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solid_mechanics_model_RVE.cc
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			/**
			* @file solid_mechanics_model_RVE.cc
			* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
			* @date Wed Jan 13 15:32:35 2016
			*
			* @brief Implementation of SolidMechanicsModelRVE
			*
			* @section LICENSE
			*
			* Copyright (©) 2010-2011 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 "solid_mechanics_model_RVE.hh"
			#include "material_elastic.hh"
			#ifdef AKANTU_USE_MUMPS
			#include "solver_mumps.hh"
			#endif
			/* -------------------------------------------------------------------------- */
			__BEGIN_AKANTU__

			/* -------------------------------------------------------------------------- */
			SolidMechanicsModelRVE::SolidMechanicsModelRVE(Mesh & mesh, bool use_RVE_mat_selector, UInt dim, const ID & id, const MemoryID & memory_id) :
			SolidMechanicsModel(mesh, dim, id, memory_id),
			volume(0.),
			use_RVE_mat_selector(use_RVE_mat_selector),
			static_communicator_dummy(StaticCommunicator::getStaticCommunicatorDummy()) {

			/// create node groups for PBCs
			mesh.createGroupsFromMeshData<std::string>("physical_names");
			/// find the four corner nodes of the RVE
			findCornerNodes();

			/// remove the corner nodes from the surface node groups:
			/// This most be done because corner nodes a not periodic
			mesh.getElementGroup("top").removeNode(corner_nodes(2));
			mesh.getElementGroup("top").removeNode(corner_nodes(3));
			mesh.getElementGroup("left").removeNode(corner_nodes(3));
			mesh.getElementGroup("left").removeNode(corner_nodes(0));
			mesh.getElementGroup("bottom").removeNode(corner_nodes(1));
			mesh.getElementGroup("bottom").removeNode(corner_nodes(0));
			mesh.getElementGroup("right").removeNode(corner_nodes(2));
			mesh.getElementGroup("right").removeNode(corner_nodes(1));

			const ElementGroup & bottom = mesh.getElementGroup("bottom");
			bottom_nodes.insert( bottom.node_begin(), bottom.node_end() );

			const ElementGroup & left = mesh.getElementGroup("left");
			left_nodes.insert( left.node_begin(), left.node_end() );

			/// enforce periodicity on the displacement fluctuations
			SurfacePair surface_pair_1 = std::make_pair("top","bottom");
			SurfacePair surface_pair_2 = std::make_pair("right","left");
			SurfacePairList surface_pairs_list;
			surface_pairs_list.push_back(surface_pair_1);
			surface_pairs_list.push_back(surface_pair_2);
			this->setPBC(surface_pairs_list);
			}

			/* -------------------------------------------------------------------------- */
			SolidMechanicsModelRVE::~SolidMechanicsModelRVE() {
			delete static_communicator_dummy;
			}

			/* -------------------------------------------------------------------------- */
			void SolidMechanicsModelRVE::initFull(const ModelOptions & options) {
			SolidMechanicsModel::initFull(options);

			this->initMaterials();

			/// compute the volume of the RVE
			FEEngine * fem = this->fems["SolidMechanicsFEEngine"];
			GhostType gt = _not_ghost;
			Mesh::type_iterator it = mesh.firstType(spatial_dimension, gt, _ek_not_defined);
			Mesh::type_iterator end = mesh.lastType(spatial_dimension, gt, _ek_not_defined);
			for(; it != end; ++it) {
			const ElementType element_type = *it;
			Array<Real> Volume(this->mesh.getNbElement(element_type) * this->fems["SolidMechanicsFEEngine"]->getNbIntegrationPoints(element_type), 1, 1.);
			this->volume = fem->integrate(Volume, element_type);
			}

			std::cout << "The volume of the RVE is " << this->volume << std::endl;

			/// dumping
			std::stringstream base_name;
			base_name << "RVE_" << this->memory_id - 1;
			this->setBaseName (base_name.str());
			this->addDumpFieldVector("displacement");
			this->addDumpField ("stress" );
			this->addDumpField ("grad_u" );
			this->addDumpField ("blocked_dofs" );
			this->addDumpField ("material_index" );

			this->dump();
			}

			/* -------------------------------------------------------------------------- */
			void SolidMechanicsModelRVE::applyBoundaryConditions(const Matrix<Real> & displacement_gradient) {

