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rAKA/test/test_model/test_solid_mechanics_model/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: Tue Dec 15 2017
* @date last modification: Dec Nov 15 2017
*
* @brief test work in dynamic simulations
*
* @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.
*
* @section LICENSE
*
* Copyright (©) 2017 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 "test_solid_mechanics_model_fixture.hh"
/* -------------------------------------------------------------------------- */
using namespace akantu;
namespace {
void test_body(SolidMechanicsModel & model, Mesh & mesh,
AnalysisMethod analysis_method, UInt steps_needed) {
const auto spatial_dimension = model.getSpatialDimension();
getStaticParser().parse("test_solid_mechanics_model_"
"work_material.dat");
/// model initialization
model.initFull(_analysis_method = analysis_method);
model.assembleMassLumped();
/// Create a node group for Neumann BCs.
auto & apply_force_grp = mesh.createNodeGroup("apply_force");
auto & fixed_grp = mesh.createNodeGroup("fixed");
const auto & pos = mesh.getNodes();
auto & lower = mesh.getLowerBounds();
auto & upper = mesh.getUpperBounds();
UInt i = 0;
for (auto && posv : make_view(pos, 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;
}
mesh.createElementGroupFromNodeGroup("el_apply_force",
"apply_force",
spatial_dimension - 1);
mesh.createElementGroupFromNodeGroup("el_fixed",
"fixed",
spatial_dimension - 1);
/// set up timestep
auto time_step = model.getStableTimeStep() * 0.1;
model.setTimeStep(time_step);
/// Do the sim
std::vector<Real> displacements{0.00, 0.01, -0.01};
for (auto && u : displacements) {
model.applyBC(BC::Dirichlet::FixedValue(u, _x), "el_fixed");
Vector<Real> surface_traction(spatial_dimension);
surface_traction(_x) = 0.5;
if (spatial_dimension == 1) { //TODO: this is a hack to work
// around non-implemented
// BC::Neumann::FromTraction for 1D
auto & force = model.getForce();
for (auto && pair : zip(make_view(pos, spatial_dimension),
make_view(force, 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 {
model.applyBC(BC::Neumann::FromTraction(surface_traction),
"el_apply_force");
}
// 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) {
model.solveStep();
}
// Again, work reported by Akantu is infinitesimal (dW) and we
// need to integrate a while to get a decent value.
double Etot0 = model.getEnergy("potential") + model.getEnergy("kinetic");
double W = 0.0;
for (UInt i = 0; i < steps_needed; ++i) {
/// Solve.
model.solveStep();
const auto dW = model.getEnergy("external work");
W += dW;
}
// Finally check.
const auto Epot = model.getEnergy("potential");
const auto Ekin = model.getEnergy("kinetic");
EXPECT_NEAR(W, Ekin + Epot - Etot0, 5e-2); // Sadly not very exact
// for such a coarse mesh.
}
}
/* TODO: this is currently disabled for terrible results and performance
TYPED_TEST(TestSMMFixtureBar, WorkImplicit) {
test_body(*(this->model), *(this->mesh), _implicit_dynamic, 500);
}
*/
TYPED_TEST(TestSMMFixtureBar, WorkExplicit) {
test_body(*(this->model), *(this->mesh), _explicit_lumped_mass, 200);
}
} // namespace
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