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material_cohesive.cc
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			/**
			* @file material_cohesive.cc
			*
			* @author Seyedeh Mohadeseh Taheri Mousavi <mohadeseh.taherimousavi@epfl.ch>
			* @author Marco Vocialta <marco.vocialta@epfl.ch>
			* @author Nicolas Richart <nicolas.richart@epfl.ch>
			*
			* @date creation: Wed Feb 22 2012
			* @date last modification: Tue Jul 29 2014
			*
			* @brief Specialization of the material class 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 "material_cohesive.hh"
			#include "solid_mechanics_model_cohesive.hh"
			#include "sparse_matrix.hh"
			#include "dof_synchronizer.hh"
			#include "aka_random_generator.hh"
			#include "shape_cohesive.hh"


			__BEGIN_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),
			opening_old("opening (old)", *this),
			tractions("tractions", *this),
			tractions_old("tractions (old)", *this),
			contact_tractions("contact_tractions", *this),
			contact_opening("contact_opening", *this),
			delta_max("delta max", *this),
			use_previous_delta_max(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, 0.,
			_pat_parsable \| _pat_readable, "Critical displacement");

			this->model->getMesh().initElementTypeMapArray(this->element_filter,
			1,
			spatial_dimension,
			false,
			_ek_cohesive);

			if (this->model->getIsExtrinsic())
			this->model->getMeshFacets().initElementTypeMapArray(facet_filter, 1,
			spatial_dimension - 1);

			AKANTU_DEBUG_OUT();
			}

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

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void MaterialCohesive::initMaterial() {
			AKANTU_DEBUG_IN();
			Material::initMaterial();

			this->reversible_energy.initialize(1 );
			this->total_energy .initialize(1 );
			this->tractions_old .initialize(spatial_dimension);
			this->tractions .initialize(spatial_dimension);
			this->opening_old .initialize(spatial_dimension);
			this->contact_tractions.initialize(spatial_dimension);
			this->contact_opening .initialize(spatial_dimension);
			this->opening .initialize(spatial_dimension);
			this->delta_max .initialize(1 );
			this->damage .initialize(1 );

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

			AKANTU_DEBUG_OUT();
			}

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

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

			Array<Real> & residual = const_cast<Array<Real> &>(model->getResidual());

			Mesh & mesh = fem_cohesive->getMesh();
			Mesh::type_iterator it = mesh.firstType(spatial_dimension,
			ghost_type, _ek_cohesive);
			Mesh::type_iterator last_type = mesh.lastType(spatial_dimension,
			ghost_type, _ek_cohesive);
			for(; it != last_type; ++it) {

			Array<UInt> & elem_filter = element_filter(*it, ghost_type);
			UInt nb_element = elem_filter.getSize();
			if (nb_element == 0) continue;

			const Array<Real> & shapes = fem_cohesive->getShapes(*it, ghost_type);
			Array<Real> & traction = tractions(*it, ghost_type);
			Array<Real> & contact_traction = contact_tractions(*it, ghost_type);

			UInt size_of_shapes = shapes.getNbComponent();
			UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(*it);
			UInt nb_quadrature_points = fem_cohesive->getNbQuadraturePoints(*it, 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);

			Array<Real>::iterator<Matrix<Real> > traction_it
			= traction.begin(spatial_dimension, 1);
			Array<Real>::iterator<Matrix<Real> > contact_traction_it
			= contact_traction.begin(spatial_dimension, 1);
			Array<Real>::const_iterator<Matrix<Real> > shapes_filtered_begin
			= shapes.begin(1, size_of_shapes);
			Array<Real>::iterator<Matrix<Real> > 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> * int_t_N = new Array<Real>(nb_element,
			spatial_dimension*size_of_shapes,
			"int_t_N");

			fem_cohesive->integrate(traction_cpy, int_t_N,
			spatial_dimension * size_of_shapes,
			*it, ghost_type,
			elem_filter);

			delete traction_cpy;

			int_t_N->extendComponentsInterlaced(2, int_t_N->getNbComponent());

			Real * int_t_N_val = int_t_N->storage();
			for (UInt el = 0; el < nb_element; ++el) {
			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;
			}

