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/**
* @file material.cc
*
* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
* @author Daniel Pino Muñoz <daniel.pinomunoz@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
* @author Marco Vocialta <marco.vocialta@epfl.ch>
*
* @date creation: Tue Jul 27 2010
* @date last modification: Tue Nov 24 2015
*
* @brief Implementation of the common part of the material class
*
* @section LICENSE
*
* Copyright (©) 2010-2012, 2014, 2015 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"
/* -------------------------------------------------------------------------- */
namespace akantu {
/* -------------------------------------------------------------------------- */
Material::Material(SolidMechanicsModel & model, const ID & id)
: Memory(id, model.getMemoryID()), Parsable(ParserType::_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), eigengradu("eigen_grad_u", *this),
gradu("grad_u", *this), green_strain("green_strain", *this),
piola_kirchhoff_2("piola_kirchhoff_2", *this),
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
element_filter.initialize(model.getMesh(),
_spatial_dimension = spatial_dimension);
// 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(ParserType::_material, id),
is_init(false), fem(fe_engine), 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),
eigengradu("eigen_grad_u", *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("piola_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();
element_filter.initialize(mesh, _spatial_dimension = spatial_dimension);
// mesh.initElementTypeMapArray(element_filter, 1, spatial_dimension, false,
// _ek_regular);
this->initialize();
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
Material::~Material() = default;
/* -------------------------------------------------------------------------- */
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
eigengradu.initialize(spatial_dimension * spatial_dimension);
gradu.initialize(spatial_dimension * spatial_dimension);
stress.initialize(spatial_dimension * spatial_dimension);
potential_energy.initialize(1);
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 (auto it = internal_vectors_real.begin();
it != internal_vectors_real.end(); ++it)
it->second->resize();
for (auto it = internal_vectors_uint.begin();
it != internal_vectors_uint.end(); ++it)
it->second->resize();
for (auto it = internal_vectors_bool.begin();
it != internal_vectors_bool.end(); ++it)
it->second->resize();
is_init = true;
updateInternalParameters();
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void Material::savePreviousState() {
AKANTU_DEBUG_IN();
for (auto 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::assembleInternalForces(GhostType ghost_type) {
AKANTU_DEBUG_IN();
UInt spatial_dimension = model.getSpatialDimension();
if (!finite_deformation) {
auto & internal_force = const_cast<Array<Real> &>(model.getInternalForce());
// Mesh & mesh = fem.getMesh();
for (auto && type :
element_filter.elementTypes(spatial_dimension, ghost_type)) {
Array<UInt> & elem_filter = element_filter(type, ghost_type);
UInt nb_element = elem_filter.size();
if (nb_element == 0)
continue;
const Array<Real> & shapes_derivatives =
fem.getShapesDerivatives(type, ghost_type);
UInt size_of_shapes_derivatives = shapes_derivatives.getNbComponent();
UInt nb_quadrature_points = fem.getNbIntegrationPoints(type, ghost_type);
UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(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");
fem.computeBtD(stress(type, ghost_type), *sigma_dphi_dx, type, ghost_type,
elem_filter);
/**
* 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, type, ghost_type, elem_filter);
delete sigma_dphi_dx;
/// assemble
model.getDOFManager().assembleElementalArrayLocalArray(
*int_sigma_dphi_dx, internal_force, type, ghost_type, -1,
elem_filter);
delete int_sigma_dphi_dx;
}
} else {
switch (spatial_dimension) {
case 1:
this->assembleInternalForces<1>(ghost_type);
break;
case 2:
this->assembleInternalForces<2>(ghost_type);
break;
case 3:
this->assembleInternalForces<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();
for (const auto & type :
element_filter.elementTypes(spatial_dimension, ghost_type)) {
