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test_cohesive_intrinsic_tetrahedron.cc
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rAKA akantu
test_cohesive_intrinsic_tetrahedron.cc
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/**
* @file test_cohesive_intrinsic_tetrahedron.cc
*
* @author Marco Vocialta <marco.vocialta@epfl.ch>
*
* @date creation: Tue Aug 27 2013
* @date last modification: Mon Dec 18 2017
*
* @brief Test for cohesive elements
*
* @section LICENSE
*
* Copyright (©) 2014-2018 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 <fstream>
#include <iostream>
#include <limits>
/* -------------------------------------------------------------------------- */
#include "material_cohesive.hh"
#include "solid_mechanics_model_cohesive.hh"
/* -------------------------------------------------------------------------- */
using namespace akantu;
class Checker {
public:
Checker(const SolidMechanicsModelCohesive & model,
const Array<UInt> & elements, ElementType type);
void check(const Vector<Real> & opening, const Matrix<Real> & rotation) {
checkTractions(opening, rotation);
checkEquilibrium();
computeEnergy(opening);
}
void updateDisplacement(const Vector<Real> & increment);
protected:
void checkTractions(const Vector<Real> & opening,
const Matrix<Real> & rotation);
void checkEquilibrium();
void checkResidual(const Matrix<Real> & rotation);
void computeEnergy(const Vector<Real> & opening);
private:
std::set<UInt> nodes_to_check;
const SolidMechanicsModelCohesive & model;
ElementType type;
// const Array<UInt> & elements;
const Material & mat_cohesive;
Real sigma_c;
const Real beta;
const Real G_c;
const Real delta_0;
const Real kappa;
Real delta_c;
const UInt spatial_dimension;
const ElementType type_facet;
const ElementType type_cohesive;
const Array<Real> & traction;
const Array<Real> & damage;
const UInt nb_quad_per_el;
const UInt nb_element;
const Real beta2_kappa2;
const Real beta2_kappa;
Vector<Real> theoretical_traction;
Vector<Real> traction_old;
Vector<Real> opening_old;
Real Ed;
};
/* -------------------------------------------------------------------------- */
int main(int argc, char * argv[]) {
initialize("material_tetrahedron.dat", argc, argv);
// debug::setDebugLevel(dblDump);
const UInt spatial_dimension = 3;
const UInt max_steps = 60;
const Real increment_constant = 0.01;
Math::setTolerance(1.e-12);
const ElementType type = _tetrahedron_10;
Mesh mesh(spatial_dimension);
mesh.read("tetrahedron.msh");
SolidMechanicsModelCohesive model(mesh);
model.getElementInserter().setLimit(_x, -0.01, 0.01);
/// model initialization
model.initFull();
Array<bool> & boundary = model.getBlockedDOFs();
boundary.set(true);
UInt nb_element = mesh.getNbElement(type);
model.setBaseName("intrinsic_tetrahedron");
model.addDumpFieldVector("displacement");
model.addDumpField("internal_force");
model.dump();
model.setBaseNameToDumper("cohesive elements",
"cohesive_elements_tetrahedron");
model.addDumpFieldVectorToDumper("cohesive elements", "displacement");
model.addDumpFieldToDumper("cohesive elements", "damage");
model.dump("cohesive elements");
/// find elements to displace
Array<UInt> elements;
Vector<Real> bary(spatial_dimension);
for (UInt el = 0; el < nb_element; ++el) {
mesh.getBarycenter({type, el, _not_ghost}, bary);
if (bary(_x) > 0.01)
elements.push_back(el);
}
/// rotate mesh
Real angle = 1.;
// clang-format off
Matrix<Real> rotation{
{std::cos(angle), std::sin(angle) * -1., 0.},
{std::sin(angle), std::cos(angle), 0.},
{0., 0., 1.}};
// clang-format on
Vector<Real> increment_tmp{increment_constant, 2. * increment_constant,
3. * increment_constant};
Vector<Real> increment = rotation * increment_tmp;
auto & position = mesh.getNodes();
auto position_it = position.begin(spatial_dimension);
auto position_end = position.end(spatial_dimension);
for (; position_it != position_end; ++position_it) {
auto & pos = *position_it;
pos = rotation * pos;
}
model.dump();
model.dump("cohesive elements");
/// find nodes to check
Checker checker(model, elements, type);
checker.updateDisplacement(increment);
Real theoretical_Ed = 0;
Vector<Real> opening(spatial_dimension, 0.);
Vector<Real> opening_old(spatial_dimension, 0.);
/// Main loop
for (UInt s = 1; s <= max_steps; ++s) {
model.solveStep();
model.dump();
model.dump("cohesive elements");
opening += increment_tmp;
checker.check(opening, rotation);
checker.updateDisplacement(increment);
}
model.dump();
model.dump("cohesive elements");
Real Ed = model.getEnergy("dissipated");
theoretical_Ed *= 4.;
std::cout << Ed << " " << theoretical_Ed << std::endl;
if (!Math::are_float_equal(Ed, theoretical_Ed) || std::isnan(Ed)) {
std::cout << "The dissipated energy is incorrect" << std::endl;
finalize();
return EXIT_FAILURE;
}
finalize();
std::cout << "OK: test_cohesive_intrinsic_tetrahedron was passed!"
