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test_material_standard_linear_solid_deviatoric_relaxation_tension.cc
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test_material_standard_linear_solid_deviatoric_relaxation_tension.cc
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/**
* @file test_material_standard_linear_solid_deviatoric_relaxation_tension.cc
*
* @author David Simon Kammer <david.kammer@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Mon Aug 09 2010
* @date last modification: Sat Dec 19 2020
*
* @brief test of the viscoelastic material: relaxation
*
*
* @section LICENSE
*
* Copyright (©) 2010-2021 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 <fstream>
#include <iostream>
#include <limits>
#include <sstream>
/* -------------------------------------------------------------------------- */
#include "solid_mechanics_model.hh"
using namespace akantu;
int main(int argc, char * argv[]) {
akantu::initialize("material_standard_linear_solid_deviatoric_relaxation.dat",
argc, argv);
// sim data
Real T = 10.;
Real eps = 0.001;
// const UInt dim = 3;
const UInt dim = 2;
Real sim_time = 25.;
// Real sim_time = 250.;
Real time_factor = 0.1;
Real tolerance = 1e-5;
Mesh mesh(dim);
mesh.read("test_material_standard_linear_solid_deviatoric_relaxation.msh");
// mesh_io.read("hexa_structured.msh",mesh);
// const ElementType element_type = _hexahedron_8;
const ElementType element_type = _quadrangle_4;
SolidMechanicsModel model(mesh);
/* ------------------------------------------------------------------------ */
/* Initialization */
/* ------------------------------------------------------------------------ */
model.initFull();
std::cout << model.getMaterial(0) << std::endl;
model.assembleMassLumped();
model.assembleInternalForces();
model.getMaterial(0).setToSteadyState();
std::stringstream filename_sstr;
filename_sstr << "test_material_standard_linear_solid_deviatoric_relaxation_"
"tension.out";
std::ofstream output_data;
output_data.open(filename_sstr.str().c_str());
output_data << "#[1]-time [2]-sigma_analytic [3+]-sigma_measurements"
<< std::endl;
Material & mat = model.getMaterial(0);
const Array<Real> & stress = mat.getStress(element_type);
Real Eta = mat.get("Eta");
Real EV = mat.get("Ev");
Real Einf = mat.get("Einf");
Real E0 = mat.get("E");
Real kpa = mat.get("kapa");
Real mu = mat.get("mu");
Real gamma = EV / E0;
Real gammainf = Einf / E0;
Real tau = Eta / EV;
std::cout << "relaxation time = " << tau << std::endl;
UInt nb_nodes = mesh.getNbNodes();
const Array<Real> & coordinate = mesh.getNodes();
Array<Real> & displacement = model.getDisplacement();
/// Setting time step
Real time_step = model.getStableTimeStep() * time_factor;
std::cout << "Time Step = " << time_step << "s" << std::endl;
model.setTimeStep(time_step);
UInt max_steps = sim_time / time_step;
UInt out_interval = 1;
Real time = 0.;
/* ------------------------------------------------------------------------ */
/* Main loop */
/* ------------------------------------------------------------------------ */
for (UInt s = 0; s <= max_steps; ++s) {
if (s % 1000 == 0)
std::cerr << "passing step " << s << "/" << max_steps << std::endl;
time = s * time_step;
// impose displacement
Real epsilon = 0.;
if (time < T) {
epsilon = eps * time / T;
} else {
epsilon = eps;
}
for (UInt n = 0; n < nb_nodes; ++n) {
for (UInt d = 0; d < dim; ++d)
displacement(n, d) = epsilon * coordinate(n, d);
}
// compute stress
model.assembleInternalForces();
// print output
if (s % out_interval == 0) {
// analytical solution
Real epskk = dim * eps;
Real solution = 0.;
if (time < T) {
solution =
2 * mu * (eps - epskk / 3.) / T *
(gammainf * time + gamma * tau * (1 - exp(-time / tau))) +
gammainf * kpa * epskk * time / T;
} else {
solution =
2 * mu * (eps - epskk / 3.) *
(gammainf +
gamma * tau / T * (exp((T - time) / tau) - exp(-time / tau))) +
gammainf * kpa * epskk;
}
output_data << s * time_step << " " << solution;
// data output
Array<Real>::const_matrix_iterator stress_it = stress.begin(dim, dim);
Array<Real>::const_matrix_iterator stress_end = stress.end(dim, dim);
for (; stress_it != stress_end; ++stress_it) {
output_data << " " << (*stress_it)(1, 1);
// test error
Real rel_error_1 = std::abs(((*stress_it)(1, 1) - solution) / solution);
if (rel_error_1 > tolerance) {
std::cerr << "Relative error: " << rel_error_1 << std::endl;
return EXIT_FAILURE;
}
}
output_data << std::endl;
}
}
finalize();
std::cout << "Test successful!" << std::endl;
return EXIT_SUCCESS;
}

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