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rAKA/src/model/phase_field/phase_field_model.cc
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phase_field_model.cc
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/**
* @file phase_field_model.cc
*
* @author Mohit Pundir <mohit.pundir@epfl.ch>
*
* @date creation: Wed Aug 01 2018
* @date last modification: Wed Aug 01 2018
*
* @brief Implementation of PhaseFieldModel class
*
* @section LICENSE
*
* Copyright (©) 2010-2018 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 "phase_field_model.hh"
#include "dumpable_inline_impl.hh"
#include "element_synchronizer.hh"
#include "generalized_trapezoidal.hh"
#include "fe_engine_template.hh"
#include "group_manager_inline_impl.cc"
#include "integrator_gauss.hh"
#include "mesh.hh"
#include "parser.hh"
#include "shape_lagrange.hh"
#ifdef AKANTU_USE_IOHELPER
#include "dumper_element_partition.hh"
#include "dumper_elemental_field.hh"
#include "dumper_internal_material_field.hh"
#include "dumper_iohelper_paraview.hh"
#endif
/* -------------------------------------------------------------------------- */
namespace akantu {
// material functor can be created
/* -------------------------------------------------------------------------- */
PhaseFieldModel::PhaseFieldModel(Mesh & mesh, UInt dim, const ID & id,
const MemoryID & memory_id)
: Model(mesh, ModelType::_phase_field_model, dim, id, memory_id),
damage_gradient("damage_gradient", id),
damage_on_qpoints("damage_on_qpoints", id),
strain_history_on_qpoints("strain_history_on_qpoints", id),
strain_on_qpoints("strain_on_qpoints", id){
AKANTU_DEBUG_IN();
this->initDOFManager();
this->registerDataAccessor(*this);
if (this->mesh.isDistributed()) {
auto & synchronizer = this->mesh.getElementSynchronizer();
this->registerSynchronizer(synchronizer, _gst_pfm_damage);
this->registerSynchronizer(synchronizer, _gst_pfm_gradient_damage);
}
registerFEEngineObject<FEEngineType>(id + ":fem", mesh, spatial_dimension);
#ifdef AKANTU_USE_IOHELPER
this->mesh.registerDumper<DumperParaview>("phase_field", id, true);
this->mesh.addDumpMesh(mesh, spatial_dimension, _not_ghost, _ek_regular);
#endif // AKANTU_USE_IOHELPER
this->registerParam("l0", l_0, 0., _pat_parsmod, "length scale");
this->registerParam("gc", g_c, _pat_parsmod, "critical local fracture energy density");
this->registerParam("lambda", lame_lambda, _pat_parsmod, "lame parameter lambda");
this->registerParam("mu", lame_mu, _pat_parsmod, "lame paramter mu");
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void PhaseFieldModel::initModel() {
auto & fem = this->getFEEngine();
fem.initShapeFunctions(_not_ghost);
fem.initShapeFunctions(_ghost);
damage_on_qpoints.initialize(fem, _nb_component = 1);
damage_gradient.initialize(fem, _nb_component = spatial_dimension);
strain_on_qpoints.initialize(fem, _nb_component = spatial_dimension);
strain_history_on_qpoints.initialize(fem, _nb_component = 1);
}
/* -------------------------------------------------------------------------- */
PhaseFieldModel::~PhaseFieldModel() = default;
/* -------------------------------------------------------------------------- */
void PhaseFieldModel::assembleMatrix(const ID & matrix_id) {
if (matrix_id == "K") {
this->assembleDamageMatrix();
} else if (matrix_id == "M") { // (and need_to_reassemble_capacity) {
this->assembleDamageGradMatrix();
}
}
/* -------------------------------------------------------------------------- */
void PhaseFieldModel::initSolver(TimeStepSolverType time_step_solver_type,
