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rAKA/src/model/solid_mechanics/material.cc
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material.cc
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/**
* @file material.cc
*
* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
* @author Marco Vocialta <marco.vocialta@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
* @author Daniel Pino Muñoz <daniel.pinomunoz@epfl.ch>
*
* @date creation: Tue Jul 27 2010
* @date last modification: Tue Sep 16 2014
*
* @brief Implementation of the common part of the material class
*
* @section LICENSE
*
* Copyright (©) 2010-2012, 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.hh"
#include "solid_mechanics_model.hh"
#include "sparse_matrix.hh"
#include "dof_synchronizer.hh"
/* -------------------------------------------------------------------------- */
__BEGIN_AKANTU__
/* -------------------------------------------------------------------------- */
Material::Material(SolidMechanicsModel & model, const ID & id) :
Memory(id, model.getMemoryID()),
Parsable(_st_material, id),
is_init(false),
fem(&(model.getFEEngine())),
finite_deformation(false),
name(""),
model(&model),
spatial_dimension(this->model->getSpatialDimension()),
element_filter("element_filter", id, this->memory_id),
stress("stress", *this),
eigenstrain("eigenstrain", *this),
gradu("grad_u", *this),
green_strain("green_strain",*this),
piola_kirchhoff_2("piola_kirchhoff_2", *this),
// potential_energy_vector(false),
potential_energy("potential_energy", *this),
is_non_local(false),
use_previous_stress(false),
use_previous_gradu(false),
interpolation_inverse_coordinates("interpolation inverse coordinates", *this),
interpolation_points_matrices("interpolation points matrices", *this) {
AKANTU_DEBUG_IN();
/// for each connectivity types allocate the element filer array of the material
model.getMesh().initElementTypeMapArray(element_filter,
1,
spatial_dimension,
false,
_ek_regular);
this->initialize();
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
Material::Material(SolidMechanicsModel & model,
UInt dim,
const Mesh & mesh,
FEEngine & fe_engine,
const ID & id) :
Memory(id, model.getMemoryID()),
Parsable(_st_material, id),
is_init(false),
fem(&(model.getFEEngine())),
finite_deformation(false),
name(""),
model(&model),
spatial_dimension(dim),
element_filter("element_filter", id, this->memory_id),
stress("stress", *this, dim, fe_engine, this->element_filter),
eigenstrain("eignestrain", *this, dim, fe_engine, this->element_filter),
gradu("gradu", *this, dim, fe_engine, this->element_filter),
green_strain("green_strain", *this, dim, fe_engine, this->element_filter),
piola_kirchhoff_2("poila_kirchhoff_2", *this, dim, fe_engine, this->element_filter),
potential_energy("potential_energy", *this, dim, fe_engine, this->element_filter),
is_non_local(false),
use_previous_stress(false),
use_previous_gradu(false),
interpolation_inverse_coordinates("interpolation inverse_coordinates", *this,
dim, fe_engine, this->element_filter),
interpolation_points_matrices("interpolation points matrices", *this,
dim, fe_engine, this->element_filter) {
AKANTU_DEBUG_IN();
mesh.initElementTypeMapArray(element_filter,
1,
spatial_dimension,
false,
_ek_regular);
this->initialize();
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
Material::~Material() {
AKANTU_DEBUG_IN();
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void Material::initialize() {
registerParam("rho" , rho , Real(0.) , _pat_parsable | _pat_modifiable, "Density");
registerParam("name" , name , std::string(), _pat_parsable | _pat_readable);
registerParam("finite_deformation" , finite_deformation , false , _pat_parsable | _pat_readable, "Is finite deformation");
registerParam("inelastic_deformation", inelastic_deformation, false , _pat_internal, "Is inelastic deformation");
/// allocate gradu stress for local elements
eigenstrain.initialize(spatial_dimension * spatial_dimension);
gradu.initialize(spatial_dimension * spatial_dimension);
stress.initialize(spatial_dimension * spatial_dimension);
this->model->registerEventHandler(*this);
}
/* -------------------------------------------------------------------------- */
void Material::initMaterial() {
AKANTU_DEBUG_IN();
if(finite_deformation) {
this->piola_kirchhoff_2.initialize(spatial_dimension * spatial_dimension);
if(use_previous_stress) this->piola_kirchhoff_2.initializeHistory();
this->green_strain.initialize(spatial_dimension * spatial_dimension);
}
if(use_previous_stress) this->stress.initializeHistory();
if(use_previous_gradu) this->gradu.initializeHistory();
for (std::map<ID, InternalField<Real> *>::iterator it = internal_vectors_real.begin();
it != internal_vectors_real.end();
++it) it->second->resize();
for (std::map<ID, InternalField<UInt> *>::iterator it = internal_vectors_uint.begin();
it != internal_vectors_uint.end();
++it) it->second->resize();
for (std::map<ID, InternalField<bool> *>::iterator it = internal_vectors_bool.begin();
it != internal_vectors_bool.end();
++it) it->second->resize();
is_init = true;
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void Material::savePreviousState() {
AKANTU_DEBUG_IN();
for (std::map<ID, InternalField<Real> *>::iterator it = internal_vectors_real.begin();
it != internal_vectors_real.end();
++it) {
if(it->second->hasHistory()) it->second->saveCurrentValues();
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
/**
* Compute the residual by assembling @f$\int_{e} \sigma_e \frac{\partial
* \varphi}{\partial X} dX @f$
*
* @param[in] displacements nodes displacements
* @param[in] ghost_type compute the residual for _ghost or _not_ghost element
*/
void Material::updateResidual(GhostType ghost_type) {
AKANTU_DEBUG_IN();
computeAllStresses(ghost_type);
assembleResidual(ghost_type);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void Material::assembleResidual(GhostType ghost_type) {
AKANTU_DEBUG_IN();
UInt spatial_dimension = model->getSpatialDimension();
if(!finite_deformation){
Array<Real> & residual = const_cast<Array<Real> &>(model->getResidual());
Mesh & mesh = fem->getMesh();
Mesh::type_iterator it = element_filter.firstType(spatial_dimension, ghost_type);
Mesh::type_iterator last_type = element_filter.lastType(spatial_dimension, ghost_type);
for(; it != last_type; ++it) {
Array<UInt> & elem_filter = element_filter(*it, ghost_type);
UInt nb_element = elem_filter.getSize();
if (nb_element) {
const Array<Real> & shapes_derivatives = fem->getShapesDerivatives(*it, ghost_type);
UInt size_of_shapes_derivatives = shapes_derivatives.getNbComponent();
UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(*it);
UInt nb_quadrature_points = fem->getNbQuadraturePoints(*it, ghost_type);
/// compute @f$\sigma \frac{\partial \varphi}{\partial X}@f$ by @f$\mathbf{B}^t \mathbf{\sigma}_q@f$
Array<Real> * sigma_dphi_dx =
new Array<Real>(nb_element*nb_quadrature_points,
size_of_shapes_derivatives, "sigma_x_dphi_/_dX");
Array<Real> * shapesd_filtered =
new Array<Real>(0, size_of_shapes_derivatives, "filtered shapesd");
FEEngine::filterElementalData(mesh, shapes_derivatives, *shapesd_filtered,
*it, ghost_type, elem_filter);
Array<Real> & stress_vect = this->stress(*it, ghost_type);
Array<Real>::matrix_iterator sigma =
stress_vect.begin(spatial_dimension, spatial_dimension);
Array<Real>::matrix_iterator B =
shapesd_filtered->begin(spatial_dimension, nb_nodes_per_element);
Array<Real>::matrix_iterator Bt_sigma_it =
sigma_dphi_dx->begin(spatial_dimension, nb_nodes_per_element);
for (UInt q = 0; q < nb_element*nb_quadrature_points; ++q, ++sigma, ++B, ++Bt_sigma_it)