			/// get the position of the nodes
			const Array<Real> & pos = mesh.getNodes();
			/// storage for the coordinates of a given node and the displacement that will be applied
			Vector<Real> x(spatial_dimension);
			Vector<Real> appl_disp(spatial_dimension);

			/// fix top right node
			UInt node = this->corner_nodes(2);
			x(0) = pos(node,0); x(1) = pos(node,1);
			appl_disp.mul<false>(displacement_gradient,x);
			(this->blocked_dofs)(node,0) = true; (this->displacement)(node,0) = appl_disp(0);
			(this->blocked_dofs)(node,1) = true; (this->displacement)(node,1) = appl_disp(1);
			// (this->blocked_dofs)(node,0) = true; (this->displacement)(node,0) = 0.;
			// (this->blocked_dofs)(node,1) = true; (this->displacement)(node,1) = 0.;

			/// apply Hx at all the other corner nodes; H: displ. gradient
			node = this->corner_nodes(0);
			x(0) = pos(node,0); x(1) = pos(node,1);
			appl_disp.mul<false>(displacement_gradient,x);
			(this->blocked_dofs)(node,0) = true; (this->displacement)(node,0) = appl_disp(0);
			(this->blocked_dofs)(node,1) = true; (this->displacement)(node,1) = appl_disp(1);

			node = this->corner_nodes(1);
			x(0) = pos(node,0); x(1) = pos(node,1);
			appl_disp.mul<false>(displacement_gradient,x);
			(this->blocked_dofs)(node,0) = true; (this->displacement)(node,0) = appl_disp(0);
			(this->blocked_dofs)(node,1) = true; (this->displacement)(node,1) = appl_disp(1);

			node = this->corner_nodes(3);
			x(0) = pos(node,0); x(1) = pos(node,1);
			appl_disp.mul<false>(displacement_gradient,x);
			(this->blocked_dofs)(node,0) = true; (this->displacement)(node,0) = appl_disp(0);
			(this->blocked_dofs)(node,1) = true; (this->displacement)(node,1) = appl_disp(1);
			}

			/* -------------------------------------------------------------------------- */
			void SolidMechanicsModelRVE::findCornerNodes() {
			mesh.computeBoundingBox();

			// find corner nodes
			const Array<Real> & position = mesh.getNodes();
			const Vector<Real> & lower_bounds = mesh.getLowerBounds();
			const Vector<Real> & upper_bounds = mesh.getUpperBounds();

			AKANTU_DEBUG_ASSERT(spatial_dimension == 2, "This is 2D only!");
			corner_nodes.resize(4);
			corner_nodes.set(UInt(-1));

			for (UInt n = 0; n < mesh.getNbNodes(); ++n) {
			// node 1
			if (Math::are_float_equal(position(n, 0), lower_bounds(0)) &&
			Math::are_float_equal(position(n, 1), lower_bounds(1))) {
			corner_nodes(0) = n;
			}
			// node 2
			else if (Math::are_float_equal(position(n, 0), upper_bounds(0)) &&
			Math::are_float_equal(position(n, 1), lower_bounds(1))) {
			corner_nodes(1) = n;
			}
			// node 3
			else if (Math::are_float_equal(position(n, 0), upper_bounds(0)) &&
			Math::are_float_equal(position(n, 1), upper_bounds(1))) {
			corner_nodes(2) = n;
			}
			// node 4
			else if (Math::are_float_equal(position(n, 0), lower_bounds(0)) &&
			Math::are_float_equal(position(n, 1), upper_bounds(1))) {
			corner_nodes(3) = n;
			}
			}

			for (UInt i = 0; i < corner_nodes.getSize(); ++i) {
			if (corner_nodes(i) == UInt(-1))
			AKANTU_DEBUG_ERROR("The corner node " << i + 1 << " wasn't found");
			}
			}

			/* -------------------------------------------------------------------------- */
			void SolidMechanicsModelRVE::advanceASR(const Matrix<Real> & prestrain) {

			/// apply the new eigenstrain
			GhostType gt = _not_ghost;

			Mesh::type_iterator it = mesh.firstType(spatial_dimension, gt, _ek_not_defined);
			Mesh::type_iterator end = mesh.lastType(spatial_dimension, gt, _ek_not_defined);
			for(; it != end; ++it) {
			const ElementType element_type = *it;
			Array<Real> & prestrain_vect = const_cast<Array<Real> &>(this->getMaterial("gel").getInternal<Real>("eigen_grad_u")(element_type, gt));
			Array<Real>::iterator< Matrix<Real> > prestrain_it = prestrain_vect.begin(spatial_dimension, spatial_dimension);
			Array<Real>::iterator< Matrix<Real> > prestrain_end = prestrain_vect.end(spatial_dimension, spatial_dimension);

			for (; prestrain_it != prestrain_end; ++prestrain_it)
			(*prestrain_it) = prestrain;
			}