NonLinearSolverType) {
DOFManager & dof_manager = this->getDOFManager();
this->allocNodalField(this->damage, "damage");
this->allocNodalField(this->external_force, "external_force");
this->allocNodalField(this->internal_force, "internal_force");
this->allocNodalField(this->blocked_dofs, "blocked_dofs");
if (!dof_manager.hasDOFs("damage")) {
dof_manager.registerDOFs("damage", *this->damage, _dst_nodal);
dof_manager.registerBlockedDOFs("damage", *this->blocked_dofs);
}
if (time_step_solver_type == _tsst_dynamic ||
time_step_solver_type == _tsst_dynamic_lumped) {
this->allocNodalField(this->damage_gradient, "damage_gradient");
if (!dof_manager.hasDOFsDerivatives("damage", 1)) {
dof_manager.registerDOFsDerivative("damage", 1,
*this->damage_gradient);
}
}
}
/* -------------------------------------------------------------------------- */
void PhaseFieldModel::assembleDamageMatrix() {
AKANTU_DEBUG_IN();
AKANTU_DEBUG_INFO("Assemble the new damage matrix");
this->computeStrainHistoryOnQuadPoints(_not_ghost);
if (!this->getDOFManager().hasMatrix("K")) {
this->getDOFManager().getNewMatrix("K", getMatrixType("K"));
}
this->getDOFManager().clearMatrix("K");
switch (mesh.getSpatialDimension()) {
case 1:
this->assembleDamageMatrix<1>(_not_ghost);
break;
case 2:
this->assembleDamageMatrix<2>(_not_ghost);
break;
case 3:
this->assembleDamageMatrix<3>(_not_ghost);
break;
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void PhaseFieldModel::assembleDamageGradMatrix() {
AKANTU_DEBUG_IN();
AKANTU_DEBUG_INFO("Assemble the new damage gradient matrix");
if (!this->getDOFManager().hasMatrix("K")) {
this->getDOFManager().getNewMatrix("K", getMatrixType("K"));
}
this->getDOFManager().clearMatrix("K");
switch (mesh.getSpatialDimension()) {
case 1:
this->assembleDamageGradMatrix<1>(_not_ghost);
break;
case 2:
this->assembleDamageGradMatrix<2>(_not_ghost);
break;
case 3:
this->assembleDamageGradMatrix<3>(_not_ghost);
break;
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
std::tuple<ID, TimeStepSolverType>
PhaseFieldModel::getDefaultSolverID(const AnalysisMethod & method) {
switch (method) {
case _explicit_lumped_mass: {
return std::make_tuple("explicit_lumped", _tsst_dynamic_lumped);
}
case _static: {
return std::make_tuple("static", _tsst_static);
}
case _implicit_dynamic: {
return std::make_tuple("implicit", _tsst_dynamic);
}
default:
return std::make_tuple("unknown", _tsst_not_defined);
}
}
/* -------------------------------------------------------------------------- */
ModelSolverOptions PhaseFieldModel::getDefaultSolverOptions(
const TimeStepSolverType & type) const {
ModelSolverOptions options;
switch (type) {
case _tsst_dynamic_lumped: {
options.non_linear_solver_type = _nls_lumped;
options.integration_scheme_type["damage"] = _ist_forward_euler;
options.solution_type["damage"] = IntegrationScheme::_gradient_damage;
break;
}
case _tsst_static: {
options.non_linear_solver_type = _nls_newton_raphson;
options.integration_scheme_type["damage"] = _ist_pseudo_time;
options.solution_type["damage"] = IntegrationScheme::_not_defined;
break;
}
case _tsst_dynamic: {
if (this->method == _explicit_consistent_mass) {
options.non_linear_solver_type = _nls_newton_raphson;
options.integration_scheme_type["damage"] = _ist_forward_euler;
options.solution_type["damage"] = IntegrationScheme::_not_defined;
} else {
options.non_linear_solver_type = _nls_newton_raphson;
options.integration_scheme_type["damage"] = _ist_backward_euler;