Bt_sigma_it->mul<false,false>(*sigma, *B);
delete shapesd_filtered;
/**
* compute @f$\int \sigma * \frac{\partial \varphi}{\partial X}dX@f$ by @f$ \sum_q \mathbf{B}^t
* \mathbf{\sigma}_q \overline w_q J_q@f$
*/
Array<Real> * int_sigma_dphi_dx = new Array<Real>(nb_element,
nb_nodes_per_element * spatial_dimension,
"int_sigma_x_dphi_/_dX");
fem->integrate(*sigma_dphi_dx, *int_sigma_dphi_dx,
size_of_shapes_derivatives,
*it, ghost_type,
elem_filter);
delete sigma_dphi_dx;
/// assemble
fem->assembleArray(*int_sigma_dphi_dx, residual,
model->getDOFSynchronizer().getLocalDOFEquationNumbers(),
residual.getNbComponent(),
*it, ghost_type, elem_filter, -1);
delete int_sigma_dphi_dx;
}
}
}
else{
switch (spatial_dimension){
case 1:
this->assembleResidual<1>(ghost_type);
break;
case 2:
this->assembleResidual<2>(ghost_type);
break;
case 3:
this->assembleResidual<3>(ghost_type);
break;
}
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
/**
* Compute the stress from the gradu
*
* @param[in] current_position nodes postition + displacements
* @param[in] ghost_type compute the residual for _ghost or _not_ghost element
*/
void Material::computeAllStresses(GhostType ghost_type) {
AKANTU_DEBUG_IN();
UInt spatial_dimension = model->getSpatialDimension();
Mesh::type_iterator it = fem->getMesh().firstType(spatial_dimension, ghost_type);
Mesh::type_iterator last_type = fem->getMesh().lastType(spatial_dimension, ghost_type);
for(; it != last_type; ++it) {
Array<UInt> & elem_filter = element_filter(*it, ghost_type);
if (elem_filter.getSize() == 0) continue;
Array<Real> & gradu_vect = gradu(*it, ghost_type);
/// compute @f$\nabla u@f$
fem->gradientOnQuadraturePoints(model->getDisplacement(), gradu_vect,
spatial_dimension,
*it, ghost_type, elem_filter);
gradu_vect -= eigenstrain(*it, ghost_type);
/// compute @f$\mathbf{\sigma}_q@f$ from @f$\nabla u@f$
computeStress(*it, ghost_type);
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void Material::computeAllCauchyStresses(GhostType ghost_type) {
AKANTU_DEBUG_IN();
AKANTU_DEBUG_ASSERT(finite_deformation,"The Cauchy stress can only be computed if you are working in finite deformation.");
//resizeInternalArray(stress);
Mesh::type_iterator it = fem->getMesh().firstType(spatial_dimension, ghost_type);
Mesh::type_iterator last_type = fem->getMesh().lastType(spatial_dimension, ghost_type);
for(; it != last_type; ++it)
switch (spatial_dimension){
case 1:
this->computeCauchyStress<1>(*it, ghost_type);
break;
case 2:
this->computeCauchyStress<2>(*it, ghost_type);
break;
case 3:
this->computeCauchyStress<3>(*it, ghost_type);
break;
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template<UInt dim>
void Material::computeCauchyStress(ElementType el_type, GhostType ghost_type) {
AKANTU_DEBUG_IN();
Array<Real>::matrix_iterator gradu_it =
this->gradu(el_type, ghost_type).begin(dim, dim);
Array<Real>::matrix_iterator gradu_end =
this->gradu(el_type, ghost_type).end(dim, dim);
Array<Real>::matrix_iterator piola_it =
this->piola_kirchhoff_2(el_type, ghost_type).begin(dim, dim);
Array<Real>::matrix_iterator stress_it =
this->stress(el_type, ghost_type).begin(dim, dim);
Matrix<Real> F_tensor(dim, dim);
for (; gradu_it != gradu_end; ++gradu_it, ++piola_it, ++stress_it) {
Matrix<Real> & grad_u = *gradu_it;
Matrix<Real> & piola = *piola_it;
Matrix<Real> & sigma = *stress_it;
gradUToF<dim > (grad_u, F_tensor);
this->computeCauchyStressOnQuad<dim >(F_tensor, piola, sigma);
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void Material::setToSteadyState(GhostType ghost_type) {
AKANTU_DEBUG_IN();
const Array<Real> & displacement = model->getDisplacement();
//resizeInternalArray(gradu);
UInt spatial_dimension = model->getSpatialDimension();
Mesh::type_iterator it = fem->getMesh().firstType(spatial_dimension, ghost_type);
Mesh::type_iterator last_type = fem->getMesh().lastType(spatial_dimension, ghost_type);
for(; it != last_type; ++it) {
Array<UInt> & elem_filter = element_filter(*it, ghost_type);
Array<Real> & gradu_vect = gradu(*it, ghost_type);
/// compute @f$\nabla u@f$
fem->gradientOnQuadraturePoints(displacement, gradu_vect,
spatial_dimension,
*it, ghost_type, elem_filter);
setToSteadyState(*it, ghost_type);
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
/**
* Compute the stiffness matrix by assembling @f$\int_{\omega} B^t \times D
* \times B d\omega @f$
*
* @param[in] current_position nodes postition + displacements
* @param[in] ghost_type compute the residual for _ghost or _not_ghost element
*/
void Material::assembleStiffnessMatrix(GhostType ghost_type) {
AKANTU_DEBUG_IN();
UInt spatial_dimension = model->getSpatialDimension();
Mesh::type_iterator it = element_filter.firstType(spatial_dimension, ghost_type);
Mesh::type_iterator last_type = element_filter.lastType(spatial_dimension, ghost_type);
for(; it != last_type; ++it) {
if(finite_deformation){
switch (spatial_dimension) {
case 1:
{
assembleStiffnessMatrixNL < 1 > (*it, ghost_type);
assembleStiffnessMatrixL2 < 1 > (*it, ghost_type);
break;
}
case 2:
{
assembleStiffnessMatrixNL < 2 > (*it, ghost_type);
assembleStiffnessMatrixL2 < 2 > (*it, ghost_type);
break;
}
case 3:
{
assembleStiffnessMatrixNL < 3 > (*it, ghost_type);
assembleStiffnessMatrixL2 < 3 > (*it, ghost_type);
break;
}
}
} else {
switch(spatial_dimension) {
case 1: { assembleStiffnessMatrix<1>(*it, ghost_type); break; }
case 2: { assembleStiffnessMatrix<2>(*it, ghost_type); break; }
case 3: { assembleStiffnessMatrix<3>(*it, ghost_type); break; }
}
}
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template<UInt dim>
void Material::assembleStiffnessMatrix(const ElementType & type,
GhostType ghost_type) {
AKANTU_DEBUG_IN();
Array<UInt> & elem_filter = element_filter(type, ghost_type);
if (elem_filter.getSize()) {
SparseMatrix & K = const_cast<SparseMatrix &>(model->getStiffnessMatrix());
const Array<Real> & shapes_derivatives = fem->getShapesDerivatives(type,
ghost_type);
Array<Real> & gradu_vect = gradu(type, ghost_type);
UInt nb_element = elem_filter.getSize();
UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
UInt nb_quadrature_points = fem->getNbQuadraturePoints(type,
ghost_type);
gradu_vect.resize(nb_quadrature_points * nb_element);
fem->gradientOnQuadraturePoints(model->getDisplacement(),
gradu_vect, dim, type, ghost_type,
elem_filter);
UInt tangent_size = getTangentStiffnessVoigtSize(dim);
Array<Real> * tangent_stiffness_matrix =
new Array<Real>(nb_element*nb_quadrature_points, tangent_size * tangent_size,
"tangent_stiffness_matrix");
tangent_stiffness_matrix->clear();
computeTangentModuli(type, *tangent_stiffness_matrix, ghost_type);
Array<Real> * shapesd_filtered =
new Array<Real>(0, dim * nb_nodes_per_element, "filtered shapesd");
FEEngine::filterElementalData(fem->getMesh(), shapes_derivatives,
*shapesd_filtered, type, ghost_type, elem_filter);
/// compute @f$\mathbf{B}^t * \mathbf{D} * \mathbf{B}@f$
UInt bt_d_b_size = dim * nb_nodes_per_element;
Array<Real> * bt_d_b = new Array<Real>(nb_element * nb_quadrature_points,
bt_d_b_size * bt_d_b_size,
"B^t*D*B");
Matrix<Real> B(tangent_size, dim * nb_nodes_per_element);
Matrix<Real> Bt_D(dim * nb_nodes_per_element, tangent_size);
Array<Real>::matrix_iterator shapes_derivatives_filtered_it =
shapesd_filtered->begin(dim, nb_nodes_per_element);
Array<Real>::matrix_iterator Bt_D_B_it
= bt_d_b->begin(dim*nb_nodes_per_element, dim*nb_nodes_per_element);
Array<Real>::matrix_iterator D_it
= tangent_stiffness_matrix->begin(tangent_size, tangent_size);
Array<Real>::matrix_iterator D_end
