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solid_mechanics_model_RVE.cc
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/**
* @file solid_mechanics_model_RVE.cc
* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
* @date Wed Jan 13 15:32:35 2016
*
* @brief Implementation of SolidMechanicsModelRVE
*
* @section LICENSE
*
* Copyright (©) 2010-2011 EPFL (Ecole Polytechnique Fédérale de Lausanne)
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
* Akantu is free software: you can redistribute it and/or modify it under the
* terms of the GNU Lesser General Public License as published by the Free
* Software Foundation, either version 3 of the License, or (at your option) any
* later version.
*
* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
* details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
*
*/
/* -------------------------------------------------------------------------- */
#include "solid_mechanics_model_RVE.hh"
#include "element_group.hh"
#include "material_damage_iterative.hh"
#include "node_group.hh"
#include "non_linear_solver.hh"
#include "parser.hh"
#include "sparse_matrix.hh"
/* -------------------------------------------------------------------------- */
namespace akantu {
/* -------------------------------------------------------------------------- */
SolidMechanicsModelRVE::SolidMechanicsModelRVE(Mesh & mesh,
bool use_RVE_mat_selector,
UInt nb_gel_pockets, UInt dim,
const ID & id,
const MemoryID & memory_id)
: SolidMechanicsModel(mesh, dim, id, memory_id), volume(0.),
use_RVE_mat_selector(use_RVE_mat_selector),
nb_gel_pockets(nb_gel_pockets), nb_dumps(0) {
AKANTU_DEBUG_IN();
/// find the four corner nodes of the RVE
findCornerNodes();
/// remove the corner nodes from the surface node groups:
/// This most be done because corner nodes a not periodic
mesh.getElementGroup("top").removeNode(corner_nodes(2));
mesh.getElementGroup("top").removeNode(corner_nodes(3));
mesh.getElementGroup("left").removeNode(corner_nodes(3));
mesh.getElementGroup("left").removeNode(corner_nodes(0));
mesh.getElementGroup("bottom").removeNode(corner_nodes(1));
mesh.getElementGroup("bottom").removeNode(corner_nodes(0));
mesh.getElementGroup("right").removeNode(corner_nodes(2));
mesh.getElementGroup("right").removeNode(corner_nodes(1));
const auto & bottom = mesh.getElementGroup("bottom").getNodeGroup();
bottom_nodes.insert(bottom.begin(), bottom.end());
const auto & left = mesh.getElementGroup("left").getNodeGroup();
left_nodes.insert(left.begin(), left.end());
// /// enforce periodicity on the displacement fluctuations
// auto surface_pair_1 = std::make_pair("top", "bottom");
// auto surface_pair_2 = std::make_pair("right", "left");
// SurfacePairList surface_pairs_list;
// surface_pairs_list.push_back(surface_pair_1);
// surface_pairs_list.push_back(surface_pair_2);
// TODO: To Nicolas correct the PBCs
// this->setPBC(surface_pairs_list);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
SolidMechanicsModelRVE::~SolidMechanicsModelRVE() = default;
/* -------------------------------------------------------------------------- */
void SolidMechanicsModelRVE::initFullImpl(const ModelOptions & options) {
AKANTU_DEBUG_IN();
auto options_cp(options);
options_cp.analysis_method = AnalysisMethod::_static;
SolidMechanicsModel::initFullImpl(options_cp);
this->initMaterials();
auto & fem = this->getFEEngine("SolidMechanicsFEEngine");
/// compute the volume of the RVE
GhostType gt = _not_ghost;
for (auto element_type : this->mesh.elementTypes(spatial_dimension, gt, _ek_not_defined)) {
