
			}

			/// loop over non cohesive materials
			for (UInt m = 0; m < materials.size(); ++m) {
			try {
			MaterialCohesive & mat __attribute__((unused)) =
			dynamic_cast<MaterialCohesive &>(*materials[m]);
			} catch(std::bad_cast&) {
			/// initialize the interpolation function
			materials[m]->initElementalFieldInterpolation(elements_quad_facets);
			}
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void SolidMechanicsModelCohesive::updateResidual(bool need_initialize) {
			AKANTU_DEBUG_IN();

			if (need_initialize) initializeUpdateResidualData();

			// f -= fint
			std::vector<Material *>::iterator mat_it;
			for(mat_it = materials.begin(); mat_it != materials.end(); ++mat_it) {
			try {
			MaterialCohesive & mat = dynamic_cast<MaterialCohesive &>(**mat_it);
			mat.computeTraction(_not_ghost);
			} catch (std::bad_cast & bce) { }
			}

			SolidMechanicsModel::updateResidual(false);

			for(mat_it = materials.begin(); mat_it != materials.end(); ++mat_it) {
			try {
			MaterialCohesive & mat = dynamic_cast<MaterialCohesive &>(**mat_it);
			mat.computeEnergies();
			} catch (std::bad_cast & bce) { }
			}


			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void SolidMechanicsModelCohesive::computeNormals() {
			AKANTU_DEBUG_IN();

			Mesh & mesh_facets = inserter->getMeshFacets();
			getFEEngine("FacetsFEEngine").computeNormalsOnControlPoints(_not_ghost);

			/**
			* @todo store tangents while computing normals instead of
			* recomputing them as follows:
			*/
			/* ------------------------------------------------------------------------ */
			UInt tangent_components = spatial_dimension * (spatial_dimension - 1);

			mesh_facets.initElementTypeMapArray(tangents,
			tangent_components,
			spatial_dimension - 1);

			Mesh::type_iterator it = mesh_facets.firstType(spatial_dimension - 1);
			Mesh::type_iterator last = mesh_facets.lastType(spatial_dimension - 1);

			for (; it != last; ++it) {
			ElementType facet_type = *it;

			const Array<Real> & normals =
			getFEEngine("FacetsFEEngine").getNormalsOnQuadPoints(facet_type);

			UInt nb_quad = normals.getSize();

			Array<Real> & tang = tangents(facet_type);
			tang.resize(nb_quad);

			Real * normal_it = normals.storage();
			Real * tangent_it = tang.storage();

			/// compute first tangent
			for (UInt q = 0; q < nb_quad; ++q) {

			/// if normal is orthogonal to xy plane, arbitrarly define tangent
			if ( Math::are_float_equal(Math::norm2(normal_it), 0) )
			tangent_it[0] = 1;
			else
			Math::normal2(normal_it, tangent_it);

			normal_it += spatial_dimension;
			tangent_it += tangent_components;
			}

			/// compute second tangent (3D case)
			if (spatial_dimension == 3) {
			normal_it = normals.storage();
			tangent_it = tang.storage();

			for (UInt q = 0; q < nb_quad; ++q) {
			Math::normal3(normal_it, tangent_it, tangent_it + spatial_dimension);
			normal_it += spatial_dimension;
			tangent_it += tangent_components;
			}
			}
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void SolidMechanicsModelCohesive::interpolateStress() {
			for (UInt m = 0; m < materials.size(); ++m) {
			try {
			MaterialCohesive & mat __attribute__((unused)) =
			dynamic_cast<MaterialCohesive &>(*materials[m]);
			} catch(std::bad_cast&) {
			/// interpolate stress on facet quadrature points positions
			materials[m]->interpolateStressOnFacets(facet_stress);
			}
			}

			#if defined(AKANTU_DEBUG_TOOLS)
			debug::element_manager.printData(debug::_dm_model_cohesive,
			"Interpolated stresses before",
			facet_stress);
			#endif

			synch_registry->synchronize(_gst_smmc_facets_stress);

			#if defined(AKANTU_DEBUG_TOOLS)
			debug::element_manager.printData(debug::_dm_model_cohesive,
			"Interpolated stresses",
			facet_stress);
			#endif
			}

			/* -------------------------------------------------------------------------- */
			bool SolidMechanicsModelCohesive::checkCohesiveStress() {
			interpolateStress();

			for (UInt m = 0; m < materials.size(); ++m) {
			try {
			MaterialCohesive & mat_cohesive = dynamic_cast<MaterialCohesive &>(*materials[m]);
			/// check which not ghost cohesive elements are to be created
			mat_cohesive.checkInsertion();
			} catch(std::bad_cast&) { }
			}

			/* if(static and extrinsic) {
			check max mean stresses
			and change inserter.getInsertionFacets(type_facet);
			}
			*/

			/// communicate data among processors
			synch_registry->synchronize(_gst_smmc_facets);

			/// insert cohesive elements
			return inserter->insertElements();
			}

			/* -------------------------------------------------------------------------- */
			void SolidMechanicsModelCohesive::onElementsAdded(const Array<Element> & element_list,
			const NewElementsEvent & event) {
			AKANTU_DEBUG_IN();

			#if defined(AKANTU_PARALLEL_COHESIVE_ELEMENT)
			updateCohesiveSynchronizers();
			#endif