= tangent_stiffness_matrix->end (tangent_size, tangent_size);
for(; D_it != D_end; ++D_it, ++Bt_D_B_it, ++shapes_derivatives_filtered_it) {
Matrix<Real> & D = *D_it;
Matrix<Real> & Bt_D_B = *Bt_D_B_it;
VoigtHelper<dim>::transferBMatrixToSymVoigtBMatrix(
*shapes_derivatives_filtered_it, B, nb_nodes_per_element);
Bt_D.mul<true, false>(B, D);
Bt_D_B.mul<false, false>(Bt_D, B);
}
delete tangent_stiffness_matrix;
delete shapesd_filtered;
/// compute @f$ k_e = \int_e \mathbf{B}^t * \mathbf{D} * \mathbf{B}@f$
Array<Real> * K_e = new Array<Real>(nb_element,
bt_d_b_size * bt_d_b_size,
"K_e");
fem->integrate(*bt_d_b, *K_e,
bt_d_b_size * bt_d_b_size,
type, ghost_type,
elem_filter);
delete bt_d_b;
fem->assembleMatrix(*K_e, K, spatial_dimension, type, ghost_type,
elem_filter);
delete K_e;
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template<UInt dim>
void Material::assembleStiffnessMatrixNL(const ElementType & type,
GhostType ghost_type) {
AKANTU_DEBUG_IN();
SparseMatrix & K = const_cast<SparseMatrix &> (model->getStiffnessMatrix());
const Array<Real> & shapes_derivatives = fem->getShapesDerivatives(type, ghost_type);
Array<UInt> & elem_filter = element_filter(type, ghost_type);
//Array<Real> & gradu_vect = delta_gradu(type, ghost_type);
UInt nb_element = elem_filter.getSize();
UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
UInt nb_quadrature_points = fem->getNbQuadraturePoints(type, ghost_type);
//gradu_vect.resize(nb_quadrature_points * nb_element);
// fem->gradientOnQuadraturePoints(model->getIncrement(), gradu_vect,
// dim, type, ghost_type, &elem_filter);
Array<Real> * shapes_derivatives_filtered = new Array<Real > (nb_element * nb_quadrature_points,
dim * nb_nodes_per_element,
"shapes derivatives filtered");
Array<Real>::const_matrix_iterator shapes_derivatives_it = shapes_derivatives.begin(spatial_dimension,
nb_nodes_per_element);
Array<Real>::matrix_iterator shapes_derivatives_filtered_it = shapes_derivatives_filtered->begin(spatial_dimension,
nb_nodes_per_element);
UInt * elem_filter_val = elem_filter.storage();
for (UInt e = 0; e < nb_element; ++e, ++elem_filter_val)
for (UInt q = 0; q < nb_quadrature_points; ++q, ++shapes_derivatives_filtered_it)
*shapes_derivatives_filtered_it = shapes_derivatives_it[*elem_filter_val * nb_quadrature_points + q];
/// compute @f$\mathbf{B}^t * \mathbf{D} * \mathbf{B}@f$
UInt bt_s_b_size = dim * nb_nodes_per_element;
Array<Real> * bt_s_b = new Array<Real > (nb_element * nb_quadrature_points,
bt_s_b_size * bt_s_b_size,
"B^t*D*B");
UInt piola_matrix_size = getCauchyStressMatrixSize(dim);
Matrix<Real> B(piola_matrix_size, bt_s_b_size);
Matrix<Real> Bt_S(bt_s_b_size, piola_matrix_size);
Matrix<Real> S(piola_matrix_size, piola_matrix_size);
shapes_derivatives_filtered_it = shapes_derivatives_filtered->begin(spatial_dimension, nb_nodes_per_element);
Array<Real>::matrix_iterator Bt_S_B_it = bt_s_b->begin(bt_s_b_size,
bt_s_b_size);
Array<Real>::matrix_iterator Bt_S_B_end = bt_s_b->end(bt_s_b_size,
bt_s_b_size);
Array<Real>::matrix_iterator piola_it = piola_kirchhoff_2(type, ghost_type).begin(dim, dim);
for (; Bt_S_B_it != Bt_S_B_end; ++Bt_S_B_it, ++shapes_derivatives_filtered_it, ++piola_it) {
Matrix<Real> & Bt_S_B = *Bt_S_B_it;
Matrix<Real> & Piola_kirchhoff_matrix = *piola_it;
setCauchyStressMatrix< dim >(Piola_kirchhoff_matrix, S);
VoigtHelper<dim>::transferBMatrixToBNL(*shapes_derivatives_filtered_it, B, nb_nodes_per_element);
Bt_S.mul < true, false > (B, S);
Bt_S_B.mul < false, false > (Bt_S, B);
}
delete shapes_derivatives_filtered;
/// compute @f$ k_e = \int_e \mathbf{B}^t * \mathbf{D} * \mathbf{B}@f$
Array<Real> * K_e = new Array<Real > (nb_element,
bt_s_b_size * bt_s_b_size,
"K_e");
fem->integrate(*bt_s_b, *K_e,
bt_s_b_size * bt_s_b_size,
type, ghost_type,
elem_filter);
delete bt_s_b;
fem->assembleMatrix(*K_e, K, spatial_dimension, type, ghost_type, elem_filter);
delete K_e;
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template<UInt dim>
void Material::assembleStiffnessMatrixL2(const ElementType & type,
GhostType ghost_type) {
AKANTU_DEBUG_IN();
SparseMatrix & K = const_cast<SparseMatrix &> (model->getStiffnessMatrix());
const Array<Real> & shapes_derivatives = fem->getShapesDerivatives(type, ghost_type);
Array<UInt> & elem_filter = element_filter(type, ghost_type);
Array<Real> & gradu_vect = gradu(type, ghost_type);
UInt nb_element = elem_filter.getSize();
UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
UInt nb_quadrature_points = fem->getNbQuadraturePoints(type, ghost_type);
gradu_vect.resize(nb_quadrature_points * nb_element);
fem->gradientOnQuadraturePoints(model->getDisplacement(), gradu_vect,
dim, type, ghost_type, elem_filter);
UInt tangent_size = getTangentStiffnessVoigtSize(dim);
Array<Real> * tangent_stiffness_matrix =
new Array<Real > (nb_element*nb_quadrature_points, tangent_size * tangent_size,
"tangent_stiffness_matrix");
tangent_stiffness_matrix->clear();
computeTangentModuli(type, *tangent_stiffness_matrix, ghost_type);
Array<Real> * shapes_derivatives_filtered = new Array<Real > (nb_element * nb_quadrature_points,
dim * nb_nodes_per_element,
"shapes derivatives filtered");
Array<Real>::const_matrix_iterator shapes_derivatives_it = shapes_derivatives.begin(spatial_dimension,
nb_nodes_per_element);
Array<Real>::matrix_iterator shapes_derivatives_filtered_it = shapes_derivatives_filtered->begin(spatial_dimension,
nb_nodes_per_element);
UInt * elem_filter_val = elem_filter.storage();
for (UInt e = 0; e < nb_element; ++e, ++elem_filter_val)
for (UInt q = 0; q < nb_quadrature_points; ++q, ++shapes_derivatives_filtered_it)
*shapes_derivatives_filtered_it = shapes_derivatives_it[*elem_filter_val * nb_quadrature_points + q];
/// compute @f$\mathbf{B}^t * \mathbf{D} * \mathbf{B}@f$
UInt bt_d_b_size = dim * nb_nodes_per_element;
Array<Real> * bt_d_b = new Array<Real > (nb_element * nb_quadrature_points,
bt_d_b_size * bt_d_b_size,
"B^t*D*B");
Matrix<Real> B(tangent_size, dim * nb_nodes_per_element);
Matrix<Real> B2(tangent_size, dim * nb_nodes_per_element);
Matrix<Real> Bt_D(dim * nb_nodes_per_element, tangent_size);
shapes_derivatives_filtered_it = shapes_derivatives_filtered->begin(spatial_dimension, nb_nodes_per_element);
Array<Real>::matrix_iterator Bt_D_B_it = bt_d_b->begin(dim*nb_nodes_per_element,
dim * nb_nodes_per_element);
Array<Real>::matrix_iterator grad_u_it = gradu_vect.begin(dim, dim);
Array<Real>::matrix_iterator D_it = tangent_stiffness_matrix->begin(tangent_size,
tangent_size);
Array<Real>::matrix_iterator D_end = tangent_stiffness_matrix->end(tangent_size,
tangent_size);
for (; D_it != D_end; ++D_it, ++Bt_D_B_it, ++shapes_derivatives_filtered_it, ++grad_u_it) {
Matrix<Real> & grad_u = *grad_u_it;
Matrix<Real> & D = *D_it;
Matrix<Real> & Bt_D_B = *Bt_D_B_it;
//transferBMatrixToBL1<dim > (*shapes_derivatives_filtered_it, B, nb_nodes_per_element);
VoigtHelper<dim>::transferBMatrixToSymVoigtBMatrix(*shapes_derivatives_filtered_it, B, nb_nodes_per_element);
VoigtHelper<dim>::transferBMatrixToBL2(*shapes_derivatives_filtered_it, grad_u, B2, nb_nodes_per_element);
B += B2;
Bt_D.mul < true, false > (B, D);
Bt_D_B.mul < false, false > (Bt_D, B);
}
delete tangent_stiffness_matrix;
delete shapes_derivatives_filtered;
/// compute @f$ k_e = \int_e \mathbf{B}^t * \mathbf{D} * \mathbf{B}@f$
Array<Real> * K_e = new Array<Real > (nb_element,
bt_d_b_size * bt_d_b_size,
"K_e");
fem->integrate(*bt_d_b, *K_e,
bt_d_b_size * bt_d_b_size,
type, ghost_type,
elem_filter);
delete bt_d_b;
fem->assembleMatrix(*K_e, K, spatial_dimension, type, ghost_type, elem_filter);
delete K_e;