Array<Real> Volume(this->mesh.getNbElement(element_type) *
fem.getNbIntegrationPoints(element_type),
1, 1.);
this->volume = fem.integrate(Volume, element_type);
}
std::cout << "The volume of the RVE is " << this->volume << std::endl;
/// dumping
std::stringstream base_name;
base_name << this->id; // << this->memory_id - 1;
this->setBaseName(base_name.str());
this->addDumpFieldVector("displacement");
this->addDumpField("stress");
this->addDumpField("grad_u");
this->addDumpField("eigen_grad_u");
this->addDumpField("blocked_dofs");
this->addDumpField("material_index");
this->addDumpField("damage");
this->addDumpField("Sc");
this->addDumpField("external_force");
this->addDumpField("equivalent_stress");
this->addDumpField("internal_force");
this->dump();
this->nb_dumps += 1;
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void SolidMechanicsModelRVE::applyBoundaryConditions(
const Matrix<Real> & displacement_gradient) {
AKANTU_DEBUG_IN();
/// get the position of the nodes
const Array<Real> & pos = mesh.getNodes();
/// storage for the coordinates of a given node and the displacement that will
/// be applied
Vector<Real> x(spatial_dimension);
Vector<Real> appl_disp(spatial_dimension);
/// fix top right node
UInt node = this->corner_nodes(2);
x(0) = pos(node, 0);
x(1) = pos(node, 1);
appl_disp.mul<false>(displacement_gradient, x);
(*this->blocked_dofs)(node, 0) = true;
(*this->displacement)(node, 0) = appl_disp(0);
(*this->blocked_dofs)(node, 1) = true;
(*this->displacement)(node, 1) = appl_disp(1);
// (*this->blocked_dofs)(node,0) = true; (*this->displacement)(node,0) = 0.;
// (*this->blocked_dofs)(node,1) = true; (*this->displacement)(node,1) = 0.;
/// apply Hx at all the other corner nodes; H: displ. gradient
node = this->corner_nodes(0);
x(0) = pos(node, 0);
x(1) = pos(node, 1);
appl_disp.mul<false>(displacement_gradient, x);
(*this->blocked_dofs)(node, 0) = true;
(*this->displacement)(node, 0) = appl_disp(0);
(*this->blocked_dofs)(node, 1) = true;
(*this->displacement)(node, 1) = appl_disp(1);
node = this->corner_nodes(1);
x(0) = pos(node, 0);
x(1) = pos(node, 1);
appl_disp.mul<false>(displacement_gradient, x);
(*this->blocked_dofs)(node, 0) = true;
(*this->displacement)(node, 0) = appl_disp(0);
(*this->blocked_dofs)(node, 1) = true;
(*this->displacement)(node, 1) = appl_disp(1);
node = this->corner_nodes(3);
x(0) = pos(node, 0);
x(1) = pos(node, 1);
appl_disp.mul<false>(displacement_gradient, x);
(*this->blocked_dofs)(node, 0) = true;
(*this->displacement)(node, 0) = appl_disp(0);
(*this->blocked_dofs)(node, 1) = true;
(*this->displacement)(node, 1) = appl_disp(1);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void SolidMechanicsModelRVE::findCornerNodes() {
AKANTU_DEBUG_IN();
// find corner nodes
const auto & position = mesh.getNodes();
const auto & lower_bounds = mesh.getLowerBounds();
const auto & upper_bounds = mesh.getUpperBounds();
AKANTU_DEBUG_ASSERT(spatial_dimension == 2, "This is 2D only!");
corner_nodes.resize(4);
corner_nodes.set(UInt(-1));
for (auto && data : enumerate(make_view(position, spatial_dimension))) {
auto node = std::get<0>(data);
const auto & X = std::get<1>(data);
auto distance = X.distance(lower_bounds);
// node 1
if (Math::are_float_equal(distance, 0)) {
corner_nodes(0) = node;
}
// node 2
else if (Math::are_float_equal(X(_x), upper_bounds(_x)) &&
Math::are_float_equal(X(_y), lower_bounds(_y))) {
corner_nodes(1) = node;
}
// node 3
else if (Math::are_float_equal(X(_x), upper_bounds(_x)) &&
