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test_solid_mechanics_model_work_dynamics.cc
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test_solid_mechanics_model_work_dynamics.cc
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/**
* @file test_solid_mechanics_model_work_dynamics.cc
*
* @author Tobias Brink <tobias.brink@epfl.ch>
*
* @date creation: Fri Dec 15 2017
* @date last modification: Fri Jan 26 2018
*
* @brief test work in dynamic simulations
*
* @section LICENSE
*
* Copyright (©) 2016-2018 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/>.
*
* @section description
*
* Assuming that the kinetic energy and the potential energy of the
* linear elastic material are bug free, the work in a dynamic
* simulation must equal the change in internal energy (first law of
* thermodynamics). Work in dynamics is an infinitesimal work Fds,
* thus we need to integrate it and compare at the end. In this test,
* we use one Dirichlet boundary condition (with u = 0.0, 0.01, and
* -0.01) and one Neumann boundary condition for F on the opposite
* side. Then we do a few steps to get reference energies for work and
* internal energy. After more steps, the change in both work and
* internal energy must be equal.
*
*/
/* -------------------------------------------------------------------------- */
#include "../test_solid_mechanics_model_fixture.hh"
/* -------------------------------------------------------------------------- */
using namespace akantu;
namespace {
template <typename type_>
class TestSMMFixtureWorkDynamic : public TestSMMFixture<type_> {
public:
void SetUp() override {
this->mesh_file =
"../../patch_tests/data/bar" + std::to_string(this->type) + ".msh";
TestSMMFixture<type_>::SetUp();
getStaticParser().parse("test_solid_mechanics_model_"
"work_material.dat");
/// model initialization
this->model->initFull();
/// Create a node group for Neumann BCs.
auto & apply_force_grp = this->mesh->createNodeGroup("apply_force");
auto & fixed_grp = this->mesh->createNodeGroup("fixed");
const auto & pos = this->mesh->getNodes();
const auto & lower = this->mesh->getLowerBounds();
const auto & upper = this->mesh->getUpperBounds();
UInt i = 0;
for (auto && posv : make_view(pos, this->spatial_dimension)) {
if (posv(_x) > upper(_x) - 1e-6) {
apply_force_grp.add(i);
} else if (posv(_x) < lower(_x) + 1e-6) {
fixed_grp.add(i);
}
++i;
}
this->mesh->createElementGroupFromNodeGroup("el_apply_force", "apply_force",
this->spatial_dimension - 1);
this->mesh->createElementGroupFromNodeGroup("el_fixed", "fixed",
this->spatial_dimension - 1);
Vector<Real> surface_traction(this->spatial_dimension);
surface_traction(_x) = 0.5;
if (this->spatial_dimension == 1) {
// TODO: this is a hack to work
// around non-implemented
// BC::Neumann::FromTraction for 1D
auto & force = this->model->getExternalForce();
for (auto && pair : zip(make_view(pos, this->spatial_dimension),
make_view(force, this->spatial_dimension))) {
auto & posv = std::get<0>(pair);
auto & forcev = std::get<1>(pair);
if (posv(_x) > upper(_x) - 1e-6) {
forcev(_x) = surface_traction(_x);
}
}
} else {
this->model->applyBC(BC::Neumann::FromTraction(surface_traction),
"el_apply_force");
}
/// set up timestep
auto time_step = this->model->getStableTimeStep() * 0.1;
this->model->setTimeStep(time_step);
}
};
TYPED_TEST_SUITE(TestSMMFixtureWorkDynamic, gtest_element_types);
/* TODO: this is currently disabled for terrible results and performance
TYPED_TEST(TestSMMFixtureBar, WorkImplicit) {
test_body(*(this->model), *(this->mesh), _implicit_dynamic, 500);
}
*/
// model.assembleMassLumped();
TYPED_TEST(TestSMMFixtureWorkDynamic, WorkExplicit) {
/// Do the sim
std::vector<Real> displacements{0.00, 0.01, -0.01};
for (auto && u : displacements) {
this->model->applyBC(BC::Dirichlet::FixedValue(u, _x), "el_fixed");
// First, "equilibrate" a bit to get a reference state of total
// energy and work. This is needed when we have a Dirichlet with
// finite displacement on one side.
for (UInt i = 0; i < 25; ++i) {
this->model->solveStep();
}
// Again, work reported by Akantu is infinitesimal (dW) and we
// need to integrate a while to get a decent value.
double Etot0 =
this->model->getEnergy("potential") + this->model->getEnergy("kinetic");
double W = 0.0;
for (UInt i = 0; i < 200; ++i) {
/// Solve.
this->model->solveStep();
const auto dW = this->model->getEnergy("external work");
W += dW;
}
// Finally check.
const auto Epot = this->model->getEnergy("potential");
const auto Ekin = this->model->getEnergy("kinetic");
EXPECT_NEAR(W, Ekin + Epot - Etot0, 5e-2);
// Sadly not very exact for such a coarse mesh.
}
}
} // namespace

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