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template<UInt dim>
void Material::assembleResidual(GhostType ghost_type){
AKANTU_DEBUG_IN();
Array<Real> & residual = const_cast<Array<Real> &> (model->getResidual());
Mesh & mesh = fem->getMesh();
Mesh::type_iterator it = element_filter.firstType(dim, ghost_type);
Mesh::type_iterator last_type = element_filter.lastType(dim, ghost_type);
for (; it != last_type; ++it) {
const Array<Real> & shapes_derivatives = fem->getShapesDerivatives(*it, ghost_type);
Array<UInt> & elem_filter = element_filter(*it, ghost_type);
if (elem_filter.getSize() == 0) continue;
UInt size_of_shapes_derivatives = shapes_derivatives.getNbComponent();
UInt nb_element = elem_filter.getSize();
UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(*it);
UInt nb_quadrature_points = fem->getNbQuadraturePoints(*it, ghost_type);
Array<Real> * shapesd_filtered =
new Array<Real>(0, size_of_shapes_derivatives, "filtered shapesd");
FEEngine::filterElementalData(mesh, shapes_derivatives, *shapesd_filtered,
*it, ghost_type, elem_filter);
Array<Real>::matrix_iterator shapes_derivatives_filtered_it = shapesd_filtered->begin(dim,
nb_nodes_per_element);
//Set stress vectors
UInt stress_size = getTangentStiffnessVoigtSize(dim);
//Set matrices B and BNL*
UInt bt_s_size = dim * nb_nodes_per_element;
Array<Real> * bt_s = new Array<Real > (nb_element * nb_quadrature_points,
bt_s_size,
"B^t*S");
Array<Real>::matrix_iterator grad_u_it = this->gradu(*it, ghost_type).begin(dim, dim);
Array<Real>::matrix_iterator grad_u_end = this->gradu(*it, ghost_type).end(dim, dim);
Array<Real>::matrix_iterator stress_it = this->piola_kirchhoff_2(*it, ghost_type).begin(dim, dim);
shapes_derivatives_filtered_it = shapesd_filtered->begin(dim, nb_nodes_per_element);
Array<Real>::matrix_iterator bt_s_it = bt_s->begin(bt_s_size, 1);
Matrix<Real> S_vect(stress_size, 1);
Matrix<Real> B_tensor(stress_size, bt_s_size);
Matrix<Real> B2_tensor(stress_size, bt_s_size);
for (; grad_u_it != grad_u_end; ++grad_u_it, ++stress_it, ++shapes_derivatives_filtered_it, ++bt_s_it) {
Matrix<Real> & grad_u = *grad_u_it;
Matrix<Real> & r_it = *bt_s_it;
Matrix<Real> & S_it = *stress_it;
SetCauchyStressArray <dim> (S_it, S_vect);
VoigtHelper<dim>::transferBMatrixToSymVoigtBMatrix(*shapes_derivatives_filtered_it, B_tensor, nb_nodes_per_element);
VoigtHelper<dim>::transferBMatrixToBL2(*shapes_derivatives_filtered_it, grad_u, B2_tensor, nb_nodes_per_element);
B_tensor += B2_tensor;
r_it.mul < true, false > (B_tensor, S_vect);
}
delete shapesd_filtered;
/// compute @f$ k_e = \int_e \mathbf{B}^t * \mathbf{D} * \mathbf{B}@f$
Array<Real> * r_e = new Array<Real > (nb_element,
bt_s_size, "r_e");
fem->integrate(*bt_s, *r_e,
bt_s_size,
*it, ghost_type,
elem_filter);
delete bt_s;
fem->assembleArray(*r_e, residual,
model->getDOFSynchronizer().getLocalDOFEquationNumbers(),
residual.getNbComponent(),
*it, ghost_type, elem_filter, -1);
delete r_e;
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void Material::computeAllStressesFromTangentModuli(GhostType ghost_type) {
AKANTU_DEBUG_IN();
UInt spatial_dimension = model->getSpatialDimension();
Mesh::type_iterator it = element_filter.firstType(spatial_dimension, ghost_type);
Mesh::type_iterator last_type = element_filter.lastType(spatial_dimension, ghost_type);
for(; it != last_type; ++it) {
switch(spatial_dimension) {
case 1: { computeAllStressesFromTangentModuli<1>(*it, ghost_type); break; }
case 2: { computeAllStressesFromTangentModuli<2>(*it, ghost_type); break; }
case 3: { computeAllStressesFromTangentModuli<3>(*it, ghost_type); break; }
}
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template<UInt dim>
void Material::computeAllStressesFromTangentModuli(const ElementType & type,
GhostType ghost_type) {
AKANTU_DEBUG_IN();
const Array<Real> & shapes_derivatives = fem->getShapesDerivatives(type, ghost_type);
Array<UInt> & elem_filter = element_filter(type, ghost_type);
Array<Real> & gradu_vect = gradu(type, ghost_type);
UInt nb_element = elem_filter.getSize();
if (nb_element) {
UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
UInt nb_quadrature_points = fem->getNbQuadraturePoints(type, ghost_type);
gradu_vect.resize(nb_quadrature_points * nb_element);
Array<Real> & disp = model->getDisplacement();
fem->gradientOnQuadraturePoints(disp, gradu_vect,
dim, type, ghost_type, elem_filter);
UInt tangent_moduli_size = getTangentStiffnessVoigtSize(dim);
Array<Real> * tangent_moduli_tensors =
new Array<Real>(nb_element*nb_quadrature_points, tangent_moduli_size * tangent_moduli_size,
"tangent_moduli_tensors");
tangent_moduli_tensors->clear();
computeTangentModuli(type, *tangent_moduli_tensors, ghost_type);
Array<Real> * shapesd_filtered =
new Array<Real>(0, dim* nb_nodes_per_element, "filtered shapesd");
FEEngine::filterElementalData(fem->getMesh(), shapes_derivatives, *shapesd_filtered,
type, ghost_type, elem_filter);
Array<Real> filtered_u(nb_element, nb_nodes_per_element * spatial_dimension);
FEEngine::extractNodalToElementField(fem->getMesh(), disp, filtered_u,
type, ghost_type, elem_filter);
/// compute @f$\mathbf{D} \mathbf{B} \mathbf{u}@f$
Array<Real>::matrix_iterator shapes_derivatives_filtered_it =
shapesd_filtered->begin(dim, nb_nodes_per_element);
Array<Real>::matrix_iterator D_it = tangent_moduli_tensors->begin(tangent_moduli_size,
tangent_moduli_size);
Array<Real>::matrix_iterator sigma_it = stress(type, ghost_type).begin(spatial_dimension,
spatial_dimension);
Array<Real>::vector_iterator u_it = filtered_u.begin(spatial_dimension * nb_nodes_per_element);
Matrix<Real> B(tangent_moduli_size, spatial_dimension * nb_nodes_per_element);
Vector<Real> Bu(tangent_moduli_size);
Vector<Real> DBu(tangent_moduli_size);
for (UInt e = 0; e < nb_element; ++e, ++u_it) {
for (UInt q = 0; q < nb_quadrature_points; ++q, ++D_it, ++shapes_derivatives_filtered_it, ++sigma_it) {
Vector<Real> & u = *u_it;
Matrix<Real> & sigma = *sigma_it;
Matrix<Real> & D = *D_it;
VoigtHelper<dim>::transferBMatrixToSymVoigtBMatrix(*shapes_derivatives_filtered_it, B, nb_nodes_per_element);
Bu.mul<false>(B, u);
DBu.mul<false>(D, Bu);
// Voigt notation to full symmetric tensor
for (UInt i = 0; i < dim; ++i) sigma(i, i) = DBu(i);
if(dim == 2) {
sigma(0,1) = sigma(1,0) = DBu(2);
} else if(dim == 3) {
sigma(1,2) = sigma(2,1) = DBu(3);
sigma(0,2) = sigma(2,0) = DBu(4);
sigma(0,1) = sigma(1,0) = DBu(5);
}
}
}
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void Material::computePotentialEnergyByElements() {
AKANTU_DEBUG_IN();
Mesh::type_iterator it = element_filter.firstType(spatial_dimension);
Mesh::type_iterator last_type = element_filter.lastType(spatial_dimension);
for(; it != last_type; ++it) {
computePotentialEnergy(*it);
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void Material::computePotentialEnergy(ElementType el_type, GhostType ghost_type) {
AKANTU_DEBUG_IN();
if(!potential_energy.exists(el_type, ghost_type)) {
UInt nb_element = element_filter(el_type, ghost_type).getSize();
UInt nb_quadrature_points = fem->getNbQuadraturePoints(el_type, _not_ghost);
potential_energy.alloc(nb_element * nb_quadrature_points, 1,
el_type, ghost_type);
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
Real Material::getPotentialEnergy() {
AKANTU_DEBUG_IN();
Real epot = 0.;
computePotentialEnergyByElements();
/// integrate the potential energy for each type of elements
Mesh::type_iterator it = element_filter.firstType(spatial_dimension);
Mesh::type_iterator last_type = element_filter.lastType(spatial_dimension);
for(; it != last_type; ++it) {