Math::are_float_equal(X(_y), upper_bounds(_y))) {
corner_nodes(2) = node;
}
// node 4
else if (Math::are_float_equal(X(_x), lower_bounds(_x)) &&
Math::are_float_equal(X(_y), upper_bounds(_y))) {
corner_nodes(3) = node;
}
}
for (UInt i = 0; i < corner_nodes.size(); ++i) {
if (corner_nodes(i) == UInt(-1))
AKANTU_DEBUG_ERROR("The corner node " << i + 1 << " wasn't found");
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void SolidMechanicsModelRVE::advanceASR(const Matrix<Real> & prestrain) {
AKANTU_DEBUG_IN();
AKANTU_DEBUG_ASSERT(spatial_dimension == 2, "This is 2D only!");
/// apply the new eigenstrain
for (auto element_type : mesh.elementTypes(_element_kind = _ek_not_defined)) {
Array<Real> & prestrain_vect =
const_cast<Array<Real> &>(this->getMaterial("gel").getInternal<Real>(
"eigen_grad_u")(element_type));
auto prestrain_it =
prestrain_vect.begin(spatial_dimension, spatial_dimension);
auto prestrain_end =
prestrain_vect.end(spatial_dimension, spatial_dimension);
for (; prestrain_it != prestrain_end; ++prestrain_it)
(*prestrain_it) = prestrain;
}
/// advance the damage
MaterialDamageIterative<2> & mat_paste =
dynamic_cast<MaterialDamageIterative<2> &>(*this->materials[1]);
MaterialDamageIterative<2> & mat_aggregate =
dynamic_cast<MaterialDamageIterative<2> &>(*this->materials[0]);
UInt nb_damaged_elements = 0;
Real max_eq_stress_aggregate = 0;
Real max_eq_stress_paste = 0;
auto & solver = this->getNonLinearSolver();
solver.set("max_iterations", 2);
solver.set("threshold", 1e-6);
solver.set("convergence_type", _scc_solution);
do {
this->solveStep();
/// compute damage
max_eq_stress_aggregate = mat_aggregate.getNormMaxEquivalentStress();
max_eq_stress_paste = mat_paste.getNormMaxEquivalentStress();
nb_damaged_elements = 0;
if (max_eq_stress_aggregate > max_eq_stress_paste)
nb_damaged_elements = mat_aggregate.updateDamage();
else if (max_eq_stress_aggregate < max_eq_stress_paste)
nb_damaged_elements = mat_paste.updateDamage();
else
nb_damaged_elements =
(mat_paste.updateDamage() + mat_aggregate.updateDamage());
std::cout << "the number of damaged elements is " << nb_damaged_elements
<< std::endl;
} while (nb_damaged_elements);
if (this->nb_dumps % 10 == 0) {
this->dump();
}
this->nb_dumps += 1;
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
Real SolidMechanicsModelRVE::averageTensorField(UInt row_index, UInt col_index,
const ID & field_type) {
AKANTU_DEBUG_IN();
auto & fem = this->getFEEngine("SolidMechanicsFEEngine");
Real average = 0;
for (auto element_type : mesh.elementTypes(_element_kind = _ek_not_defined)) {
if (field_type == "stress") {
for (UInt m = 0; m < this->materials.size(); ++m) {
const auto & stress_vec = this->materials[m]->getStress(element_type);
const auto & elem_filter =
this->materials[m]->getElementFilter(element_type);
Array<Real> int_stress_vec(elem_filter.size(),
spatial_dimension * spatial_dimension,
"int_of_stress");
fem.integrate(stress_vec, int_stress_vec,
spatial_dimension * spatial_dimension, element_type,
_not_ghost, elem_filter);
for (UInt k = 0; k < elem_filter.size(); ++k)
average += int_stress_vec(
k, row_index * spatial_dimension + col_index); // 3 is the value
// for the yy (in
// 3D, the value is
// 4)
}
} else if (field_type == "strain") {
for (UInt m = 0; m < this->materials.size(); ++m) {
const auto & gradu_vec = this->materials[m]->getGradU(element_type);
const auto & elem_filter =
this->materials[m]->getElementFilter(element_type);
Array<Real> int_gradu_vec(elem_filter.size(),