			/// solve the system for the given boundary conditions
			Real error = 0;
			bool converged = this->solveStep<_scm_newton_raphson_tangent, _scc_increment>(1e-10, error, 2, false, *static_communicator_dummy);
			AKANTU_DEBUG_ASSERT(converged, "Did not converge");
			}


			/* -------------------------------------------------------------------------- */
			Real SolidMechanicsModelRVE::averageTensorField(UInt row_index, UInt col_index, const ID & field_type) {

			FEEngine * fem = this->fems["SolidMechanicsFEEngine"];
			Real average = 0;
			GhostType gt = _not_ghost;

			Mesh::type_iterator it = mesh.firstType(spatial_dimension, gt, _ek_not_defined);
			Mesh::type_iterator end = mesh.lastType(spatial_dimension, gt, _ek_not_defined);
			for(; it != end; ++it) {
			const ElementType element_type = *it;
			if (field_type == "stress") {
			for(UInt m = 0; m < this->materials.size(); ++m) {
			const Array<Real> & stress_vec = this->materials[m]->getStress(element_type);
			const Array<UInt> & elem_filter = this->materials[m]->getElementFilter(element_type);
			Array<Real> int_stress_vec(elem_filter.getSize(), spatial_dimension*spatial_dimension, "int_of_stress");

			fem->integrate(stress_vec, int_stress_vec, spatial_dimension*spatial_dimension, element_type, _not_ghost, elem_filter);

			for (UInt k = 0; k < elem_filter.getSize(); ++k)
			average += int_stress_vec(k, row_index * spatial_dimension + col_index); //3 is the value for the yy (in 3D, the value is 4)
			}
			}

			else if (field_type == "strain") {
			for(UInt m = 0; m < this->materials.size(); ++m) {
			const Array<Real> & gradu_vec = this->materials[m]->getGradU(element_type);
			const Array<UInt> & elem_filter = this->materials[m]->getElementFilter(element_type);
			Array<Real> int_gradu_vec(elem_filter.getSize(), spatial_dimension*spatial_dimension, "int_of_gradu");

			fem->integrate(gradu_vec, int_gradu_vec, spatial_dimension*spatial_dimension, element_type, _not_ghost, elem_filter);

			for (UInt k = 0; k < elem_filter.getSize(); ++k)
			/// averaging is done only for normal components, so stress and strain are equal
			average += 0.5 * (int_gradu_vec(k, row_index * spatial_dimension + col_index) + int_gradu_vec(k, col_index * spatial_dimension + row_index));
			}
			}

			else if (field_type == "eigen_grad_u") {
			for(UInt m = 0; m < this->materials.size(); ++m) {
			const Array<Real> & eigen_gradu_vec = this->materials[m]->getInternal<Real>("eigen_grad_u")(element_type);
			const Array<UInt> & elem_filter = this->materials[m]->getElementFilter(element_type);
			Array<Real> int_eigen_gradu_vec(elem_filter.getSize(), spatial_dimension*spatial_dimension, "int_of_gradu");

			fem->integrate(eigen_gradu_vec, int_eigen_gradu_vec, spatial_dimension*spatial_dimension, element_type, _not_ghost, elem_filter);

			for (UInt k = 0; k < elem_filter.getSize(); ++k)
			/// averaging is done only for normal components, so stress and strain are equal
			average += int_eigen_gradu_vec(k, row_index * spatial_dimension + col_index);
			}
			}

			else
			AKANTU_DEBUG_ERROR("Averaging not implemented for this field!!!");
			}
			return average/this->volume;
			}

			/* -------------------------------------------------------------------------- */
			void SolidMechanicsModelRVE::homogenizeStiffness(Matrix<Real> & C_macro) {

			const UInt dim = 2;
			AKANTU_DEBUG_ASSERT(this->spatial_dimension == dim, "Is only implemented for 2D!!!");

			/// apply three independent loading states to determine C
			/// 1. eps_el = (1;0;0) 2. eps_el = (0,1,0) 3. eps_el = (0,0,0.5)