epot += fem->integrate(potential_energy(*it, _not_ghost), *it,
_not_ghost, element_filter(*it, _not_ghost));
}
AKANTU_DEBUG_OUT();
return epot;
}
/* -------------------------------------------------------------------------- */
Real Material::getPotentialEnergy(ElementType & type, UInt index) {
AKANTU_DEBUG_IN();
Real epot = 0.;
Vector<Real> epot_on_quad_points(fem->getNbQuadraturePoints(type));
computePotentialEnergyByElement(type, index, epot_on_quad_points);
epot = fem->integrate(epot_on_quad_points, type, element_filter(type)(index));
AKANTU_DEBUG_OUT();
return epot;
}
/* -------------------------------------------------------------------------- */
Real Material::getEnergy(std::string type) {
AKANTU_DEBUG_IN();
if(type == "potential") return getPotentialEnergy();
AKANTU_DEBUG_OUT();
return 0.;
}
/* -------------------------------------------------------------------------- */
Real Material::getEnergy(std::string energy_id, ElementType type, UInt index) {
AKANTU_DEBUG_IN();
if(energy_id == "potential") return getPotentialEnergy(type, index);
AKANTU_DEBUG_OUT();
return 0.;
}
/* -------------------------------------------------------------------------- */
void Material::computeQuadraturePointsCoordinates(ElementTypeMapArray<Real> & quadrature_points_coordinates,
const GhostType & ghost_type) const {
AKANTU_DEBUG_IN();
const Mesh & mesh = this->model->getMesh();
Array<Real> nodes_coordinates(mesh.getNodes(), true);
nodes_coordinates += this->model->getDisplacement();
Mesh::type_iterator it = this->element_filter.firstType(spatial_dimension, ghost_type);
Mesh::type_iterator last_type = this->element_filter.lastType(spatial_dimension, ghost_type);
for(; it != last_type; ++it) {
const Array<UInt> & elem_filter = this->element_filter(*it, ghost_type);
UInt nb_element = elem_filter.getSize();
if (nb_element == 0) continue;
UInt nb_tot_quad = this->fem->getNbQuadraturePoints(*it, ghost_type) * nb_element;
Array<Real> & quads = quadrature_points_coordinates(*it, ghost_type);
quads.resize(nb_tot_quad);
this->fem->interpolateOnQuadraturePoints(nodes_coordinates,
quads, spatial_dimension,
*it, ghost_type, elem_filter);
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void Material::initElementalFieldInterpolation(const ElementTypeMapArray<Real> & interpolation_points_coordinates) {
AKANTU_DEBUG_IN();
const Mesh & mesh = fem->getMesh();
ElementTypeMapArray<Real> quadrature_points_coordinates("quadrature_points_coordinates_for_interpolation", getID());
mesh.initElementTypeMapArray(quadrature_points_coordinates, spatial_dimension, spatial_dimension);
for (ghost_type_t::iterator gt = ghost_type_t::begin();
gt != ghost_type_t::end(); ++gt) {
GhostType ghost_type = *gt;
computeQuadraturePointsCoordinates(quadrature_points_coordinates, ghost_type);
Mesh::type_iterator it = element_filter.firstType(spatial_dimension, ghost_type);
Mesh::type_iterator last = element_filter.lastType(spatial_dimension, ghost_type);
for (; it != last; ++it) {
ElementType type = *it;
UInt nb_element = mesh.getNbElement(type, ghost_type);
if (nb_element == 0) continue;
const Array<Real> & interp_points_coord = interpolation_points_coordinates(type, ghost_type);
UInt nb_interpolation_points_per_elem = interp_points_coord.getSize() / nb_element;
AKANTU_DEBUG_ASSERT(interp_points_coord.getSize() % nb_element == 0,
"Number of interpolation points is wrong");
#define AKANTU_INIT_INTERPOLATE_ELEMENTAL_FIELD(type) \
initElementalFieldInterpolation<type>(quadrature_points_coordinates(type, ghost_type), \
interp_points_coord, \
nb_interpolation_points_per_elem, \
ghost_type) \
AKANTU_BOOST_REGULAR_ELEMENT_SWITCH(AKANTU_INIT_INTERPOLATE_ELEMENTAL_FIELD);
#undef AKANTU_INIT_INTERPOLATE_ELEMENTAL_FIELD
}
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <ElementType type>
void Material::initElementalFieldInterpolation(const Array<Real> & quad_coordinates,
const Array<Real> & interpolation_points_coordinates,
const UInt nb_interpolation_points_per_elem,
const GhostType ghost_type) {
AKANTU_DEBUG_IN();
Array<UInt> & elem_fil = element_filter(type, ghost_type);
UInt nb_element = elem_fil.getSize();
UInt nb_quad_per_element = fem->getNbQuadraturePoints(type, ghost_type);
if(!interpolation_inverse_coordinates.exists(type, ghost_type))
interpolation_inverse_coordinates.alloc(nb_element,
nb_quad_per_element*nb_quad_per_element,
type, ghost_type);
else
interpolation_inverse_coordinates(type, ghost_type).resize(nb_element);
if(!interpolation_points_matrices.exists(type, ghost_type))
interpolation_points_matrices.alloc(nb_element,
nb_interpolation_points_per_elem * nb_quad_per_element,
type, ghost_type);
else
interpolation_points_matrices(type, ghost_type).resize(nb_element);
Array<Real> & interp_inv_coord = interpolation_inverse_coordinates(type, ghost_type);
Array<Real> & interp_points_mat = interpolation_points_matrices(type, ghost_type);
Matrix<Real> quad_coord_matrix(nb_quad_per_element, nb_quad_per_element);
Array<Real>::const_matrix_iterator quad_coords_it =
quad_coordinates.begin_reinterpret(spatial_dimension,
nb_quad_per_element,
nb_element);
Array<Real>::const_matrix_iterator points_coords_begin =
interpolation_points_coordinates.begin_reinterpret(spatial_dimension,
nb_interpolation_points_per_elem,
interpolation_points_coordinates.getSize() / nb_interpolation_points_per_elem);
Array<Real>::matrix_iterator inv_quad_coord_it =
interp_inv_coord.begin(nb_quad_per_element, nb_quad_per_element);
Array<Real>::matrix_iterator inv_points_mat_it =
interp_points_mat.begin(nb_interpolation_points_per_elem, nb_quad_per_element);
/// loop over the elements of the current material and element type
for (UInt el = 0; el < nb_element; ++el, ++inv_quad_coord_it,
++inv_points_mat_it, ++quad_coords_it) {
/// matrix containing the quadrature points coordinates
const Matrix<Real> & quad_coords = *quad_coords_it;
/// matrix to store the matrix inversion result
Matrix<Real> & inv_quad_coord_matrix = *inv_quad_coord_it;
/// insert the quad coordinates in a matrix compatible with the interpolation
buildElementalFieldInterpolationCoodinates<type>(quad_coords,
quad_coord_matrix);
/// invert the interpolation matrix
inv_quad_coord_matrix.inverse(quad_coord_matrix);
/// matrix containing the interpolation points coordinates
const Matrix<Real> & points_coords = points_coords_begin[elem_fil(el)];
/// matrix to store the interpolation points coordinates
/// compatible with these functions
Matrix<Real> & inv_points_coord_matrix = *inv_points_mat_it;
/// insert the quad coordinates in a matrix compatible with the interpolation
buildElementalFieldInterpolationCoodinates<type>(points_coords,
inv_points_coord_matrix);
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void Material::interpolateStress(ElementTypeMapArray<Real> & result,
const GhostType ghost_type) {
interpolateElementalField(stress, result, ghost_type);
}
/* -------------------------------------------------------------------------- */
void Material::interpolateElementalField(const ElementTypeMapArray<Real> & field,
ElementTypeMapArray<Real> & result,
const GhostType ghost_type) {
AKANTU_DEBUG_IN();
Mesh::type_iterator it = element_filter.firstType(spatial_dimension, ghost_type);
Mesh::type_iterator last = element_filter.lastType(spatial_dimension, ghost_type);
for (; it != last; ++it) {
ElementType type = *it;
Array<UInt> & elem_fil = element_filter(type, ghost_type);
UInt nb_element = elem_fil.getSize();
UInt nb_quad_per_element = fem->getNbQuadraturePoints(type, ghost_type);
const Array<Real> & field_vec = field(type, ghost_type);