options.solution_type["damage"] = IntegrationScheme::_damage;
}
break;
}
default:
AKANTU_EXCEPTION(type << " is not a valid time step solver type");
}
return options;
}
/* -------------------------------------------------------------------------- */
template<UInt dim>
void PhaseFieldModel::assembleDamageMatrix(const GhostType & ghost_type) {
AKANTU_DEBUG_IN();
auto & fem = this->getFEEngine();
for (auto && type : mesh.elementTypes(spatial_dimension, ghost_type)) {
auto nb_element = mesh.getNbElement(type, ghost_type);
auto nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
auto nb_quadrature_points = fem.getNbIntegrationPoints(type, ghost_type);
auto nt_d_n = std::make_unique<Array<Real>>(
nb_element * nb_quadrature_points,
nb_nodes_per_element * nb_nodes_per_element, "N^t*D*N");
// conductivity_on_qpoints = gc*l0 = scalar
fem.computeNtDN(conductivity_on_qpoints(type, ghost_type), *nt_d_n, type,
ghost_type);
/// compute @f$ K_d = \int_e \mathbf{N}^t * \mathbf{D} *
/// \mathbf{N}@f$
auto K_d = std::make_unique<Array<Real>>(
nb_element, nb_nodes_per_element * nb_nodes_per_element, "K_d");
fem.integrate(*nt_d_n, *K_d, nb_nodes_per_element * nb_nodes_per_element,
type, ghost_type);
this->getDOFManager().assembleElementalMatricesToMatrix(
"K", "phasefield", *K_d, type, ghost_type, _symmetric);
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template<UInt dim>
void PhaseFieldModel::assembleDamageGradMatrix(const GhostType & ghost_type) {
AKANTU_DEBUG_IN();
auto & fem = this->getFEEngine();
for (auto && type : mesh.elementTypes(spatial_dimension, ghost_type)) {
auto nb_element = mesh.getNbElement(type, ghost_type);
auto nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
auto nb_quadrature_points = fem.getNbIntegrationPoints(type, ghost_type);
auto bt_d_b = std::make_unique<Array<Real>>(
nb_element * nb_quadrature_points,
nb_nodes_per_element * nb_nodes_per_element, "B^t*D*B");
// conductivity_on_qpoints = gc*l0 = scalar
fem.computeBtDB(conductivity_on_qpoints(type, ghost_type), *bt_d_b, type,
ghost_type);
/// compute @f$ K_{\grad d} = \int_e \mathbf{B}^t * \mathbf{W} *
/// \mathbf{B}@f$
auto K_b = std::make_unique<Array<Real>>(
nb_element, nb_nodes_per_element * nb_nodes_per_element, "K_b");
fem.integrate(*bt_d_b, *K_b, nb_nodes_per_element * nb_nodes_per_element,
type, ghost_type);
this->getDOFManager().assembleElementalMatricesToMatrix(
"K", "phasefield", *K_b, type, ghost_type, _symmetric);
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void PhaseFieldModel::computeStrainHistoryOnQuadPoints(
const GhostType & ghost_type) {
Matrix<Real> epsilon_plus(spatial_dimension, spatial_dimension);
Matrix<Real> epsilon_minus(spatial_dimension, spatial_dimension);
Matrix<Real> epsilon_dir(spatial_dimension, spatial_dimension);
Matrix<Real> epsilon_diag_plus(spatial_dimension, spatial_dimension);
Matrix<Real> epsilon_diag_minus(spatial_dimension, spatial_dimension);
Vector<Real> eigen_values(spatial_dimension);
Real trace_plus, trace_minus, phi_plus;
for (auto & type : mesh.elementTypes(spatial_dimension, ghost_type)) {
for (auto && values :
zip(make_view(strain_on_qpoints(type, ghost_type),
spatial_dimension, spatial_dimension),
make_view(strain_history_on_qpoints(type, ghost_type)))) {
auto & epsilon = std::get<0>(values);
auto & phi_history = std::get<1>(values);
epsilon_plus.clear();
epsilon_minus.clear();
epsilon_dir.clear();
eigen_values.clear();
epsilon_diag_plus.clear();
epsilon_diag_minus.clear();
epsilon.eig(eigen_values, epsilon_dir);