<< std::endl;
return EXIT_SUCCESS;
}
/* -------------------------------------------------------------------------- */
void Checker::updateDisplacement(const Vector<Real> & increment) {
Mesh & mesh = model.getFEEngine().getMesh();
const auto & connectivity = mesh.getConnectivity(type);
auto & displacement = model.getDisplacement();
Array<bool> update(displacement.size());
update.clear();
auto conn_it = connectivity.begin(connectivity.getNbComponent());
auto conn_end = connectivity.begin(connectivity.getNbComponent());
for (; conn_it != conn_end; ++conn_it) {
const auto & conn = *conn_it;
for (UInt n = 0; n < conn.size(); ++n) {
UInt node = conn(n);
if (!update(node)) {
Vector<Real> node_disp(displacement.data() +
node * spatial_dimension,
spatial_dimension);
node_disp += increment;
update(node) = true;
}
}
}
}
/* -------------------------------------------------------------------------- */
Checker::Checker(const SolidMechanicsModelCohesive & model,
const Array<UInt> & elements, ElementType type)
: model(model), type(std::move(type)), // elements(elements),
mat_cohesive(model.getMaterial(1)), sigma_c(mat_cohesive.get("sigma_c")),
beta(mat_cohesive.get("beta")), G_c(mat_cohesive.get("G_c")),
delta_0(mat_cohesive.get("delta_0")), kappa(mat_cohesive.get("kappa")),
spatial_dimension(model.getSpatialDimension()),
type_facet(Mesh::getFacetType(type)),
type_cohesive(FEEngine::getCohesiveElementType(type_facet)),
traction(mat_cohesive.getArray<Real>("tractions", type_cohesive)),
damage(mat_cohesive.getArray<Real>("damage", type_cohesive)),
nb_quad_per_el(model.getFEEngine("CohesiveFEEngine")
.getNbIntegrationPoints(type_cohesive)),
nb_element(model.getMesh().getNbElement(type_cohesive)),
beta2_kappa2(beta * beta / kappa / kappa),
beta2_kappa(beta * beta / kappa) {
const Mesh & mesh = model.getMesh();
const auto & connectivity = mesh.getConnectivity(type);
const auto & position = mesh.getNodes();
auto conn_it = connectivity.begin(connectivity.getNbComponent());
for (const auto & element : elements) {
Vector<UInt> conn_el(conn_it[element]);
for (UInt n = 0; n < conn_el.size(); ++n) {
UInt node = conn_el(n);
if (Math::are_float_equal(position(node, _x), 0.))
nodes_to_check.insert(node);
}
}
delta_c = 2 * G_c / sigma_c;
sigma_c *= delta_c / (delta_c - delta_0);
}
/* -------------------------------------------------------------------------- */
void Checker::checkTractions(const Vector<Real> & opening,
const Matrix<Real> & rotation) {
auto normal_opening = opening * Vector<Real>{1., 0., 0.};
auto tangential_opening = opening - normal_opening;
const Real normal_opening_norm = normal_opening.norm();
const Real tangential_opening_norm = tangential_opening.norm();
const Real delta =
std::max(std::sqrt(tangential_opening_norm * tangential_opening_norm *
beta2_kappa2 +
normal_opening_norm * normal_opening_norm),
0.);
Real theoretical_damage = std::min(delta / delta_c, 1.);
theoretical_traction = (tangential_opening * beta2_kappa + normal_opening) *
sigma_c / delta * (1. - theoretical_damage);
// adjust damage
theoretical_damage = std::max((delta - delta_0) / (delta_c - delta_0), 0.);
theoretical_damage = std::min(theoretical_damage, 1.);
Vector<Real> theoretical_traction_rotated = rotation * theoretical_traction;
std::for_each(
traction.begin(spatial_dimension), traction.end(spatial_dimension),
[&theoretical_traction_rotated](auto && traction) {
Real diff =
Vector<Real>(theoretical_traction_rotated - traction).norm<L_inf>();
if (diff > 1e-14)
throw std::domain_error("Tractions are incorrect");
});
std::for_each(damage.begin(), damage.end(),
[&theoretical_damage](auto && damage) {
if (not Math::are_float_equal(theoretical_damage, damage))
throw std::domain_error("Damage is incorrect");
});
}
/* -------------------------------------------------------------------------- */
void Checker::computeEnergy(const Vector<Real> & opening) {
/// compute energy
auto Do = opening - opening_old;
auto Dt = traction_old + theoretical_traction;
Ed += .5 * Do.dot(Dt);
opening_old = opening;
traction_old = theoretical_traction;
}
/* -------------------------------------------------------------------------- */
void Checker::checkEquilibrium() {
Vector<Real> residual_sum(spatial_dimension, 0.);
const auto & residual = model.getInternalForce();
auto res_it = residual.begin(spatial_dimension);
auto res_end = residual.end(spatial_dimension);
for (; res_it != res_end; ++res_it)
residual_sum += *res_it;
if (!Math::are_float_equal(residual_sum.norm<L_inf>(), 0.))
throw std::domain_error("System is not in equilibrium!");
}
/* -------------------------------------------------------------------------- */
void Checker::checkResidual(const Matrix<Real> & rotation) {
Vector<Real> total_force(spatial_dimension, 0.);
const auto & residual = model.getInternalForce();
for (auto node : nodes_to_check) {
Vector<Real> res(residual.begin(spatial_dimension)[node]);
total_force += res;
}
Vector<Real> theoretical_total_force(spatial_dimension);
theoretical_total_force.mul<false>(rotation, theoretical_traction);
theoretical_total_force *= -1 * 2 * 2;
for (UInt s = 0; s < spatial_dimension; ++s) {
if (!Math::are_float_equal(total_force(s), theoretical_total_force(s))) {
std::cout << "Total force isn't correct!" << std::endl;
std::terminate();
}
}
}
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