Array<UInt> & elem_filter = element_filter(type, ghost_type);
if (elem_filter.size() == 0)
continue;
Array<Real> & gradu_vect = gradu(type, ghost_type);
/// compute @f$\nabla u@f$
fem.gradientOnIntegrationPoints(model.getDisplacement(), gradu_vect,
spatial_dimension, type, ghost_type,
elem_filter);
gradu_vect -= eigengradu(type, ghost_type);
/// compute @f$\mathbf{\sigma}_q@f$ from @f$\nabla u@f$
computeStress(type, 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.");
for (auto type : element_filter.elementTypes(spatial_dimension, ghost_type)) {
switch (spatial_dimension) {
case 1:
this->computeCauchyStress<1>(type, ghost_type);
break;
case 2:
this->computeCauchyStress<2>(type, ghost_type);
break;
case 3:
this->computeCauchyStress<3>(type, 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();
for (auto type : element_filter.elementTypes(spatial_dimension, ghost_type)) {
Array<UInt> & elem_filter = element_filter(type, ghost_type);
Array<Real> & gradu_vect = gradu(type, ghost_type);
/// compute @f$\nabla u@f$
fem.gradientOnIntegrationPoints(displacement, gradu_vect, spatial_dimension,
type, ghost_type, elem_filter);
setToSteadyState(type, 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();
for (auto type : element_filter.elementTypes(spatial_dimension, ghost_type)) {
if (finite_deformation) {
switch (spatial_dimension) {
case 1: {
assembleStiffnessMatrixNL<1>(type, ghost_type);
assembleStiffnessMatrixL2<1>(type, ghost_type);
break;
}
case 2: {
assembleStiffnessMatrixNL<2>(type, ghost_type);
assembleStiffnessMatrixL2<2>(type, ghost_type);
break;
}
case 3: {
assembleStiffnessMatrixNL<3>(type, ghost_type);
assembleStiffnessMatrixL2<3>(type, ghost_type);
break;
}
}
} else {
switch (spatial_dimension) {
case 1: {
assembleStiffnessMatrix<1>(type, ghost_type);
break;
}
case 2: {
assembleStiffnessMatrix<2>(type, ghost_type);
break;
}
case 3: {
assembleStiffnessMatrix<3>(type, 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.size() == 0) {
AKANTU_DEBUG_OUT();
return;
}
// const Array<Real> & shapes_derivatives =
// fem.getShapesDerivatives(type, ghost_type);
Array<Real> & gradu_vect = gradu(type, ghost_type);
UInt nb_element = elem_filter.size();
UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
UInt nb_quadrature_points = fem.getNbIntegrationPoints(type, ghost_type);
gradu_vect.resize(nb_quadrature_points * nb_element);
fem.gradientOnIntegrationPoints(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);
/// 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");
fem.computeBtDB(*tangent_stiffness_matrix, *bt_d_b, 4, type, ghost_type,
elem_filter);
delete tangent_stiffness_matrix;
/// 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;
model.getDOFManager().assembleElementalMatricesToMatrix(
"K", "displacement", *K_e, type, ghost_type, _symmetric, elem_filter);
delete K_e;
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <UInt dim>
void Material::assembleStiffnessMatrixNL(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 = delta_gradu(type, ghost_type);
UInt nb_element = elem_filter.size();
UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
UInt nb_quadrature_points = fem.getNbIntegrationPoints(type, ghost_type);
Array<Real> * shapes_derivatives_filtered = new Array<Real>(
nb_element * nb_quadrature_points, dim * nb_nodes_per_element,
"shapes derivatives filtered");
fem.filterElementalData(fem.getMesh(), shapes_derivatives,
*shapes_derivatives_filtered, type, ghost_type,
elem_filter);
/// 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);
auto shapes_derivatives_filtered_it = shapes_derivatives_filtered->begin(
spatial_dimension, nb_nodes_per_element);
auto Bt_S_B_it = bt_s_b->begin(bt_s_b_size, bt_s_b_size);
auto Bt_S_B_end = bt_s_b->end(bt_s_b_size, bt_s_b_size);
auto 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) {
auto & Bt_S_B = *Bt_S_B_it;
const auto & 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.template mul<true, false>(B, S);
Bt_S_B.template 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;
model.getDOFManager().assembleElementalMatricesToMatrix(
"K", "displacement", *K_e, type, ghost_type, _symmetric, elem_filter);
delete K_e;
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <UInt dim>