			SolidMechanicsModel::onElementsAdded(element_list, event);

			#if defined(AKANTU_PARALLEL_COHESIVE_ELEMENT)
			if (cohesive_distributed_synchronizer != NULL)
			cohesive_distributed_synchronizer->computeAllBufferSizes(*this);
			#endif

			/// update shape functions
			getFEEngine("CohesiveFEEngine").initShapeFunctions(_not_ghost);
			getFEEngine("CohesiveFEEngine").initShapeFunctions(_ghost);

			if (is_extrinsic) resizeFacetStress();

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void SolidMechanicsModelCohesive::onNodesAdded(const Array<UInt> & doubled_nodes,
			__attribute__((unused)) const NewNodesEvent & event) {
			AKANTU_DEBUG_IN();

			UInt nb_new_nodes = doubled_nodes.getSize();
			Array<UInt> nodes_list(nb_new_nodes);

			for (UInt n = 0; n < nb_new_nodes; ++n)
			nodes_list(n) = doubled_nodes(n, 1);

			SolidMechanicsModel::onNodesAdded(nodes_list, event);

			for (UInt n = 0; n < nb_new_nodes; ++n) {

			UInt old_node = doubled_nodes(n, 0);
			UInt new_node = doubled_nodes(n, 1);

			for (UInt dim = 0; dim < spatial_dimension; ++dim) {
			(displacement)(new_node, dim) = (displacement)(old_node, dim);
			(velocity) (new_node, dim) = (velocity) (old_node, dim);
			(acceleration)(new_node, dim) = (acceleration)(old_node, dim);
			(blocked_dofs)(new_node, dim) = (blocked_dofs)(old_node, dim);

			if (current_position)
			(current_position)(new_node, dim) = (current_position)(old_node, dim);

			if (increment_acceleration)
			(*increment_acceleration)(new_node, dim)
			= (*increment_acceleration)(old_node, dim);

			if (increment)
			(increment)(new_node, dim) = (increment)(old_node, dim);

			if (previous_displacement)
			(*previous_displacement)(new_node, dim)
			= (*previous_displacement)(old_node, dim);
			}
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void SolidMechanicsModelCohesive::onEndSolveStep(const AnalysisMethod & method) {

			AKANTU_DEBUG_IN();

			/******************************************************************************
			This is required because the Cauchy stress is the stress measure that is used
			to check the insertion of cohesive elements
			******************************************************************************/

			std::vector<Material *>::iterator mat_it;
			for(mat_it = materials.begin(); mat_it != materials.end(); ++mat_it) {
			Material & mat = **mat_it;
			if(mat.isFiniteDeformation())
			mat.computeAllCauchyStresses(_not_ghost);
			}

			AKANTU_DEBUG_OUT();
			}


			/* -------------------------------------------------------------------------- */
			void SolidMechanicsModelCohesive::printself(std::ostream & stream, int indent) const {
			std::string space;
			for(Int i = 0; i < indent; i++, space += AKANTU_INDENT);

			stream << space << "SolidMechanicsModelCohesive [" << std::endl;

			SolidMechanicsModel::printself(stream, indent + 1);

			stream << space << "]" << std::endl;
			}

			/* -------------------------------------------------------------------------- */
			void SolidMechanicsModelCohesive::resizeFacetStress() {
			AKANTU_DEBUG_IN();

			Mesh & mesh_facets = inserter->getMeshFacets();

			for (ghost_type_t::iterator gt = ghost_type_t::begin();
			gt != ghost_type_t::end();
			++gt) {
			GhostType ghost_type = *gt;

			Mesh::type_iterator it = mesh_facets.firstType(spatial_dimension - 1, ghost_type);
			Mesh::type_iterator end = mesh_facets.lastType(spatial_dimension - 1, ghost_type);
			for(; it != end; ++it) {
			ElementType type = *it;

			UInt nb_facet = mesh_facets.getNbElement(type, ghost_type);

			UInt nb_quadrature_points =
			getFEEngine("FacetsFEEngine").getNbQuadraturePoints(type, ghost_type);

			UInt new_size = nb_facet * nb_quadrature_points;

			facet_stress(type, ghost_type).resize(new_size);
			}
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void SolidMechanicsModelCohesive::addDumpGroupFieldToDumper(const std::string & dumper_name,
			const std::string & field_id,
			const std::string & group_name,
			const ElementKind & element_kind,
			bool padding_flag) {
			AKANTU_DEBUG_IN();

			ElementKind _element_kind = element_kind;
			if (dumper_name == "cohesive elements") {
			_element_kind = _ek_cohesive;
			}
			SolidMechanicsModel::addDumpGroupFieldToDumper(dumper_name,
			field_id,
			group_name,
			_element_kind,
			padding_flag);

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */

			void SolidMechanicsModelCohesive::onDump(){
			this->flattenAllRegisteredInternals(_ek_cohesive);
			SolidMechanicsModel::onDump();
			}

			/* -------------------------------------------------------------------------- */



			__END_AKANTU__

rAKA/src/model/solid_mechanics/solid_mechanics_model_cohesive.cc9be3d58a8aa0features/heat_transfer_…

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rAKA/src/model/solid_mechanics/solid_mechanics_model_cohesive.cc
9be3d58a8aa0features/heat_transfer_…

solid_mechanics_model_cohesive.cc
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