			/// storage for results of 3 different loading states
			UInt voigt_size = VoigtHelper<dim>::size;
			Matrix<Real> stresses(voigt_size, voigt_size, 0.);
			Matrix<Real> strains(voigt_size, voigt_size, 0.);
			Matrix<Real> H(dim, dim, 0.);

			/// virtual test 1:
			H(0,0) = 1;
			this->performVirtualTesting(H, stresses, strains, 0);

			/// virtual test 2:
			H.clear();
			H(1,1) = 1.;
			this->performVirtualTesting(H, stresses, strains, 1);

			/// virtual test 3:
			H.clear();
			H(0,1) = 1.;
			this->performVirtualTesting(H, stresses, strains, 2);

			/// compute effective stiffness
			Matrix<Real> eps_inverse(voigt_size, voigt_size);
			eps_inverse.inverse(strains);
			C_macro.mul<false, false>(stresses, eps_inverse);
			}

			/* -------------------------------------------------------------------------- */
			void SolidMechanicsModelRVE::performVirtualTesting(const Matrix<Real> & H, Matrix<Real> & eff_stresses, Matrix<Real> & eff_strains, const UInt test_no) {

			this->applyBoundaryConditions(H);

			/// solve system
			this->assembleStiffnessMatrix();
			Real error = 0;
			bool converged= this->solveStep<_scm_newton_raphson_tangent_not_computed, _scc_increment>(1e-12, error, 2, false, *static_communicator_dummy);
			AKANTU_DEBUG_ASSERT(converged, "Did not converge");

			/// get average stress and strain
			eff_stresses(0, test_no) = this->averageTensorField(0,0, "stress");
			eff_strains(0, test_no) = this->averageTensorField(0,0, "strain");
			eff_stresses(1, test_no) = this->averageTensorField(1,1, "stress");
			eff_strains(1, test_no) = this->averageTensorField(1,1, "strain");
			eff_stresses(2, test_no) = this->averageTensorField(1,0, "stress");
			eff_strains(2, test_no) = 2. * this->averageTensorField(1,0, "strain");

			}

			/* -------------------------------------------------------------------------- */
			void SolidMechanicsModelRVE::homogenizeEigenGradU(Matrix<Real> & eigen_gradu_macro) {
			eigen_gradu_macro(0,0) = this->averageTensorField(0,0, "eigen_grad_u");
			eigen_gradu_macro(1,1) = this->averageTensorField(1,1, "eigen_grad_u");
			eigen_gradu_macro(0,1) = this->averageTensorField(0,1, "eigen_grad_u");
			eigen_gradu_macro(1,0) = this->averageTensorField(1,0, "eigen_grad_u");
			}

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

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

			if (use_RVE_mat_selector) {
			const Vector<Real> & lowerBounds = mesh.getLowerBounds();
			const Vector<Real> & upperBounds = mesh.getUpperBounds();
			Real bottom = lowerBounds(1);
			Real top = upperBounds(1);
			Real box_size = std::abs(top-bottom);
			Real eps = box_size * 1e-6;


			if(is_default_material_selector) delete material_selector;
			material_selector = new GelMaterialSelector(*this, box_size, "gel", 1, eps);
			is_default_material_selector = false;
			}

			SolidMechanicsModel::initMaterials();

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void SolidMechanicsModelRVE::initSolver(__attribute__((unused)) SolverOptions & options) {
			#if !defined(AKANTU_USE_MUMPS) && !defined(AKANTU_USE_PETSC)// or other solver in the future \todo add AKANTU_HAS_SOLVER in CMake
			AKANTU_DEBUG_ERROR("You should at least activate one solver.");
			#else
			UInt nb_global_nodes = mesh.getNbGlobalNodes();

			delete jacobian_matrix;
			std::stringstream sstr; sstr << id << ":jacobian_matrix";