void Material::assembleStiffnessMatrixL2(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.size();
UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
UInt nb_quadrature_points = fem.getNbIntegrationPoints(type, ghost_type);
gradu_vect.resize(nb_quadrature_points * nb_element);
fem.gradientOnIntegrationPoints(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");
fem.filterElementalData(fem.getMesh(), shapes_derivatives,
*shapes_derivatives_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> B2(tangent_size, dim * nb_nodes_per_element);
Matrix<Real> Bt_D(dim * nb_nodes_per_element, tangent_size);
auto shapes_derivatives_filtered_it = shapes_derivatives_filtered->begin(
spatial_dimension, nb_nodes_per_element);
auto Bt_D_B_it = bt_d_b->begin(bt_d_b_size, bt_d_b_size);
auto grad_u_it = gradu_vect.begin(dim, dim);
auto D_it = tangent_stiffness_matrix->begin(tangent_size, tangent_size);
auto 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) {
const auto & grad_u = *grad_u_it;
const auto & D = *D_it;
auto & 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.template mul<true, false>(B, D);
Bt_D_B.template 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;
model.getDOFManager().assembleElementalMatricesToMatrix(
"K", "displacement", *K_e, type, ghost_type, _symmetric, elem_filter);
delete K_e;
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <UInt dim>
void Material::assembleInternalForces(GhostType ghost_type) {
AKANTU_DEBUG_IN();
Array<Real> & internal_force = model.getInternalForce();
Mesh & mesh = fem.getMesh();
for (auto type : element_filter.elementTypes(spatial_dimension, ghost_type)) {
const Array<Real> & shapes_derivatives =
fem.getShapesDerivatives(type, ghost_type);
Array<UInt> & elem_filter = element_filter(type, ghost_type);
if (elem_filter.size() == 0)
continue;
UInt size_of_shapes_derivatives = shapes_derivatives.getNbComponent();
UInt nb_element = elem_filter.size();
UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
UInt nb_quadrature_points = fem.getNbIntegrationPoints(type, ghost_type);
Array<Real> * shapesd_filtered = new Array<Real>(
nb_element, size_of_shapes_derivatives, "filtered shapesd");
fem.filterElementalData(mesh, shapes_derivatives, *shapesd_filtered, type,
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;
auto * bt_s =
new Array<Real>(nb_element * nb_quadrature_points, bt_s_size, "B^t*S");
auto grad_u_it = this->gradu(type, ghost_type).begin(dim, dim);
auto grad_u_end = this->gradu(type, ghost_type).end(dim, dim);
auto stress_it = this->piola_kirchhoff_2(type, 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) {
auto & grad_u = *grad_u_it;
auto & r_it = *bt_s_it;
auto & 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.template 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, type, ghost_type, elem_filter);
delete bt_s;
model.getDOFManager().assembleElementalArrayLocalArray(
*r_e, internal_force, type, ghost_type, -1., elem_filter);
delete r_e;
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void Material::computePotentialEnergyByElements() {
AKANTU_DEBUG_IN();
for (auto type : element_filter.elementTypes(spatial_dimension, _not_ghost)) {
computePotentialEnergy(type);
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void Material::computePotentialEnergy(ElementType, GhostType) {
AKANTU_DEBUG_IN();
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
Real Material::getPotentialEnergy() {
AKANTU_DEBUG_IN();
Real epot = 0.;
computePotentialEnergyByElements();
/// integrate the potential energy for each type of elements
for (auto type : element_filter.elementTypes(spatial_dimension, _not_ghost)) {
epot += fem.integrate(potential_energy(type, _not_ghost), type, _not_ghost,
element_filter(type, _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.getNbIntegrationPoints(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(const std::string & type) {
AKANTU_DEBUG_IN();
if (type == "potential")
return getPotentialEnergy();
AKANTU_DEBUG_OUT();
return 0.;
}
/* -------------------------------------------------------------------------- */
Real Material::getEnergy(const 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::initElementalFieldInterpolation(