spatial_dimension * spatial_dimension,
"int_of_gradu");
fem.integrate(gradu_vec, int_gradu_vec,
spatial_dimension * spatial_dimension, element_type,
_not_ghost, elem_filter);
for (UInt k = 0; k < elem_filter.size(); ++k)
/// averaging is done only for normal components, so stress and strain
/// are equal
average +=
0.5 *
(int_gradu_vec(k, row_index * spatial_dimension + col_index) +
int_gradu_vec(k, col_index * spatial_dimension + row_index));
}
} else if (field_type == "eigen_grad_u") {
for (UInt m = 0; m < this->materials.size(); ++m) {
const auto & eigen_gradu_vec =
this->materials[m]->getInternal<Real>("eigen_grad_u")(element_type);
const auto & elem_filter =
this->materials[m]->getElementFilter(element_type);
Array<Real> int_eigen_gradu_vec(elem_filter.size(),
spatial_dimension * spatial_dimension,
"int_of_gradu");
fem.integrate(eigen_gradu_vec, int_eigen_gradu_vec,
spatial_dimension * spatial_dimension, element_type,
_not_ghost, elem_filter);
for (UInt k = 0; k < elem_filter.size(); ++k)
/// averaging is done only for normal components, so stress and strain
/// are equal
average +=
int_eigen_gradu_vec(k, row_index * spatial_dimension + col_index);
}
} else {
AKANTU_DEBUG_ERROR("Averaging not implemented for this field!!!");
}
}
return average / this->volume;
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void SolidMechanicsModelRVE::homogenizeStiffness(Matrix<Real> & C_macro) {
AKANTU_DEBUG_IN();
const UInt dim = 2;
AKANTU_DEBUG_ASSERT(this->spatial_dimension == dim,
"Is only implemented for 2D!!!");
/// apply three independent loading states to determine C
/// 1. eps_el = (1;0;0) 2. eps_el = (0,1,0) 3. eps_el = (0,0,0.5)
/// clear the eigenstrain
Matrix<Real> zero_eigengradu(dim, dim, 0.);
GhostType gt = _not_ghost;
for (auto element_type : mesh.elementTypes(dim, gt, _ek_not_defined)) {
auto & prestrain_vect =
const_cast<Array<Real> &>(this->getMaterial("gel").getInternal<Real>(
"eigen_grad_u")(element_type));
auto prestrain_it =
prestrain_vect.begin(spatial_dimension, spatial_dimension);
auto prestrain_end =
prestrain_vect.end(spatial_dimension, spatial_dimension);
for (; prestrain_it != prestrain_end; ++prestrain_it)
(*prestrain_it) = zero_eigengradu;
}
/// storage for results of 3 different loading states
UInt voigt_size = VoigtHelper<dim>::size;
Matrix<Real> stresses(voigt_size, voigt_size, 0.);
Matrix<Real> strains(voigt_size, voigt_size, 0.);
Matrix<Real> H(dim, dim, 0.);
/// save the damage state before filling up cracks
// ElementTypeMapReal saved_damage("saved_damage");
// saved_damage.initialize(getFEEngine(), _nb_component = 1, _default_value =
// 0);
// this->fillCracks(saved_damage);
/// virtual test 1:
H(0, 0) = 0.01;
this->performVirtualTesting(H, stresses, strains, 0);
/// virtual test 2:
H.clear();
H(1, 1) = 0.01;
this->performVirtualTesting(H, stresses, strains, 1);
/// virtual test 3:
H.clear();
H(0, 1) = 0.01;
this->performVirtualTesting(H, stresses, strains, 2);
/// drain cracks
// this->drainCracks(saved_damage);
/// compute effective stiffness
Matrix<Real> eps_inverse(voigt_size, voigt_size);
eps_inverse.inverse(strains);
C_macro.mul<false, false>(stresses, eps_inverse);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void SolidMechanicsModelRVE::performVirtualTesting(const Matrix<Real> & H,
Matrix<Real> & eff_stresses,
Matrix<Real> & eff_strains,
const UInt test_no) {
AKANTU_DEBUG_IN();
this->applyBoundaryConditions(H);
auto & solver = this->getNonLinearSolver();
solver.set("max_iterations", 2);
solver.set("threshold", 1e-6);