for (UInt i=0; i < spatial_dimension; i++) {
epsilon_diag_plus(i, i) = std::max(Real(0.), eigen_values(i));
epsilon_diag_minus(i, i) = std::min(Real(0.), eigen_values(i));
}
Matrix<Real> mat_tmp(spatial_dimension, spatial_dimension);
Matrix<Real> sigma_plus(spatial_dimension, spatial_dimension);
Matrix<Real> sigma_minus(spatial_dimension, spatial_dimension);
mat_tmp.mul<false,true>(epsilon_diag_plus, epsilon_dir);
epsilon_plus.mul<false, false>(epsilon_dir, mat_tmp);
mat_tmp.mul<false, true>(epsilon_diag_minus, epsilon_dir);
epsilon_minus.mul<false, true>(epsilon_dir, mat_tmp);
trace_plus = std::max(Real(0.), epsilon.trace());
trace_minus = std::min(Real(0.), epsilon.trace());
for (UInt i=0; i < spatial_dimension; i++) {
for (UInt j=0; j < spatial_dimension; j++) {
sigma_plus(i, j) = (i==j) * lame_lambda * trace_plus
+ 2 * lame_mu * epsilon_plus(i, j);
sigma_minus(i, j) = (i==j) * lame_lambda * trace_minus
+ 2 * lame_mu * epsilon_minus(i, j);
}
}
phi_plus = 1./2 * sigma_plus.doubleDot(epsilon);
if (phi_plus > phi_history) {
phi_history = phi_plus;
}
}
}
}
/* -------------------------------------------------------------------------- */
void PhaseFieldModel::assembleResidual() {
AKANTU_DEBUG_IN();
this->assembleInternalForces();
this->getDOFManager().assembleToResidual("damage",
*this->external_force, 1);
this->getDOFManager().assembleToResidual("damage",
*this->internal_force, 1);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void PhaseFieldModel::assembleInternalForces() {
AKANTU_DEBUG_IN();
this->internal_force->clear();
this->synchronize(_gst_pfm_damage);
auto & fem = this->getFEEngine();
for (auto ghost_type: ghost_types) {
for (auto type: mesh.elementTypes(spatial_dimension, ghost_type)) {
UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
auto & strain_history_on_qpoints_vect = strain_history_on_qpoints(type, ghost_type);
UInt nb_quad_points = strain_history_on_qpoints_vect.size();
Array<Real> nt_strain_history(nb_quad_points, nb_nodes_per_element);
fem.computeNtb(strain_history_on_qpoints_vect, nt_strain_history, type, ghost_type);
UInt nb_elements = mesh.getNbElement(type, ghost_type);
Array<Real> int_nt_srain_history(nb_elements, nb_nodes_per_element);
fem.integrate(nt_strain_history, int_nt_srain_history, nb_nodes_per_element, type,
ghost_type);
this->getDOFManager().assembleElementalArrayLocalArray(
int_nt_srain_history, *this->internal_force, type, ghost_type, -1);
}
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void PhaseFieldModel::readMaterials() {
auto sect = this->getParserSection();
if (not std::get<1>(sect)) {
const auto & section = std::get<0>(sect);
this->parseSection(section);
}
gc_on_qpoints.set(g_c);
}
/* -------------------------------------------------------------------------- */
void PhaseFieldModel::initFullImpl(const ModelOptions & options) {
Model::initFullImpl(options);
readMaterials();
}
/* -------------------------------------------------------------------------- */
UInt PhaseFieldModel::getNbData(const Array<Element> & elements,
const SynchronizationTag & tag) const {
AKANTU_DEBUG_IN();
UInt size = 0;
UInt nb_nodes_per_element = 0;
for (const Element & el : elements) {
nb_nodes_per_element += Mesh::getNbNodesPerElement(el.type);
}
switch (tag) {
case _gst_material_id: {
size += elements.size() * sizeof(UInt);
break;
}
case _gst_pfm_damage: {
size += nb_nodes_per_element * sizeof(Real); // damage
break;
}
case _gst_pfm_gradient_damage: {
size += getNbIntegrationPoints(elements) * spatial_dimension * sizeof(Real);