Array<Real> & result_vec = result(type, ghost_type);
Matrix<Real> coefficients(nb_quad_per_element, field_vec.getNbComponent());
const Array<Real> & interp_inv_coord = interpolation_inverse_coordinates(type, ghost_type);
const Array<Real> & interp_points_coord = interpolation_points_matrices(type, ghost_type);
UInt nb_interpolation_points_per_elem
= interp_points_coord.getNbComponent() / nb_quad_per_element;
Array<Real>::const_matrix_iterator field_it
= field_vec.begin_reinterpret(field_vec.getNbComponent(),
nb_quad_per_element,
nb_element);
Array<Real>::const_matrix_iterator interpolation_points_coordinates_it =
interp_points_coord.begin(nb_interpolation_points_per_elem, nb_quad_per_element);
Array<Real>::matrix_iterator result_begin
= result_vec.begin_reinterpret(field_vec.getNbComponent(),
nb_interpolation_points_per_elem,
result_vec.getSize() / nb_interpolation_points_per_elem);
Array<Real>::const_matrix_iterator inv_quad_coord_it =
interp_inv_coord.begin(nb_quad_per_element, nb_quad_per_element);
/// loop over the elements of the current material and element type
for (UInt el = 0; el < nb_element;
++el, ++field_it, ++inv_quad_coord_it, ++interpolation_points_coordinates_it) {
/**
* matrix containing the inversion of the quadrature points'
* coordinates
*/
const Matrix<Real> & inv_quad_coord_matrix = *inv_quad_coord_it;
/**
* multiply it by the field values over quadrature points to get
* the interpolation coefficients
*/
coefficients.mul<false, true>(inv_quad_coord_matrix, *field_it);
/// matrix containing the points' coordinates
const Matrix<Real> & coord = *interpolation_points_coordinates_it;
/// multiply the coordinates matrix by the coefficients matrix and store the result
Matrix<Real> res(result_begin[elem_fil(el)]);
res.mul<true, true>(coefficients, coord);
}
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void Material::interpolateStressOnFacets(ElementTypeMapArray<Real> & result,
const GhostType ghost_type) {
interpolateElementalFieldOnFacets(stress, result, ghost_type);
}
/* -------------------------------------------------------------------------- */
void Material::interpolateElementalFieldOnFacets(const ElementTypeMapArray<Real> & field,
ElementTypeMapArray<Real> & result,
const GhostType ghost_type) {
AKANTU_DEBUG_IN();
UInt sp2 = spatial_dimension * spatial_dimension;
const Mesh & mesh = this->model->getMesh();
const Mesh & mesh_facets = mesh.getMeshFacets();
Mesh::type_iterator it = element_filter.firstType(spatial_dimension, ghost_type);
Mesh::type_iterator last = element_filter.lastType(spatial_dimension, ghost_type);
for (; it != last; ++it) {
ElementType type = *it;
Array<UInt> & elem_fil = element_filter(type, ghost_type);
UInt nb_element = elem_fil.getSize();
UInt nb_quad_per_element = fem->getNbQuadraturePoints(type, ghost_type);
const Array<Real> & field_vec = field(type, ghost_type);
Matrix<Real> coefficients(nb_quad_per_element, field_vec.getNbComponent());
const Array<Real> & interp_inv_coord = interpolation_inverse_coordinates(type, ghost_type);
const Array<Real> & interp_points_coord = interpolation_points_matrices(type, ghost_type);
UInt nb_interpolation_points_per_elem
= interp_points_coord.getNbComponent() / nb_quad_per_element;
Array<Real>::const_matrix_iterator field_it
= field_vec.begin_reinterpret(field_vec.getNbComponent(),
nb_quad_per_element,
nb_element);
Array<Real>::const_matrix_iterator interpolation_points_coordinates_it =
interp_points_coord.begin(nb_interpolation_points_per_elem, nb_quad_per_element);
Array<Real>::const_matrix_iterator inv_quad_coord_it =
interp_inv_coord.begin(nb_quad_per_element, nb_quad_per_element);
Matrix<Real> result_tmp(sp2, nb_interpolation_points_per_elem);
const Array<Element> & facet_to_element =
mesh_facets.getSubelementToElement(type, ghost_type);
ElementType type_facet = Mesh::getFacetType(type);
UInt nb_facet_per_elem = facet_to_element.getNbComponent();
UInt nb_quad_per_facet = nb_interpolation_points_per_elem / nb_facet_per_elem;
Element element_for_comparison(type, 0, ghost_type);
const Array< std::vector<Element> > * element_to_facet = NULL;
GhostType current_ghost_type = _casper;
Array<Real> * result_vec = NULL;
/// loop over the elements of the current material and element type
for (UInt el = 0; el < nb_element;
++el, ++field_it, ++inv_quad_coord_it, ++interpolation_points_coordinates_it) {
/**
* matrix containing the inversion of the quadrature points'
* coordinates
*/
const Matrix<Real> & inv_quad_coord_matrix = *inv_quad_coord_it;
/**
* multiply it by the field values over quadrature points to get
* the interpolation coefficients
*/
coefficients.mul<false, true>(inv_quad_coord_matrix, *field_it);
/// matrix containing the points' coordinates
const Matrix<Real> & coord = *interpolation_points_coordinates_it;
/// multiply the coordinates matrix by the coefficients matrix and store the result
result_tmp.mul<true, true>(coefficients, coord);
UInt global_el = elem_fil(el);
element_for_comparison.element = global_el;
for (UInt f = 0; f < nb_facet_per_elem; ++f) {
Element facet_elem = facet_to_element(global_el, f);
UInt global_facet = facet_elem.element;
if (facet_elem.ghost_type != current_ghost_type) {
current_ghost_type = facet_elem.ghost_type;
element_to_facet = &mesh_facets.getElementToSubelement(type_facet,
current_ghost_type);
result_vec = &result(type_facet, current_ghost_type);
}
bool is_second_element = (*element_to_facet)(global_facet)[0] != element_for_comparison;
for (UInt q = 0; q < nb_quad_per_facet; ++q) {
Vector<Real> result_local(result_vec->storage()
+ (global_facet * nb_quad_per_facet + q) * result_vec->getNbComponent()
+ is_second_element * sp2,
sp2);
result_local = result_tmp(f * nb_quad_per_facet + q);
}
}
}
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template<typename T>
const Array<T> & Material::getArray(const ID & vect_id, const ElementType & type, const GhostType & ghost_type) const {
AKANTU_DEBUG_TO_IMPLEMENT();
return NULL;
}
/* -------------------------------------------------------------------------- */
template<typename T>
Array<T> & Material::getArray(const ID & vect_id, const ElementType & type, const GhostType & ghost_type) {
AKANTU_DEBUG_TO_IMPLEMENT();
return NULL;
}
/* -------------------------------------------------------------------------- */
template<>
const Array<Real> & Material::getArray(const ID & vect_id, const ElementType & type, const GhostType & ghost_type) const {
std::stringstream sstr;
std::string ghost_id = "";
if (ghost_type == _ghost) ghost_id = ":ghost";
sstr << getID() << ":" << vect_id << ":" << type << ghost_id;
ID fvect_id = sstr.str();
try {
return Memory::getArray<Real>(fvect_id);
} catch(debug::Exception & e) {
AKANTU_SILENT_EXCEPTION("The material " << name << "(" <<getID() << ") does not contain a vector " << vect_id << "(" << fvect_id << ") [" << e << "]");
}
}
/* -------------------------------------------------------------------------- */
template<>
Array<Real> & Material::getArray(const ID & vect_id, const ElementType & type, const GhostType & ghost_type) {
std::stringstream sstr;
std::string ghost_id = "";
if (ghost_type == _ghost) ghost_id = ":ghost";
sstr << getID() << ":" << vect_id << ":" << type << ghost_id;
ID fvect_id = sstr.str();
try {
return Memory::getArray<Real>(fvect_id);
} catch(debug::Exception & e) {
AKANTU_SILENT_EXCEPTION("The material " << name << "(" << getID() << ") does not contain a vector " << vect_id << "(" << fvect_id << ") [" << e << "]");
}
}
/* -------------------------------------------------------------------------- */
template<typename T>
