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test_plastic_materials.cc
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/**
* @file test_plastic_materials.cc
*
* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
*
* @date creation: Fri Nov 17 2017
* @date last modification: Wed Feb 21 2018
*
* @brief Tests the plastic material
*
* @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/>.
*
*/
/* -------------------------------------------------------------------------- */
#include "material_linear_isotropic_hardening.hh"
#include "solid_mechanics_model.hh"
#include "test_material_fixtures.hh"
#include <gtest/gtest.h>
#include <type_traits>
/* -------------------------------------------------------------------------- */
using namespace akantu;
using mat_types = ::testing::Types<
// Traits<MaterialLinearIsotropicHardening, 1>,
// Traits<MaterialLinearIsotropicHardening, 2>,
Traits<MaterialLinearIsotropicHardening, 3>>;
/* -------------------------------------------------------------------------- */
template <>
void FriendMaterial<MaterialLinearIsotropicHardening<3>>::testComputeStress() {
Real E = 1.;
// Real nu = .3;
Real nu = 0.;
Real rho = 1.;
Real sigma_0 = 1.;
Real h = 0.;
Real bulk_modulus_K = E / 3. / (1 - 2. * nu);
Real shear_modulus_mu = 0.5 * E / (1 + nu);
setParam("E", E);
setParam("nu", nu);
setParam("rho", rho);
setParam("sigma_y", sigma_0);
setParam("h", h);
auto rotation_matrix = getRandomRotation();
Real max_strain = 10.;
Real strain_steps = 100;
Real dt = max_strain / strain_steps;
std::vector<double> steps(strain_steps);
std::iota(steps.begin(), steps.end(), 0.);
Matrix<Real> previous_grad_u_rot(3, 3, 0.);
Matrix<Real> previous_sigma(3, 3, 0.);
Matrix<Real> previous_sigma_rot(3, 3, 0.);
Matrix<Real> inelastic_strain_rot(3, 3, 0.);
Matrix<Real> inelastic_strain(3, 3, 0.);
Matrix<Real> previous_inelastic_strain(3, 3, 0.);
Matrix<Real> previous_inelastic_strain_rot(3, 3, 0.);
Matrix<Real> sigma_rot(3, 3, 0.);
Real iso_hardening = 0.;
Real previous_iso_hardening = 0.;
// hydrostatic loading (should not plastify)
for (auto && i : steps) {
auto t = i * dt;
auto grad_u = this->getHydrostaticStrain(t);
auto grad_u_rot = this->applyRotation(grad_u, rotation_matrix);
this->computeStressOnQuad(grad_u_rot, previous_grad_u_rot, sigma_rot,
previous_sigma_rot, inelastic_strain_rot,
previous_inelastic_strain_rot, iso_hardening,
previous_iso_hardening, 0., 0.);
auto sigma = this->reverseRotation(sigma_rot, rotation_matrix);
Matrix<Real> sigma_expected =
t * 3. * bulk_modulus_K * Matrix<Real>::eye(3, 1.);
Real stress_error = (sigma - sigma_expected).norm<L_inf>();
ASSERT_NEAR(stress_error, 0., 1e-13);
ASSERT_NEAR(inelastic_strain_rot.norm<L_inf>(), 0., 1e-13);
previous_grad_u_rot = grad_u_rot;
previous_sigma_rot = sigma_rot;
previous_inelastic_strain_rot = inelastic_strain_rot;
previous_iso_hardening = iso_hardening;
}
// deviatoric loading (should plastify)
// stress at onset of plastication
Real beta = sqrt(42);
Real t_P = sigma_0 / 2. / shear_modulus_mu / beta;
Matrix<Real> sigma_P = sigma_0 / beta * this->getDeviatoricStrain(1.);
for (auto && i : steps) {
auto t = i * dt;
auto grad_u = this->getDeviatoricStrain(t);
auto grad_u_rot = this->applyRotation(grad_u, rotation_matrix);
Real iso_hardening, previous_iso_hardening;
this->computeStressOnQuad(grad_u_rot, previous_grad_u_rot, sigma_rot,
previous_sigma_rot, inelastic_strain_rot,
previous_inelastic_strain_rot, iso_hardening,
previous_iso_hardening, 0., 0.);
auto sigma = this->reverseRotation(sigma_rot, rotation_matrix);
auto inelastic_strain =
this->reverseRotation(inelastic_strain_rot, rotation_matrix);
if (t < t_P) {
Matrix<Real> sigma_expected =
shear_modulus_mu * (grad_u + grad_u.transpose());
Real stress_error = (sigma - sigma_expected).norm<L_inf>();
ASSERT_NEAR(stress_error, 0., 1e-13);
ASSERT_NEAR(inelastic_strain_rot.norm<L_inf>(), 0., 1e-13);
} else if (t > t_P + dt) {
// skip the transition from non plastic to plastic
auto delta_lambda_expected =
dt / t * previous_sigma.doubleDot(grad_u + grad_u.transpose()) / 2.;
auto delta_inelastic_strain_expected =
delta_lambda_expected * 3. / 2. / sigma_0 * previous_sigma;
auto inelastic_strain_expected =
delta_inelastic_strain_expected + previous_inelastic_strain;
ASSERT_NEAR((inelastic_strain - inelastic_strain_expected).norm<L_inf>(),
0., 1e-13);
auto delta_sigma_expected =
2. * shear_modulus_mu *
(0.5 * dt / t * (grad_u + grad_u.transpose()) -
delta_inelastic_strain_expected);
auto delta_sigma = sigma - previous_sigma;
ASSERT_NEAR((delta_sigma_expected - delta_sigma).norm<L_inf>(), 0.,
1e-13);
}
previous_sigma = sigma;
previous_sigma_rot = sigma_rot;
previous_grad_u_rot = grad_u_rot;
previous_inelastic_strain = inelastic_strain;
previous_inelastic_strain_rot = inelastic_strain_rot;
}
}
namespace {
template <typename T>
class TestPlasticMaterialFixture : public ::TestMaterialFixture<T> {};
TYPED_TEST_SUITE(TestPlasticMaterialFixture, mat_types);
TYPED_TEST(TestPlasticMaterialFixture, ComputeStress) {
this->material->testComputeStress();
}
TYPED_TEST(TestPlasticMaterialFixture, DISABLED_EnergyDensity) {
this->material->testEnergyDensity();
}
TYPED_TEST(TestPlasticMaterialFixture, DISABLED_ComputeTangentModuli) {
this->material->testComputeTangentModuli();
}
TYPED_TEST(TestPlasticMaterialFixture, DISABLED_ComputeCelerity) {
this->material->testCelerity();
}
}
/*****************************************************************/
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