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test_solid_mechanics_model_linear_elastic_potential_energy.cc
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test_solid_mechanics_model_linear_elastic_potential_energy.cc
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/**
* @file test_solid_mechanics_model_potential_energy.cc
*
* @author Tobias Brink <tobias.brink@epfl.ch>
*
* @date creation: Tue Nov 14 2017
* @date last modification: Tue Nov 14 2017
*
* @brief test potential energy of the linear elasticity model
*
* @section description
*
* This test uses a linear elastic material with density = 1, Young's
* modulus = 1, and Poisson's ratio = 0 and applies a linear
* displacement from 0 to ε in x direction. The resulting potential
* energy density should be 0.5*Y*ε² = ε²/2. Since the mesh always has
* a volume of 1, the energy density equals the total energy. We test
* 3 different strains.
*
* @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 {
TYPED_TEST(TestSMMFixture, LinearElasticPotentialEnergy) {
const auto spatial_dimension = this->spatial_dimension;
getStaticParser().parse("test_solid_mechanics_model_linear_elastic_"
"potential_energy_material.dat");
this->model->initFull(_analysis_method = _static);
auto & lower = this->mesh->getLowerBounds();
auto & upper = this->mesh->getUpperBounds();
auto length = upper(_x) - lower(_x);
const auto & pos = this->mesh->getNodes();
auto & disp = this->model->getDisplacement();
auto & boun = this->model->getBlockedDOFs();
std::vector<Real> strains{0.0, 0.1, 0.2, 0.3};
for (auto && eps : strains) {
/// boundary conditions
for (auto && pair : zip(make_view(pos, spatial_dimension),
make_view(disp, spatial_dimension),
make_view(boun, spatial_dimension))) {
auto & posv = std::get<0>(pair);
auto & dispv = std::get<1>(pair);
auto & bounv = std::get<2>(pair);
auto reduced_x = (posv(_x) - lower(_x)) / length;
dispv(_x) = reduced_x * eps;
bounv(_x) = true;
}
/// "solve" a step (solution is imposed)
this->model->solveStep();
/// compare energy to analytical solution
const auto E_ref = 0.5 * eps * eps;
auto E_pot = this->model->getEnergy("potential");
EXPECT_NEAR(E_ref, E_pot, 1e-8);
}
}
} // namespace

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