const InternalField<T> & Material::getInternal(const ID & int_id) const {
AKANTU_DEBUG_TO_IMPLEMENT();
return NULL;
}
/* -------------------------------------------------------------------------- */
template<typename T>
InternalField<T> & Material::getInternal(const ID & int_id) {
AKANTU_DEBUG_TO_IMPLEMENT();
return NULL;
}
/* -------------------------------------------------------------------------- */
template<>
const InternalField<Real> & Material::getInternal(const ID & int_id) const {
std::map<ID, InternalField<Real> *>::const_iterator it = internal_vectors_real.find(getID() + ":" + int_id);
if(it == internal_vectors_real.end()) {
AKANTU_SILENT_EXCEPTION("The material " << name << "(" << getID()
<< ") does not contain an internal "
<< int_id << " (" << (getID() + ":" + int_id) << ")");
}
return *it->second;
}
/* -------------------------------------------------------------------------- */
template<>
InternalField<Real> & Material::getInternal(const ID & int_id) {
std::map<ID, InternalField<Real> *>::iterator it = internal_vectors_real.find(getID() + ":" + int_id);
if(it == internal_vectors_real.end()) {
AKANTU_SILENT_EXCEPTION("The material " << name << "(" << getID()
<< ") does not contain an internal "
<< int_id << " (" << (getID() + ":" + int_id) << ")");
}
return *it->second;
}
/* -------------------------------------------------------------------------- */
template<>
const InternalField<UInt> & Material::getInternal(const ID & int_id) const {
std::map<ID, InternalField<UInt> *>::const_iterator it = internal_vectors_uint.find(getID() + ":" + int_id);
if(it == internal_vectors_uint.end()) {
AKANTU_SILENT_EXCEPTION("The material " << name << "(" << getID()
<< ") does not contain an internal "
<< int_id << " (" << (getID() + ":" + int_id) << ")");
}
return *it->second;
}
/* -------------------------------------------------------------------------- */
template<>
InternalField<UInt> & Material::getInternal(const ID & int_id) {
std::map<ID, InternalField<UInt> *>::iterator it = internal_vectors_uint.find(getID() + ":" + int_id);
if(it == internal_vectors_uint.end()) {
AKANTU_SILENT_EXCEPTION("The material " << name << "(" << getID()
<< ") does not contain an internal "
<< int_id << " (" << (getID() + ":" + int_id) << ")");
}
return *it->second;
}
/* -------------------------------------------------------------------------- */
void Material::addElements(const Array<Element> & elements_to_add) {
AKANTU_DEBUG_IN();
UInt mat_id = model->getInternalIndexFromID(getID());
Array<Element>::const_iterator<Element> el_begin = elements_to_add.begin();
Array<Element>::const_iterator<Element> el_end = elements_to_add.end();
for(;el_begin != el_end; ++el_begin) {
const Element & element = *el_begin;
Array<UInt> & mat_indexes = model->getMaterialByElement (element.type, element.ghost_type);
Array<UInt> & mat_loc_num = model->getMaterialLocalNumbering(element.type, element.ghost_type);
UInt index = this->addElement(element.type, element.element, element.ghost_type);
mat_indexes(element.element) = mat_id;
mat_loc_num(element.element) = index;
}
this->resizeInternals();
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void Material::removeElements(const Array<Element> & elements_to_remove) {
AKANTU_DEBUG_IN();
Array<Element>::const_iterator<Element> el_begin = elements_to_remove.begin();
Array<Element>::const_iterator<Element> el_end = elements_to_remove.end();
if(el_begin==el_end)
return;
ElementTypeMapArray<UInt> material_local_new_numbering("remove mat filter elem", getID());
Element element;
for (ghost_type_t::iterator gt = ghost_type_t::begin(); gt != ghost_type_t::end(); ++gt) {
GhostType ghost_type = *gt;
element.ghost_type = ghost_type;
ElementTypeMapArray<UInt>::type_iterator it = element_filter.firstType(_all_dimensions, ghost_type, _ek_not_defined);
ElementTypeMapArray<UInt>::type_iterator end = element_filter.lastType(_all_dimensions, ghost_type, _ek_not_defined);
for(; it != end; ++it) {
ElementType type = *it;
element.type = type;
Array<UInt> & elem_filter = this->element_filter(type, ghost_type);
Array<UInt> & mat_loc_num = this->model->getMaterialLocalNumbering(type, ghost_type);
if(!material_local_new_numbering.exists(type, ghost_type))
material_local_new_numbering.alloc(elem_filter.getSize(), 1, type, ghost_type);
Array<UInt> & mat_renumbering = material_local_new_numbering(type, ghost_type);
UInt nb_element = elem_filter.getSize();
element.kind=(*el_begin).kind;
Array<UInt> elem_filter_tmp;
UInt new_id = 0;
for (UInt el = 0; el < nb_element; ++el) {
element.element = elem_filter(el);
if(std::find(el_begin, el_end, element) == el_end) {
elem_filter_tmp.push_back(element.element);
mat_renumbering(el) = new_id;
mat_loc_num(element.element) = new_id;
++new_id;
} else {
mat_renumbering(el) = UInt(-1);
}
}
elem_filter.resize(elem_filter_tmp.getSize());
elem_filter.copy(elem_filter_tmp);
}
}
for (std::map<ID, InternalField<Real> *>::iterator it = internal_vectors_real.begin();
it != internal_vectors_real.end();
++it) it->second->removeQuadraturePoints(material_local_new_numbering);
for (std::map<ID, InternalField<UInt> *>::iterator it = internal_vectors_uint.begin();
it != internal_vectors_uint.end();
++it) it->second->removeQuadraturePoints(material_local_new_numbering);
for (std::map<ID, InternalField<bool> *>::iterator it = internal_vectors_bool.begin();
it != internal_vectors_bool.end();
++it) it->second->removeQuadraturePoints(material_local_new_numbering);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void Material::resizeInternals() {
AKANTU_DEBUG_IN();
for (std::map<ID, InternalField<Real> *>::iterator it = internal_vectors_real.begin();
it != internal_vectors_real.end();
++it) it->second->resize();
for (std::map<ID, InternalField<UInt> *>::iterator it = internal_vectors_uint.begin();
it != internal_vectors_uint.end();
++it) it->second->resize();
for (std::map<ID, InternalField<bool> *>::iterator it = internal_vectors_bool.begin();
it != internal_vectors_bool.end();
++it) it->second->resize();
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void Material::onElementsAdded(__attribute__((unused)) const Array<Element> & element_list,
__attribute__((unused)) const NewElementsEvent & event) {
this->resizeInternals();
}
/* -------------------------------------------------------------------------- */
void Material::onElementsRemoved(const Array<Element> & element_list,
const ElementTypeMapArray<UInt> & new_numbering,
__attribute__((unused)) const RemovedElementsEvent & event) {
UInt my_num = model->getInternalIndexFromID(getID());
ElementTypeMapArray<UInt> material_local_new_numbering("remove mat filter elem", getID());
Array<Element>::const_iterator<Element> el_begin = element_list.begin();
Array<Element>::const_iterator<Element> el_end = element_list.end();
for (ghost_type_t::iterator g = ghost_type_t::begin(); g != ghost_type_t::end(); ++g) {
GhostType gt = *g;
ElementTypeMapArray<UInt>::type_iterator it = new_numbering.firstType(_all_dimensions, gt, _ek_not_defined);
ElementTypeMapArray<UInt>::type_iterator end = new_numbering.lastType (_all_dimensions, gt, _ek_not_defined);
for (; it != end; ++it) {
ElementType type = *it;
if(element_filter.exists(type, gt) && element_filter(type, gt).getSize()){
Array<UInt> & elem_filter = element_filter(type, gt);
Array<UInt> & mat_indexes = this->model->getMaterialByElement (*it, gt);
Array<UInt> & mat_loc_num = this->model->getMaterialLocalNumbering(*it, gt);
UInt nb_element = this->model->getMesh().getNbElement(type, gt);
// all materials will resize of the same size...