			#ifdef AKANTU_USE_PETSC
			jacobian_matrix = new PETScMatrix(nb_global_nodes * spatial_dimension, _symmetric, sstr.str(), memory_id);
			#else
			jacobian_matrix = new SparseMatrix(nb_global_nodes * spatial_dimension, _unsymmetric, sstr.str(), memory_id, 1);
			#endif //AKANTU_USE PETSC
			jacobian_matrix->buildProfile(mesh, *dof_synchronizer, spatial_dimension);

			if (!isExplicit()) {
			delete stiffness_matrix;
			std::stringstream sstr_sti; sstr_sti << id << ":stiffness_matrix";
			#ifdef AKANTU_USE_PETSC
			stiffness_matrix = new SparseMatrix(nb_global_nodes * spatial_dimension, _symmetric, sstr.str(), memory_id, 1);
			stiffness_matrix->buildProfile(mesh, *dof_synchronizer, spatial_dimension);
			#else
			stiffness_matrix = new SparseMatrix(*jacobian_matrix, sstr_sti.str(), memory_id);
			#endif //AKANTU_USE_PETSC
			}

			delete solver;
			std::stringstream sstr_solv; sstr_solv << id << ":solver";
			#ifdef AKANTU_USE_PETSC
			solver = new SolverPETSc(*jacobian_matrix, sstr_solv.str(), memory_id);
			#elif defined(AKANTU_USE_MUMPS)
			solver = new SolverMumps(*jacobian_matrix, sstr_solv.str(), memory_id,
			*static_communicator_dummy);
			dof_synchronizer->initScatterGatherCommunicationScheme();
			#else
			AKANTU_DEBUG_ERROR("You should at least activate one solver.");
			#endif //AKANTU_USE_MUMPS

			SolverMumpsOptions opt(SolverMumpsOptions::_not_parallel);

			if(solver)
			solver->initialize(opt);
			#endif //AKANTU_HAS_SOLVER
			}

			/* -------------------------------------------------------------------------- */
			void SolidMechanicsModelRVE::initArrays() {
			AKANTU_DEBUG_IN();

			UInt nb_nodes = mesh.getNbNodes();
			std::stringstream sstr_disp; sstr_disp << id << ":displacement";
			// std::stringstream sstr_mass; sstr_mass << id << ":mass";
			std::stringstream sstr_velo; sstr_velo << id << ":velocity";
			std::stringstream sstr_acce; sstr_acce << id << ":acceleration";
			std::stringstream sstr_forc; sstr_forc << id << ":force";
			std::stringstream sstr_resi; sstr_resi << id << ":residual";
			std::stringstream sstr_boun; sstr_boun << id << ":blocked_dofs";

			displacement = &(alloc<Real>(sstr_disp.str(), nb_nodes, spatial_dimension, REAL_INIT_VALUE));
			// mass = &(alloc<Real>(sstr_mass.str(), nb_nodes, spatial_dimension, 0));
			velocity = &(alloc<Real>(sstr_velo.str(), nb_nodes, spatial_dimension, REAL_INIT_VALUE));
			acceleration = &(alloc<Real>(sstr_acce.str(), nb_nodes, spatial_dimension, REAL_INIT_VALUE));
			force = &(alloc<Real>(sstr_forc.str(), nb_nodes, spatial_dimension, REAL_INIT_VALUE));
			residual = &(alloc<Real>(sstr_resi.str(), nb_nodes, spatial_dimension, REAL_INIT_VALUE));
			blocked_dofs = &(alloc<bool>(sstr_boun.str(), nb_nodes, spatial_dimension, false));

			std::stringstream sstr_curp; sstr_curp << id << ":current_position";
			current_position = &(alloc<Real>(sstr_curp.str(), 0, spatial_dimension, REAL_INIT_VALUE));

			for(UInt g = _not_ghost; g <= _ghost; ++g) {
			GhostType gt = (GhostType) g;
			Mesh::type_iterator it = mesh.firstType(spatial_dimension, gt, _ek_not_defined);
			Mesh::type_iterator end = mesh.lastType(spatial_dimension, gt, _ek_not_defined);
			for(; it != end; ++it) {
			UInt nb_element = mesh.getNbElement(*it, gt);
			material_index.alloc(nb_element, 1, *it, gt);
			material_local_numbering.alloc(nb_element, 1, *it, gt);
			}
			}

			dof_synchronizer = new DOFSynchronizer(mesh, spatial_dimension,
			*static_communicator_dummy);
			dof_synchronizer->initLocalDOFEquationNumbers();
			dof_synchronizer->initGlobalDOFEquationNumbers();

			AKANTU_DEBUG_OUT();
			}


			__END_AKANTU__

rAKA/src/material_FE2/solid_mechanics_model_RVE.cc0cfe38a37116features/9-generate-a…

solid_mechanics_model_RVE.ccView Options

rAKA/src/material_FE2/solid_mechanics_model_RVE.cc
0cfe38a37116features/9-generate-a…

solid_mechanics_model_RVE.cc
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