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rAKA/test/test_model/test_solid_mechanics_model/test_energies/test_solid_mechanics_model_work_quasistatic.cc
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test_solid_mechanics_model_work_quasistatic.cc
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/**
* @file test_solid_mechanics_model_work_quasistatic.cc
*
* @author Tobias Brink <tobias.brink@epfl.ch>
*
* @date creation: Wed Nov 29 2017
* @date last modification: Fri Jan 26 2018
*
* @brief test work in quasistatic
*
* @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 potential energy of a linear elastic material
* works correctly, the work in a static simulation must equal the
* potential energy of the material. Since the work in static is an
* infinitesimal work Fds, we need to integrate by increasing F from 0
* to F_final in steps. This test uses one Dirichlet boundary
* condition (with u = 0.0, 0.1, and -0.1) and one Neumann boundary
* condition for F on the opposite side. The final work must be the
* same for all u.
*
*/
/* -------------------------------------------------------------------------- */
#include "../test_solid_mechanics_model_fixture.hh"
#include "mesh_utils.hh"
/* -------------------------------------------------------------------------- */
using namespace akantu;
namespace {
TYPED_TEST(TestSMMFixture, WorkQuasistatic) {
const auto spatial_dimension = this->spatial_dimension;
getStaticParser().parse("test_solid_mechanics_model_"
"work_material.dat");
/// model initialization
this->model->initFull(_analysis_method = _static);
/// 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();
auto & flags = this->model->getBlockedDOFs();
auto & lower = this->mesh->getLowerBounds();
auto & upper = this->mesh->getUpperBounds();
UInt i = 0;
for (auto && data : zip(make_view(pos, spatial_dimension),
make_view(flags, spatial_dimension))) {
const auto & posv = std::get<0>(data);
auto & flag = std::get<1>(data);
if (posv(_x) > upper(_x) - 1e-6) {
apply_force_grp.add(i);
} else if (posv(_x) < lower(_x) + 1e-6) {
fixed_grp.add(i);
if ((spatial_dimension > 1) and (posv(_y) < lower(_y) + 1e-6)) {
flag(_y) = true;
if ((spatial_dimension > 2) and (posv(_z) < lower(_z) + 1e-6)) {
flag(_z) = true;
}
}
}
++i;
}
this->mesh->createElementGroupFromNodeGroup("el_apply_force", "apply_force",
spatial_dimension - 1);
this->mesh->createElementGroupFromNodeGroup("el_fixed", "fixed",
spatial_dimension - 1);
std::vector<Real> displacements{0.0, 0.1, -0.1};
for (auto && u : displacements) {
this->model->applyBC(BC::Dirichlet::FixedValue(u, _x), "el_fixed");
Vector<Real> surface_traction(spatial_dimension);
Real work = 0.0;
Real Epot;
static const UInt N = 100;
for (UInt i = 0; i <= N; ++i) {
this->model->getExternalForce().clear(); // reset external forces to zero
surface_traction(_x) = (1.0 * i) / N;
if (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, 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 {
this->model->applyBC(BC::Neumann::FromTraction(surface_traction),
"el_apply_force");
}
/// Solve.
this->model->solveStep();
Epot = this->model->getEnergy("potential");
// In static, this is infinitesimal work!
auto Fds = this->model->getEnergy("external work");
work += Fds; // integrate
/// Check that no work was done for zero force.
if (i == 0) {
EXPECT_NEAR(work, 0.0, 1e-12);
}
}
// Due to the finite integration steps, we make a rather large error
// in our work integration, thus the allowed delta is 1e-2.
EXPECT_NEAR(work, Epot, 1e-2);
}
}
} // namespace
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