size += nb_nodes_per_element * sizeof(Real);
break;
}
default: { AKANTU_ERROR("Unknown ghost synchronization tag : " << tag); }
}
AKANTU_DEBUG_OUT();
return size;
}
/* -------------------------------------------------------------------------- */
void PhaseFieldModel::packData(CommunicationBuffer & buffer,
const Array<Element> & elements,
const SynchronizationTag & tag) const {
switch (tag) {
case _gst_pfm_damage: {
packNodalDataHelper(*damage, buffer, elements, mesh);
break;
}
case _gst_pfm_gradient_damage: {
packElementalDataHelper(damage_gradient, buffer, elements, true,
getFEEngine());
packNodalDataHelper(*damage, buffer, elements, mesh);
break;
}
default: { AKANTU_ERROR("Unknown ghost synchronization tag : " << tag); }
}
}
/* -------------------------------------------------------------------------- */
void PhaseFieldModel::unpackData(CommunicationBuffer & buffer,
const Array<Element> & elements,
const SynchronizationTag & tag) {
switch (tag) {
case _gst_pfm_damage: {
unpackNodalDataHelper(*damage, buffer, elements, mesh);
break;
}
case _gst_pfm_gradient_damage: {
unpackElementalDataHelper(damage_gradient, buffer, elements, true,
getFEEngine());
unpackNodalDataHelper(*damage, buffer, elements, mesh);
break;
}
default: { AKANTU_ERROR("Unknown ghost synchronization tag : " << tag); }
}
}
/* -------------------------------------------------------------------------- */
void PhaseFieldModel::getNbData(const Array<UInt> & indexes,
const SynchronizationTag & tag) const {
AKANTU_DEBUG_IN();
UInt size = 0;
UInt nb_nodes = indexes.size();
switch (tag) {
case _gst_pfm_damage: {
size += nb_nodes * sizeof(Real);
break;
}
default: { AKANTU_ERROR("Unknown ghost synchronization tag : " << tag); }
}
AKANTU_DEBUG_OUT();
return size;
}
/* -------------------------------------------------------------------------- */
void PhaseFieldModel::packData(CommunicationBuffer & buffer,
const Array<UInt> & indexes,
const SynchronizationTag & tag) const {
AKANTU_DEBUG_IN();
for (auto index : indexes) {
switch (tag) {
case _gst_pfm_damage: {
buffer << (*damage)(index);
break;
}
default: { AKANTU_ERROR("Unknown ghost synchronization tag : " << tag); }
}
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void PhaseFieldModel::unpackData(CommunicationBuffer & buffer,
const Array<UInt> & indexes,
const SynchronizationTag & tag) {
AKANTU_DEBUG_IN();
for (auto index : indexes) {
switch (tag) {
case _gst_pfm_damage: {
buffer >> (*damage)(index);
break;
}
default: { AKANTU_ERROR("Unknown ghost synchronization tag : " << tag); }
}
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
/* -------------------------------------------------------------------------- */
#ifdef AKANTU_USE_IOHELPER
dumper::Field * PhaseFieldModel::createNodalFieldBool(
const std::string & field_name, const std::string & group_name,
__attribute__((unused)) bool padding_flag ) {
std::map<std::string, Array<bool> *> uint_nodal_fields;
uint_nodal_fields["blocked_dofs"] = blocked_dofs;
dumper::Field * field = nullptr;
field = mesh.createNodalFieldBool(uint_nodal_fields[field_name], group_name);
return field;
}
/* -------------------------------------------------------------------------- */
dumper::Field * PhaseFieldModel::createNodalFieldReal(
const std::string & field_name, const std::string & group_name,
__attribute__((unused)) bool padding_flag) {
if (field_name == "capacity_lumped") {
AKANTU_EXCEPTION("Capacity lumped is a nodal field now stored in the DOF manager."
