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phasefield.cc
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phasefield.cc
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/**
* Copyright (©) 2020-2023 EPFL (Ecole Polytechnique Fédérale de Lausanne)
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
* This file is part of Akantu
*
* 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 "phasefield.hh"
#include "aka_common.hh"
#include "phase_field_model.hh"
#include "random_internal_field.hh"
/* -------------------------------------------------------------------------- */
namespace akantu {
/* -------------------------------------------------------------------------- */
PhaseField::PhaseField(PhaseFieldModel & model, const ID & id,
const ID & fe_engine_id)
: Parent(model, id, model.getSpatialDimension(), _ek_regular, fe_engine_id),
g_c(this->registerInternal<Real, DefaultRandomInternalField>(
"g_c", 1, fe_engine_id)),
damage_on_qpoints(this->registerInternal("damage", 1, fe_engine_id)),
gradd(this->registerInternal("grad_d", spatial_dimension, fe_engine_id)),
phi(this->registerInternal("phi", 1, fe_engine_id)),
strain(this->registerInternal(
"strain", spatial_dimension * spatial_dimension, fe_engine_id)),
driving_force(this->registerInternal("driving_force", 1, fe_engine_id)),
driving_energy(this->registerInternal("driving_energy", spatial_dimension,
fe_engine_id)),
damage_energy(this->registerInternal(
"damage_energy", spatial_dimension * spatial_dimension,
fe_engine_id)),
damage_energy_density(
this->registerInternal("damage_energy_density", 1, fe_engine_id)),
dissipated_energy(
this->registerInternal("dissipated_energy", 1, fe_engine_id)) {
this->phi.initializeHistory();
this->registerParam("l0", l0, Real(0.), _pat_parsable | _pat_readable,
"length scale parameter");
this->registerParam("gc", g_c, _pat_parsable | _pat_readable,
"critical local fracture energy density");
this->registerParam("E", E, _pat_parsable | _pat_readable, "Young's modulus");
this->registerParam("nu", nu, _pat_parsable | _pat_readable, "Poisson ratio");
this->registerParam("isotropic", isotropic, true,
_pat_parsable | _pat_readable,
"Use isotropic formulation");
}
/* -------------------------------------------------------------------------- */
void PhaseField::updateInternalParameters() {
this->lambda = this->nu * this->E / ((1 + this->nu) * (1 - 2 * this->nu));
this->mu = this->E / (2 * (1 + this->nu));
Parent::updateInternalParameters();
}
/* -------------------------------------------------------------------------- */
void PhaseField::computeAllDrivingForces(GhostType ghost_type) {
auto & damage = handler.getDamage();
auto & fem = this->getFEEngine();
for (const auto & type : this->getElementFilter().elementTypes(
this->spatial_dimension, ghost_type)) {
auto & elem_filter = this->getElementFilter(type, ghost_type);
if (elem_filter.empty()) {
continue;
}
// compute the damage on quadrature points
auto & damage_interpolated = damage_on_qpoints(type, ghost_type);
fem.interpolateOnIntegrationPoints(damage, damage_interpolated, 1, type,
ghost_type);
auto & gradd_vect = gradd(type, _not_ghost);
/// compute @f$\nabla u@f$
fem.gradientOnIntegrationPoints(damage, gradd_vect, 1, type, ghost_type,
elem_filter);
computeDrivingForce(type, ghost_type);
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void PhaseField::assembleInternalForces(GhostType ghost_type) {
Array<Real> & internal_force = handler.getInternalForce();
auto & fem = this->getFEEngine();
for (auto type : getElementFilter().elementTypes(_ghost_type = ghost_type)) {
auto & elem_filter = getElementFilter(type, ghost_type);
if (elem_filter.empty()) {
continue;
}
auto nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
auto & driving_force_vect = driving_force(type, ghost_type);
Array<Real> nt_driving_force(0, nb_nodes_per_element);
fem.computeNtb(driving_force_vect, nt_driving_force, type, ghost_type,
elem_filter);
Array<Real> int_nt_driving_force(0, nb_nodes_per_element);
fem.integrate(nt_driving_force, int_nt_driving_force, nb_nodes_per_element,
type, ghost_type, elem_filter);
handler.getDOFManager().assembleElementalArrayLocalArray(
int_nt_driving_force, internal_force, type, ghost_type, -1,
elem_filter);
// damage_energy_on_qpoints = gc*l0 = scalar
auto & driving_energy_vect = driving_energy(type, ghost_type);
Array<Real> bt_driving_energy(0, nb_nodes_per_element);
fem.computeBtD(driving_energy_vect, bt_driving_energy, type, ghost_type,
elem_filter);