const ElementTypeMapArray<Real> & interpolation_points_coordinates) {
AKANTU_DEBUG_IN();
this->fem.initElementalFieldInterpolationFromIntegrationPoints(
interpolation_points_coordinates, this->interpolation_points_matrices,
this->interpolation_inverse_coordinates, &(this->element_filter));
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void Material::interpolateStress(ElementTypeMapArray<Real> & result,
const GhostType ghost_type) {
this->fem.interpolateElementalFieldFromIntegrationPoints(
this->stress, this->interpolation_points_matrices,
this->interpolation_inverse_coordinates, result, ghost_type,
&(this->element_filter));
}
/* -------------------------------------------------------------------------- */
void Material::interpolateStressOnFacets(
ElementTypeMapArray<Real> & result,
ElementTypeMapArray<Real> & by_elem_result, const GhostType ghost_type) {
interpolateStress(by_elem_result, ghost_type);
UInt stress_size = this->stress.getNbComponent();
const Mesh & mesh = this->model.getMesh();
const Mesh & mesh_facets = mesh.getMeshFacets();
for (auto type : element_filter.elementTypes(spatial_dimension, ghost_type)) {
Array<UInt> & elem_fil = element_filter(type, ghost_type);
Array<Real> & by_elem_res = by_elem_result(type, ghost_type);
UInt nb_element = elem_fil.size();
UInt nb_element_full = this->model.getMesh().getNbElement(type, ghost_type);
UInt nb_interpolation_points_per_elem =
by_elem_res.size() / nb_element_full;
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 = nullptr;
GhostType current_ghost_type = _casper;
Array<Real> * result_vec = nullptr;
Array<Real>::const_matrix_iterator result_it =
by_elem_res.begin_reinterpret(
stress_size, nb_interpolation_points_per_elem, nb_element_full);
for (UInt el = 0; el < nb_element; ++el) {
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 * stress_size,
stress_size);
const Matrix<Real> & result_tmp(result_it[global_el]);
result_local = result_tmp(f * nb_quad_per_facet + q);
}
}
}
}
}
/* -------------------------------------------------------------------------- */
template <typename T>
const Array<T> & Material::getArray(const ID & /*vect_id*/,
const ElementType & /*type*/,
const GhostType & /*ghost_type*/) const {
AKANTU_TO_IMPLEMENT();
return NULL;
}
/* -------------------------------------------------------------------------- */
template <typename T>
Array<T> & Material::getArray(const ID & /*vect_id*/,
const ElementType & /*type*/,
const GhostType & /*ghost_type*/) {
AKANTU_TO_IMPLEMENT();
}
/* -------------------------------------------------------------------------- */
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 <>
const Array<UInt> & 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<UInt>(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<UInt> & 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<UInt>(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(__attribute__((unused))
const ID & int_id) const {
AKANTU_TO_IMPLEMENT();
return NULL;
}
/* -------------------------------------------------------------------------- */
template <typename T>
InternalField<T> & Material::getInternal(__attribute__((unused))
const ID & int_id) {
AKANTU_TO_IMPLEMENT();
return NULL;
}
/* -------------------------------------------------------------------------- */
template <>
const InternalField<Real> & Material::getInternal(const ID & int_id) const {
auto 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) {
auto 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 {
auto 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) {
auto 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(), getMemoryID());
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.size(), 1, type,
ghost_type);
Array<UInt> & mat_renumbering =
material_local_new_numbering(type, ghost_type);
UInt nb_element = elem_filter.size();
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.size());
elem_filter.copy(elem_filter_tmp);
}
}
for (auto it = internal_vectors_real.begin();
it != internal_vectors_real.end(); ++it)
it->second->removeIntegrationPoints(material_local_new_numbering);
for (auto it = internal_vectors_uint.begin();
it != internal_vectors_uint.end(); ++it)