solver.set("convergence_type", _scc_solution);
this->solveStep();
/// get average stress and strain
eff_stresses(0, test_no) = this->averageTensorField(0, 0, "stress");
eff_strains(0, test_no) = this->averageTensorField(0, 0, "strain");
eff_stresses(1, test_no) = this->averageTensorField(1, 1, "stress");
eff_strains(1, test_no) = this->averageTensorField(1, 1, "strain");
eff_stresses(2, test_no) = this->averageTensorField(1, 0, "stress");
eff_strains(2, test_no) = 2. * this->averageTensorField(1, 0, "strain");
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void SolidMechanicsModelRVE::homogenizeEigenGradU(
Matrix<Real> & eigen_gradu_macro) {
AKANTU_DEBUG_IN();
eigen_gradu_macro(0, 0) = this->averageTensorField(0, 0, "eigen_grad_u");
eigen_gradu_macro(1, 1) = this->averageTensorField(1, 1, "eigen_grad_u");
eigen_gradu_macro(0, 1) = this->averageTensorField(0, 1, "eigen_grad_u");
eigen_gradu_macro(1, 0) = this->averageTensorField(1, 0, "eigen_grad_u");
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void SolidMechanicsModelRVE::initMaterials() {
AKANTU_DEBUG_IN();
// make sure the material are instantiated
if (!are_materials_instantiated)
instantiateMaterials();
if (use_RVE_mat_selector) {
const Vector<Real> & lowerBounds = mesh.getLowerBounds();
const Vector<Real> & upperBounds = mesh.getUpperBounds();
Real bottom = lowerBounds(1);
Real top = upperBounds(1);
Real box_size = std::abs(top - bottom);
Real eps = box_size * 1e-6;
auto tmp = std::make_shared<GelMaterialSelector>(*this, box_size, "gel",
this->nb_gel_pockets, eps);
tmp->setFallback(material_selector);
material_selector = tmp;
}
SolidMechanicsModel::initMaterials();
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void SolidMechanicsModelRVE::fillCracks(ElementTypeMapReal & saved_damage) {
const auto & mat_gel = this->getMaterial("gel");
Real E_gel = mat_gel.get("E");
Real E_homogenized = 0.;
for (auto && mat : materials) {
if (mat->getName() == "gel" || mat->getName() == "FE2_mat")
continue;
Real E = mat->get("E");
auto & damage = mat->getInternal<Real>("damage");
for (auto && type : damage.elementTypes()) {
const auto & elem_filter = mat->getElementFilter(type);
auto nb_integration_point = getFEEngine().getNbIntegrationPoints(type);
auto sav_dam_it =
make_view(saved_damage(type), nb_integration_point).begin();
for (auto && data :
zip(elem_filter, make_view(damage(type), nb_integration_point))) {
auto el = std::get<0>(data);
auto & dam = std::get<1>(data);
Vector<Real> sav_dam = sav_dam_it[el];
sav_dam = dam;
for (auto q : arange(dam.size())) {
E_homogenized = (E_gel - E) * dam(q) + E;
dam(q) = 1. - (E_homogenized / E);
}
}
}
}
}
/* -------------------------------------------------------------------------- */
void SolidMechanicsModelRVE::drainCracks(
const ElementTypeMapReal & saved_damage) {
for (auto && mat : materials) {
if (mat->getName() == "gel" || mat->getName() == "FE2_mat")
continue;
auto & damage = mat->getInternal<Real>("damage");
for (auto && type : damage.elementTypes()) {
const auto & elem_filter = mat->getElementFilter(type);
auto nb_integration_point = getFEEngine().getNbIntegrationPoints(type);
auto sav_dam_it = make_view(saved_damage(type), nb_integration_point).begin();
for (auto && data :
zip(elem_filter, make_view(damage(type), nb_integration_point))) {
auto el = std::get<0>(data);
auto & dam = std::get<1>(data);
Vector<Real> sav_dam = sav_dam_it[el];
dam = sav_dam;
}
}
}
}
} // namespace akantu
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