mat_indexes.resize(nb_element);
mat_loc_num.resize(nb_element);
if(!material_local_new_numbering.exists(type, gt))
material_local_new_numbering.alloc(elem_filter.getSize(), 1, type, gt);
Array<UInt> & mat_renumbering = material_local_new_numbering(type, gt);
const Array<UInt> & renumbering = new_numbering(type, gt);
Array<UInt> elem_filter_tmp;
UInt ni = 0;
Element el;
el.type = type;
el.ghost_type = gt;
el.kind = Mesh::getKind(type);
for (UInt i = 0; i < elem_filter.getSize(); ++i) {
el.element = elem_filter(i);
if(std::find(el_begin, el_end, el) == el_end) {
UInt new_el = renumbering(el.element);
AKANTU_DEBUG_ASSERT(new_el != UInt(-1), "A not removed element as been badly renumbered");
elem_filter_tmp.push_back(new_el);
mat_renumbering(i) = ni;
mat_indexes(new_el) = my_num;
mat_loc_num(new_el) = ni;
++ni;
} else {
mat_renumbering(i) = UInt(-1);
}
}
elem_filter.resize(elem_filter_tmp.getSize());
elem_filter.copy(elem_filter_tmp);
}
}
}
for (std::map<ID, InternalField<Real> *>::iterator it = internal_vectors_real.begin();
it != internal_vectors_real.end();
++it) it->second->removeQuadraturePoints(material_local_new_numbering);
for (std::map<ID, InternalField<UInt> *>::iterator it = internal_vectors_uint.begin();
it != internal_vectors_uint.end();
++it) it->second->removeQuadraturePoints(material_local_new_numbering);
for (std::map<ID, InternalField<bool> *>::iterator it = internal_vectors_bool.begin();
it != internal_vectors_bool.end();
++it) it->second->removeQuadraturePoints(material_local_new_numbering);
}
/* -------------------------------------------------------------------------- */
void Material::onBeginningSolveStep(const AnalysisMethod & method) {
this->savePreviousState();
}
/* -------------------------------------------------------------------------- */
void Material::onEndSolveStep(const AnalysisMethod & method) {
ElementTypeMapArray<UInt>::type_iterator it
= this->element_filter.firstType(_all_dimensions, _not_ghost, _ek_not_defined);
ElementTypeMapArray<UInt>::type_iterator end
= element_filter.lastType(_all_dimensions, _not_ghost, _ek_not_defined);
for(; it != end; ++it) {
this->updateEnergies(*it, _not_ghost);
}
}
/* -------------------------------------------------------------------------- */
void Material::onDamageIteration() {
this->savePreviousState();
}
/* -------------------------------------------------------------------------- */
void Material::onDamageUpdate() {
ElementTypeMapArray<UInt>::type_iterator it
= this->element_filter.firstType(_all_dimensions, _not_ghost, _ek_not_defined);
ElementTypeMapArray<UInt>::type_iterator end
= element_filter.lastType(_all_dimensions, _not_ghost, _ek_not_defined);
for(; it != end; ++it) {
if(!this->potential_energy.exists(*it, _not_ghost)) {
UInt nb_element = this->element_filter(*it, _not_ghost).getSize();
UInt nb_quadrature_points = this->fem->getNbQuadraturePoints(*it, _not_ghost);
this->potential_energy.alloc(nb_element * nb_quadrature_points, 1,
*it, _not_ghost);
}
this->updateEnergiesAfterDamage(*it, _not_ghost);
}
}
/* -------------------------------------------------------------------------- */
void Material::onDump(){
if(this->isFiniteDeformation())
this->computeAllCauchyStresses(_not_ghost);
}
/* -------------------------------------------------------------------------- */
void Material::printself(std::ostream & stream, int indent) const {
std::string space;
for(Int i = 0; i < indent; i++, space += AKANTU_INDENT);
std::string type = getID().substr(getID().find_last_of(":") + 1);
stream << space << "Material " << type << " [" << std::endl;
Parsable::printself(stream, indent);
stream << space << "]" << std::endl;
}
/* -------------------------------------------------------------------------- */
inline ElementTypeMap<UInt> Material::getInternalDataPerElem(const ID & id,
const ElementKind & element_kind,
const ID & fe_engine_id) const {
std::map<ID, InternalField<Real> *>::const_iterator internal_array =
internal_vectors_real.find(this->getID()+":"+id);
if (internal_array == internal_vectors_real.end() ||
internal_array->second->getElementKind() != element_kind)
AKANTU_EXCEPTION("Cannot find internal field " << id << " in material " << this->name);
InternalField<Real> & internal = *internal_array->second;
InternalField<Real>::type_iterator it = internal.firstType(internal.getSpatialDimension(),
_not_ghost, element_kind);
InternalField<Real>::type_iterator last_type = internal.lastType(internal.getSpatialDimension(),
_not_ghost, element_kind);
ElementTypeMap<UInt> res;
for(; it != last_type; ++it) {
UInt nb_quadrature_points = 0;
nb_quadrature_points = model->getFEEngine(fe_engine_id).getNbQuadraturePoints(*it);
res(*it) = internal.getNbComponent() * nb_quadrature_points;
}
return res;
}
/* -------------------------------------------------------------------------- */
void Material::flattenInternal(const std::string & field_id,
ElementTypeMapArray<Real> & internal_flat,
const GhostType ghost_type,
ElementKind element_kind) const {
this->flattenInternalIntern(field_id, internal_flat,
this->spatial_dimension,
ghost_type, element_kind);
}
/* -------------------------------------------------------------------------- */
void Material::flattenInternalIntern(const std::string & field_id,
ElementTypeMapArray<Real> & internal_flat,
UInt spatial_dimension,
const GhostType ghost_type,
ElementKind element_kind,
const ElementTypeMapArray<UInt> * element_filter,
const Mesh * mesh) const {
typedef ElementTypeMapArray<UInt>::type_iterator iterator;
if(element_filter == NULL) element_filter = &(this->element_filter);
if(mesh == NULL) mesh = &(this->model->mesh);
iterator tit = element_filter->firstType(spatial_dimension,
ghost_type,
element_kind);
iterator end = element_filter->lastType(spatial_dimension,
ghost_type,
element_kind);
for (; tit != end; ++tit) {
ElementType type = *tit;
try {
__attribute__((unused)) const Array<Real> & src_vect
= this->getArray<Real>(field_id, type, ghost_type);
} catch(debug::Exception & e) {
continue;
}
const Array<Real> & src_vect = this->getArray<Real>(field_id, type, ghost_type);
const Array<UInt> & filter = (*element_filter)(type, ghost_type);
// total number of elements for a given type
UInt nb_element = mesh->getNbElement(type,ghost_type);
// number of filtered elements
UInt nb_element_src = filter.getSize();
// number of quadrature points per elem
UInt nb_quad_per_elem = 0;
// number of data per quadrature point
UInt nb_data_per_quad = src_vect.getNbComponent();
if (!internal_flat.exists(type,ghost_type)) {
internal_flat.alloc(nb_element * nb_quad_per_elem,
nb_data_per_quad,
type,
ghost_type);
}
if (nb_element_src == 0) continue;
nb_quad_per_elem = (src_vect.getSize() / nb_element_src);
// number of data per element
UInt nb_data = nb_quad_per_elem * src_vect.getNbComponent();
Array<Real> & dst_vect = internal_flat(type,ghost_type);
dst_vect.resize(nb_element*nb_quad_per_elem);
Array<UInt>::const_scalar_iterator it = filter.begin();
Array<UInt>::const_scalar_iterator end = filter.end();
Array<Real>::const_vector_iterator it_src =
src_vect.begin_reinterpret(nb_data, nb_element_src);
Array<Real>::vector_iterator it_dst =
dst_vect.begin_reinterpret(nb_data, nb_element);
for (; it != end ; ++it,++it_src) {
it_dst[*it] = *it_src;
}
}
};
/* -------------------------------------------------------------------------- */
/// extrapolate internal values
void Material::extrapolateInternal(const ID & id, const Element & element, const Matrix<Real> & point, Matrix<Real> & extrapolated) {
if (this->isInternal(id, element.kind)) {
UInt nb_element = this->element_filter(element.type, element.ghost_type).getSize();
const ID name = this->getID() + ":" + id;
UInt nb_quads = this->internal_vectors_real[name]->getFEEngine().getNbQuadraturePoints(element.type, element.ghost_type);
const Array<Real> & internal = this->getArray<Real>(id, element.type, element.ghost_type);
UInt nb_component = internal.getNbComponent();
Array<Real>::const_matrix_iterator internal_it = internal.begin_reinterpret(nb_component, nb_quads, nb_element);
Element local_element = this->convertToLocalElement(element);
/// instead of really extrapolating, here the value of the first GP
/// is copied into the result vector. This works only for linear
/// elements
/// @todo extrapolate!!!!
const Matrix<Real> & values = internal_it[local_element.element];
UInt index = 0;
Vector<Real> tmp(nb_component);
for (UInt j = 0; j < values.cols(); ++j) {
tmp = values(j);
if (tmp.norm() > 0) {
index = j;
continue;
}
}
for (UInt i = 0; i < extrapolated.size(); ++i) {
extrapolated(i) = values(index);
}
}
else {
Matrix<Real> default_values(extrapolated.rows(), extrapolated.cols(), 0.);
extrapolated = default_values;
}
}
__END_AKANTU__
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