"Therefore it cannot be used by a dumper anymore");
}
std::map<std::string, Array<Real> *> real_nodal_fields;
real_nodal_fields["damage"] = damage;
dumper::Field * field =
mesh.createNodalField(real_nodal_fields[field_name], group_name);
return field;
}
/* -------------------------------------------------------------------------- */
dumper::Field * PhaseFieldModel::createElementalField(
const std::string & field_name, const std::string & group_name,
__attribute__((unused)) bool padding_flag,
__attribute__((unused)) const UInt & spatial_dimension,
const ElementKind & element_kind) {
dumper::Field * field = nullptr;
if (field_name == "partitions")
field = mesh.createElementalField<UInt, dumper::ElementpartitionField>(
mesh.getConnectivities(), group_name, this->spatial_dimension,
element_kind);
else if (field_name == "damage_gradient") {
ElementTypeMap<UInt> nb_data_per_elem =
this->mesh.getNbDataPerElem(damage_gradient, element_kind);
field = mesh.createElementalField<Real, dumper::InternalMaterialField>(
damage_gradient, group_name, this->spatial_dimension, element_kind,
nb_data_per_elem);
} else if (field_name == "conductivity") {
ElementTypeMap<UInt> nb_data_per_elem =
this->mesh.getNbDataPerElem(conductivity_on_qpoints, element_kind);
field = mesh.createElementalField<Real, dumper::InternalMaterialField>(
conductivity_on_qpoints, group_name, this->spatial_dimension,
element_kind, nb_data_per_elem);
}
return field;
}
/* -------------------------------------------------------------------------- */
#else
/* -------------------------------------------------------------------------- */
dumper::Field * HeatTransferModel::createElementalField(
__attribute__((unused)) const std::string & field_name,
__attribute__((unused)) const std::string & group_name,
__attribute__((unused)) bool padding_flag,
__attribute__((unused)) const ElementKind & element_kind) {
return nullptr;
}
/* -------------------------------------------------------------------------- */
dumper::Field * HeatTransferModel::createNodalFieldBool(
__attribute__((unused)) const std::string & field_name,
__attribute__((unused)) const std::string & group_name,
__attribute__((unused)) bool padding_flag) {
return nullptr;
}
/* -------------------------------------------------------------------------- */
dumper::Field * HeatTransferModel::createNodalFieldReal(
__attribute__((unused)) const std::string & field_name,
__attribute__((unused)) const std::string & group_name,
__attribute__((unused)) bool padding_flag) {
return nullptr;
}
#endif
/* -------------------------------------------------------------------------- */
void PhaseFieldModel::dump(const std::string & dumper_name) {
mesh.dump(dumper_name);
}
/* -------------------------------------------------------------------------- */
void PhaseFieldModel::dump(const std::string & dumper_name, UInt step) {
mesh.dump(dumper_name, step);
}
/* -------------------------------------------------------------------------- */
void PhaseFieldModel::dump(const std::string & dumper_name, Real time,
UInt step) {
mesh.dump(dumper_name, time, step);
}
/* -------------------------------------------------------------------------- */
void PhaseFieldModel::dump() { mesh.dump(); }
/* -------------------------------------------------------------------------- */
void PhaseFieldModel::dump(UInt step) { mesh.dump(step); }
/* -------------------------------------------------------------------------- */
void PhaseFieldModel::dump(Real time, UInt step) { mesh.dump(time, step); }
/* -------------------------------------------------------------------------- */
} // akantu
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