			/// assemble
			model->getFEEngineBoundary().assembleArray(*int_t_N, residual,
			model->getDOFSynchronizer().getLocalDOFEquationNumbers(),
			residual.getNbComponent(),
			*it, ghost_type, elem_filter, 1);

			delete int_t_N;
			}

			AKANTU_DEBUG_OUT();
			}

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

			AKANTU_DEBUG_IN();

			SparseMatrix & K = const_cast<SparseMatrix &>(model->getStiffnessMatrix());

			Mesh & mesh = fem_cohesive->getMesh();

			Mesh::type_iterator it = mesh.firstType(spatial_dimension,
			ghost_type, _ek_cohesive);
			Mesh::type_iterator last_type = mesh.lastType(spatial_dimension,
			ghost_type, _ek_cohesive);

			for(; it != last_type; ++it) {
			UInt nb_quadrature_points = fem_cohesive->getNbQuadraturePoints(*it, ghost_type);
			UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(*it);

			const Array<Real> & shapes = fem_cohesive->getShapes(*it, ghost_type);
			Array<UInt> & elem_filter = element_filter(*it, ghost_type);

			UInt nb_element = elem_filter.getSize();

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

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

			/**
			* compute A matrix @f$ \mathbf{A} = \left[\begin{array}{c c c c c c c c c c c c}
			* 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 \\
			* 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 \\
			* 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 \\
			* 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 \\
			* 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 \\
			* 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1
			* \end{array} \right]@f$
			**/

			// UInt size_of_A = spatial_dimensionsize_of_shapesspatial_dimension*nb_nodes_per_element;
			// Real * A = new Real[size_of_A];
			// memset(A, 0, size_of_A*sizeof(Real));
			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;
			}

			/// compute traction
			computeTraction(ghost_type);

			/// 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, *it, ghost_type);

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

			tangent_stiffness_matrix->clear();

			computeTangentTraction(it, tangent_stiffness_matrix, normal, ghost_type);

			// delete normal;

			UInt size_at_nt_d_n_a = spatial_dimensionnb_nodes_per_elementspatial_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,
			*it, ghost_type,
			elem_filter);

			delete at_nt_d_n_a;

			model->getFEEngine().assembleMatrix(*K_e, K, spatial_dimension,
			*it, ghost_type, 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

			Mesh & mesh = fem_cohesive->getMesh();
			Mesh::type_iterator it = mesh.firstType(spatial_dimension,
			ghost_type, _ek_cohesive);
			Mesh::type_iterator last_type = mesh.lastType(spatial_dimension,
			ghost_type, _ek_cohesive);

			for(; it != last_type; ++it) {
			Array<UInt> & elem_filter = element_filter(*it, ghost_type);

			UInt nb_element = elem_filter.getSize();
			if (nb_element == 0) continue;
			UInt nb_quadrature_points =
			nb_elementfem_cohesive->getNbQuadraturePoints(it, ghost_type);

			normal.resize(nb_quadrature_points);

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

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

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

			}

			AKANTU_DEBUG_OUT();
			}


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

			if (type == _cohesive_1d_2)
			fem_cohesive->computeNormalsOnControlPoints(position,
			normal,
			type, ghost_type);
			else {
			#define COMPUTE_NORMAL(type) \
			fem_cohesive->getShapeFunctions(). \
			computeNormalsOnControlPoints<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();

			#define COMPUTE_OPENING(type) \
			fem_cohesive->getShapeFunctions(). \
			interpolateOnControlPoints<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::computeEnergies() {
			AKANTU_DEBUG_IN();

			Mesh & mesh = fem_cohesive->getMesh();
			Mesh::type_iterator it =
			mesh.firstType(spatial_dimension, _not_ghost, _ek_cohesive);
			Mesh::type_iterator last_type =
			mesh.lastType(spatial_dimension, _not_ghost, _ek_cohesive);