Array<Real> int_bt_driving_energy(0, nb_nodes_per_element);
fem.integrate(bt_driving_energy, int_bt_driving_energy,
nb_nodes_per_element, type, ghost_type, elem_filter);
handler.getDOFManager().assembleElementalArrayLocalArray(
int_bt_driving_energy, internal_force, type, ghost_type, -1,
elem_filter);
}
}
/* -------------------------------------------------------------------------- */
void PhaseField::assembleStiffnessMatrix(GhostType ghost_type) {
AKANTU_DEBUG_INFO("Assemble the new stiffness matrix");
auto & fem = this->getFEEngine();
for (auto type :
getElementFilter().elementTypes(spatial_dimension, ghost_type)) {
auto & elem_filter = getElementFilter(type, ghost_type);
if (elem_filter.empty()) {
return;
}
auto nb_element = elem_filter.size();
auto nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
auto nb_quadrature_points = fem.getNbIntegrationPoints(type, ghost_type);
auto nt_b_n = std::make_unique<Array<Real>>(
nb_element * nb_quadrature_points,
nb_nodes_per_element * nb_nodes_per_element, "N^t*b*N");
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");
// damage_energy_density_on_qpoints = gc/l0 + phi = scalar
auto & damage_energy_density_vect = damage_energy_density(type, ghost_type);
// damage_energy_on_qpoints = gc*l0 = scalar
auto & damage_energy_vect = damage_energy(type, ghost_type);
fem.computeBtDB(damage_energy_vect, *bt_d_b, 2, type, ghost_type,
elem_filter);
fem.computeNtbN(damage_energy_density_vect, *nt_b_n, type, ghost_type,
elem_filter);
/// compute @f$ K_{\grad d} = \int_e \mathbf{N}^t * \mathbf{w} *
/// \mathbf{N}@f$
auto K_n = std::make_unique<Array<Real>>(
nb_element, nb_nodes_per_element * nb_nodes_per_element, "K_n");
fem.integrate(*nt_b_n, *K_n, nb_nodes_per_element * nb_nodes_per_element,
type, ghost_type, elem_filter);
handler.getDOFManager().assembleElementalMatricesToMatrix(
"K", "damage", *K_n, type, _not_ghost, _symmetric, elem_filter);
/// 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, elem_filter);
handler.getDOFManager().assembleElementalMatricesToMatrix(
"K", "damage", *K_b, type, _not_ghost, _symmetric, elem_filter);
}
}
/* -------------------------------------------------------------------------- */
void PhaseField::computeDissipatedEnergyByElements() {
const Array<Real> & damage = handler.getDamage();
auto & fem = this->getFEEngine();
for (auto type :
getElementFilter().elementTypes(spatial_dimension, _not_ghost)) {
Array<Idx> & elem_filter = getElementFilter(type, _not_ghost);
if (elem_filter.empty()) {
continue;
}
Array<Real> & damage_interpolated = damage_on_qpoints(type, _not_ghost);
// compute the damage on quadrature points
fem.interpolateOnIntegrationPoints(damage, damage_interpolated, 1, type,
_not_ghost);
Array<Real> & gradd_vect = gradd(type, _not_ghost);
/// compute @f$\nabla u@f$
fem.gradientOnIntegrationPoints(damage, gradd_vect, 1, type, _not_ghost,
elem_filter);
computeDissipatedEnergy(type);
}
}
/* -------------------------------------------------------------------------- */
void PhaseField::computeDissipatedEnergy(ElementType /*unused*/) {
AKANTU_TO_IMPLEMENT();
}
/* -------------------------------------------------------------------------- */
PhaseFieldFactory & PhaseField::getFactory() {
return PhaseFieldFactory::getInstance();
}
/* -------------------------------------------------------------------------- */
Real PhaseField::getEnergy(const ID & energy_id) {
if (energy_id != "dissipated") {
return 0.;
}
Real edis = 0.;
auto & fem = this->getFEEngine();
computeDissipatedEnergyByElements();
/// integrate the dissipated energy for each type of elements
for (auto type :
getElementFilter().elementTypes(spatial_dimension, _not_ghost)) {
edis += fem.integrate(dissipated_energy(type, _not_ghost), type, _not_ghost,
getElementFilter(type, _not_ghost));
}
return edis;
}
/* -------------------------------------------------------------------------- */
Real PhaseField::getEnergy(const ID & energy_id, const Element & element) {
if (energy_id != "dissipated") {
return 0.;
}
auto & fem = this->getFEEngine();
Vector<Real> edis_on_quad_points(fem.getNbIntegrationPoints(element.type));
computeDissipatedEnergyByElement(element.type, element.element,
edis_on_quad_points);
return fem.integrate(edis_on_quad_points, element);
}
/* -------------------------------------------------------------------------- */
void PhaseField::beforeSolveStep() {
this->savePreviousState();
this->computeAllDrivingForces(_not_ghost);
}
} // namespace akantu

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