it->second->removeIntegrationPoints(material_local_new_numbering);
for (auto it = internal_vectors_bool.begin();
it != internal_vectors_bool.end(); ++it)
it->second->removeIntegrationPoints(material_local_new_numbering);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void Material::resizeInternals() {
AKANTU_DEBUG_IN();
for (auto it = internal_vectors_real.begin();
it != internal_vectors_real.end(); ++it)
it->second->resize();
for (auto it = internal_vectors_uint.begin();
it != internal_vectors_uint.end(); ++it)
it->second->resize();
for (auto it = internal_vectors_bool.begin();
it != internal_vectors_bool.end(); ++it)
it->second->resize();
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void Material::onElementsAdded(const Array<Element> &,
const NewElementsEvent &) {
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(), getMemoryID());
auto el_begin = element_list.begin();
auto el_end = element_list.end();
for (auto && gt : ghost_types) {
for (auto && type :
new_numbering.elementTypes(_all_dimensions, gt, _ek_not_defined)) {
if (not element_filter.exists(type, gt) ||
element_filter(type, gt).size() == 0)
continue;
auto & elem_filter = element_filter(type, gt);
auto & mat_indexes = this->model.getMaterialByElement(type, gt);
auto & mat_loc_num = this->model.getMaterialLocalNumbering(type, gt);
auto 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.size(), 1, type, gt);
auto & mat_renumbering = material_local_new_numbering(type, gt);
const auto & renumbering = new_numbering(type, gt);
Array<UInt> elem_filter_tmp;
UInt ni = 0;
Element el{type, 0, gt};
for (UInt i = 0; i < elem_filter.size(); ++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.size());
elem_filter.copy(elem_filter_tmp);
}
}
for (auto it = internal_vectors_real.begin();
it != internal_vectors_real.end(); ++it)
it->second->removeIntegrationPoints(material_local_new_numbering);
for (auto it = internal_vectors_uint.begin();
it != internal_vectors_uint.end(); ++it)
it->second->removeIntegrationPoints(material_local_new_numbering);
for (auto it = internal_vectors_bool.begin();
it != internal_vectors_bool.end(); ++it)
it->second->removeIntegrationPoints(material_local_new_numbering);
}
/* -------------------------------------------------------------------------- */
void Material::beforeSolveStep() { this->savePreviousState(); }
/* -------------------------------------------------------------------------- */
void Material::afterSolveStep() {
for (auto & type : element_filter.elementTypes(_all_dimensions, _not_ghost,
_ek_not_defined)) {
this->updateEnergies(type, _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) {
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;
}
/* -------------------------------------------------------------------------- */
/// extrapolate internal values
void Material::extrapolateInternal(const ID & id, const Element & element,
__attribute__((unused))
const Matrix<Real> & point,
Matrix<Real> & extrapolated) {
if (this->isInternal<Real>(id, element.kind())) {
UInt nb_element =
this->element_filter(element.type, element.ghost_type).size();
const ID name = this->getID() + ":" + id;
UInt nb_quads =
this->internal_vectors_real[name]->getFEEngine().getNbIntegrationPoints(
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!!!!
AKANTU_DEBUG_WARNING("This is a fix, values are not truly extrapolated");
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;
break;
}
}
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;
}
}
/* -------------------------------------------------------------------------- */
void Material::applyEigenGradU(const Matrix<Real> & prescribed_eigen_grad_u,
const GhostType ghost_type) {
for (auto && type : element_filter.elementTypes(_all_dimensions, _not_ghost,
_ek_not_defined)) {
if (!element_filter(type, ghost_type).size())
continue;
auto eigen_it = this->eigengradu(type, ghost_type)
.begin(spatial_dimension, spatial_dimension);
auto eigen_end = this->eigengradu(type, ghost_type)
.end(spatial_dimension, spatial_dimension);
for (; eigen_it != eigen_end; ++eigen_it) {
auto & current_eigengradu = *eigen_it;
current_eigengradu = prescribed_eigen_grad_u;
}
}
}
} // namespace akantu
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