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test_cohesive_extrinsic_fatigue.cc
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test_cohesive_extrinsic_fatigue.cc
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/**
* @file test_cohesive_extrinsic_fatigue.cc
*
* @author Marco Vocialta <marco.vocialta@epfl.ch>
*
* @date creation: Fri Feb 20 2015
* @date last modification: Tue Feb 20 2018
*
* @brief Test for the linear fatigue cohesive law
*
*
* @section LICENSE
*
* Copyright (©) 2015-2021 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_cohesive_linear_fatigue.hh"
#include "solid_mechanics_model_cohesive.hh"
#include <limits>
/* -------------------------------------------------------------------------- */
using namespace akantu;
// the following class contains an implementation of the 1D linear
// fatigue cohesive law
class MaterialFatigue {
public:
MaterialFatigue(Real delta_f, Real sigma_c, Real delta_c)
: delta_f(delta_f), sigma_c(sigma_c), delta_c(delta_c), delta_prec(0),
traction(sigma_c), delta_max(0),
stiff_plus(std::numeric_limits<Real>::max()),
tolerance(Math::getTolerance()){};
Real computeTraction(Real delta) {
if (delta - delta_c > -tolerance)
traction = 0;
else if (delta_max < tolerance && delta < tolerance)
traction = sigma_c;
else {
Real delta_dot = delta - delta_prec;
if (delta_dot > -tolerance) {
stiff_plus *= 1 - delta_dot / delta_f;
traction += stiff_plus * delta_dot;
Real max_traction = sigma_c * (1 - delta / delta_c);
if (traction - max_traction > -tolerance || delta_max < tolerance) {
traction = max_traction;
stiff_plus = traction / delta;
}
} else {
Real stiff_minus = traction / delta_prec;
stiff_plus += (stiff_plus - stiff_minus) * delta_dot / delta_f;
traction += stiff_minus * delta_dot;
}
}
delta_prec = delta;
delta_max = std::max(delta, delta_max);
return traction;
}
private:
const Real delta_f;
const Real sigma_c;
const Real delta_c;
Real delta_prec;
Real traction;
Real delta_max;
Real stiff_plus;
const Real tolerance;
};
void imposeOpening(SolidMechanicsModelCohesive &, Real);
void arange(Array<Real> &, Real, Real, Real);
/* -------------------------------------------------------------------------- */
int main(int argc, char * argv[]) {
initialize("material_fatigue.dat", argc, argv);
Math::setTolerance(1e-13);
const UInt spatial_dimension = 2;
const ElementType type = _quadrangle_4;
Mesh mesh(spatial_dimension);
mesh.read("fatigue.msh");
// init stuff
const ElementType type_facet = Mesh::getFacetType(type);
const ElementType type_cohesive =
FEEngine::getCohesiveElementType(type_facet);
SolidMechanicsModelCohesive model(mesh);
model.initFull(
SolidMechanicsModelCohesiveOptions(_explicit_lumped_mass, true));
MaterialCohesiveLinearFatigue<2> & numerical_material =
dynamic_cast<MaterialCohesiveLinearFatigue<2> &>(
model.getMaterial("cohesive"));
Real delta_f = numerical_material.getParam("delta_f");
Real delta_c = numerical_material.getParam("delta_c");
Real sigma_c = 1;
const Array<Real> & traction_array =
numerical_material.getTraction(type_cohesive);
MaterialFatigue theoretical_material(delta_f, sigma_c, delta_c);
// model.setBaseName("fatigue");
// model.addDumpFieldVector("displacement");
// model.addDumpField("stress");
// model.dump();
// stretch material
Real strain = 1;
Array<Real> & displacement = model.getDisplacement();
const Array<Real> & position = mesh.getNodes();
for (UInt n = 0; n < mesh.getNbNodes(); ++n)
displacement(n, 0) = position(n, 0) * strain;
model.assembleInternalForces();
// model.dump();
// insert cohesive elements
model.checkCohesiveStress();
// create the displacement sequence
Real increment = 0.01;
Array<Real> openings;
arange(openings, 0, 0.5, increment);
arange(openings, 0.5, 0.1, increment);
arange(openings, 0.1, 0.7, increment);
arange(openings, 0.7, 0.3, increment);
arange(openings, 0.3, 0.6, increment);
arange(openings, 0.6, 0.3, increment);
arange(openings, 0.3, 0.7, increment);
arange(openings, 0.7, 1.3, increment);
const Array<UInt> & switches = numerical_material.getSwitches(type_cohesive);
// std::ofstream edis("fatigue_edis.txt");
// impose openings
for (UInt i = 0; i < openings.size(); ++i) {
// compute numerical traction
imposeOpening(model, openings(i));
model.assembleInternalForces();
// model.dump();
Real numerical_traction = traction_array(0, 0);
// compute theoretical traction
Real theoretical_traction =
theoretical_material.computeTraction(openings(i));
// test traction
if (std::abs(numerical_traction - theoretical_traction) > 1e-13)
AKANTU_ERROR("The numerical traction "
<< numerical_traction << " and theoretical traction "
<< theoretical_traction << " are not coincident");
// edis << model.getEnergy("dissipated") << std::endl;
}
if (switches(0) != 7)
AKANTU_ERROR("The number of switches is wrong");
std::cout << "OK: the test_cohesive_extrinsic_fatigue passed." << std::endl;
return 0;
}
/* -------------------------------------------------------------------------- */
void imposeOpening(SolidMechanicsModelCohesive & model, Real opening) {
UInt spatial_dimension = model.getSpatialDimension();
Mesh & mesh = model.getFEEngine().getMesh();
Array<Real> & position = mesh.getNodes();
Array<Real> & displacement = model.getDisplacement();
UInt nb_nodes = mesh.getNbNodes();
Array<bool> update(nb_nodes);
update.zero();
Mesh::type_iterator it = mesh.firstType(spatial_dimension);
Mesh::type_iterator end = mesh.lastType(spatial_dimension);
for (; it != end; ++it) {
ElementType type = *it;
UInt nb_element = mesh.getNbElement(type);
UInt nb_nodes_per_element = mesh.getNbNodesPerElement(type);
const Array<UInt> & connectivity = mesh.getConnectivity(type);
Vector<Real> barycenter(spatial_dimension);
for (UInt el = 0; el < nb_element; ++el) {
mesh.getBarycenter({type, el, _not_ghost}, barycenter);
if (barycenter(0) > 1) {
for (UInt n = 0; n < nb_nodes_per_element; ++n) {
UInt node = connectivity(el, n);
if (!update(node)) {
displacement(node, 0) = opening + position(node, 0);
update(node) = true;
}
}
}
}
}
}
/* -------------------------------------------------------------------------- */
void arange(Array<Real> & openings, Real begin, Real end, Real increment) {
if (begin < end) {
for (Real opening = begin; opening < end - increment / 2.;
opening += increment)
openings.push_back(opening);
} else {
for (Real opening = begin; opening > end + increment / 2.;
opening -= increment)
openings.push_back(opening);
}
}

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