			Real * memory_space = new Real[2*spatial_dimension];
			Vector<Real> b(memory_space, spatial_dimension);
			Vector<Real> h(memory_space + spatial_dimension, spatial_dimension);

			for(; it != last_type; ++it) {
			Array<Real>::iterator<Real> erev =
			reversible_energy(*it, _not_ghost).begin();
			Array<Real>::iterator<Real> etot =
			total_energy(*it, _not_ghost).begin();
			Array<Real>::vector_iterator traction_it =
			tractions(*it, _not_ghost).begin(spatial_dimension);
			Array<Real>::vector_iterator traction_old_it =
			tractions_old(*it, _not_ghost).begin(spatial_dimension);
			Array<Real>::vector_iterator opening_it =
			opening(*it, _not_ghost).begin(spatial_dimension);
			Array<Real>::vector_iterator opening_old_it =
			opening_old(*it, _not_ghost).begin(spatial_dimension);

			Array<Real>::vector_iterator traction_end =
			tractions(*it, _not_ghost).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);
			}
			}

			delete [] memory_space;

			/// update old values
			it = mesh.firstType(spatial_dimension, _not_ghost, _ek_cohesive);
			GhostType ghost_type = _not_ghost;
			for(; it != last_type; ++it) {
			tractions_old(it, ghost_type).copy(tractions(it, ghost_type));
			opening_old(it, ghost_type).copy(opening(it, ghost_type));
			}


			AKANTU_DEBUG_OUT();
			}

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

			/// integrate reversible energy for each type of elements
			Mesh & mesh = fem_cohesive->getMesh();
			Mesh::type_iterator it = mesh.firstType(spatial_dimension,
			_not_ghost, _ek_cohesive);
			Mesh::type_iterator last_type = mesh.lastType(spatial_dimension,
			_not_ghost, _ek_cohesive);

			for(; it != last_type; ++it) {
			erev += fem_cohesive->integrate(reversible_energy(it, _not_ghost), it,
			_not_ghost, element_filter(*it, _not_ghost));
			}

			AKANTU_DEBUG_OUT();
			return erev;
			}

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

			/// integrate dissipated energy for each type of elements
			Mesh & mesh = fem_cohesive->getMesh();
			Mesh::type_iterator it = mesh.firstType(spatial_dimension,
			_not_ghost, _ek_cohesive);
			Mesh::type_iterator last_type = mesh.lastType(spatial_dimension,
			_not_ghost, _ek_cohesive);

			for(; it != last_type; ++it) {
			Array<Real> dissipated_energy(total_energy(*it, _not_ghost));
			dissipated_energy -= reversible_energy(*it, _not_ghost);
			edis += fem_cohesive->integrate(dissipated_energy, *it,
			_not_ghost, element_filter(*it, _not_ghost));
			}

			AKANTU_DEBUG_OUT();
			return edis;
			}

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

			/// integrate contact energy for each type of elements
			Mesh & mesh = fem_cohesive->getMesh();
			Mesh::type_iterator it = mesh.firstType(spatial_dimension,
			_not_ghost, _ek_cohesive);
			Mesh::type_iterator last_type = mesh.lastType(spatial_dimension,
			_not_ghost, _ek_cohesive);

			for(; it != last_type; ++it) {
			Array<UInt> & el_filter = element_filter(*it, _not_ghost);
			UInt nb_quad_per_el = fem_cohesive->getNbQuadraturePoints(*it, _not_ghost);
			UInt nb_quad_points = el_filter.getSize() * nb_quad_per_el;
			Array<Real> contact_energy(nb_quad_points);

			Array<Real>::vector_iterator contact_traction_it =
			contact_tractions(*it, _not_ghost).begin(spatial_dimension);
			Array<Real>::vector_iterator contact_opening_it =
			contact_opening(*it, _not_ghost).begin(spatial_dimension);

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

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

			econ += fem_cohesive->integrate(contact_energy, *it,
			_not_ghost, el_filter);
			}

			AKANTU_DEBUG_OUT();
			return econ;
			}

			/* -------------------------------------------------------------------------- */
			Real MaterialCohesive::getEnergy(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.;
			}

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

			__END_AKANTU__

rAKA/src/model/solid_mechanics/materials/material_cohesive/material_cohesive.ccdee5ba7b2bfbfeatures/joss-2023

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rAKA/src/model/solid_mechanics/materials/material_cohesive/material_cohesive.cc
dee5ba7b2bfbfeatures/joss-2023

material_cohesive.cc
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