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test_material_hyper_elasto_plastic1.cc
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/**
* @file test_material_hyper_elasto_plastic1.cc
*
* @author Till Junge <till.junge@altermail.ch>
*
* @date 25 Feb 2018
*
* @brief Tests for the large-strain Simo-type plastic law implemented
* using MaterialMuSpectre
*
* Copyright © 2018 Till Junge
*
* µSpectre 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, or (at
* your option) any later version.
*
* µSpectre 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
* General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with µSpectre; see the file COPYING. If not, write to the
* Free Software Foundation, Inc., 59 Temple Place - Suite 330,
* * Boston, MA 02111-1307, USA.
*
* Additional permission under GNU GPL version 3 section 7
*
* If you modify this Program, or any covered work, by linking or combining it
* with proprietary FFT implementations or numerical libraries, containing parts
* covered by the terms of those libraries' licenses, the licensors of this
* Program grant you additional permission to convey the resulting work.
*/
#include "boost/mpl/list.hpp"
#include "materials/stress_transformations_Kirchhoff.hh"
#include "materials/material_hyper_elasto_plastic1.hh"
#include "materials/materials_toolbox.hh"
#include "tests.hh"
#include "test_goodies.hh"
namespace muSpectre {
BOOST_AUTO_TEST_SUITE(material_hyper_elasto_plastic_1);
template <class Mat_t>
struct MaterialFixture {
using Mat = Mat_t;
constexpr static Real K{.833}; // bulk modulus
constexpr static Real mu{.386}; // shear modulus
constexpr static Real H{.004}; // hardening modulus
constexpr static Real tau_y0{.003}; // initial yield stress
constexpr static Real young{MatTB::convert_elastic_modulus<
ElasticModulus::Young, ElasticModulus::Bulk, ElasticModulus::Shear>(
K, mu)};
constexpr static Real poisson{MatTB::convert_elastic_modulus<
ElasticModulus::Poisson, ElasticModulus::Bulk, ElasticModulus::Shear>(
K, mu)};
MaterialFixture() : mat("Name", young, poisson, tau_y0, H) {}
constexpr static Dim_t sdim{Mat_t::sdim()};
constexpr static Dim_t mdim{Mat_t::mdim()};
Mat_t mat;
};
using mats = boost::mpl::list<
MaterialFixture<MaterialHyperElastoPlastic1<twoD, twoD>>,
MaterialFixture<MaterialHyperElastoPlastic1<twoD, threeD>>,
MaterialFixture<MaterialHyperElastoPlastic1<threeD, threeD>>>;
BOOST_FIXTURE_TEST_CASE_TEMPLATE(test_constructor, Fix, mats, Fix) {
BOOST_CHECK_EQUAL("Name", Fix::mat.get_name());
auto & mat{Fix::mat};
auto sdim{Fix::sdim};
auto mdim{Fix::mdim};
BOOST_CHECK_EQUAL(sdim, mat.sdim());
BOOST_CHECK_EQUAL(mdim, mat.mdim());
}
BOOST_FIXTURE_TEST_CASE_TEMPLATE(test_evaluate_stress, Fix, mats, Fix) {
// This test uses precomputed reference values (computed using
// elasto-plasticity.py) for the 3d case only
// need higher tol because of printout precision of reference solutions
constexpr Real hi_tol{1e-8};
constexpr Dim_t mdim{Fix::mdim}, sdim{Fix::sdim};
constexpr bool has_precomputed_values{(mdim == sdim) && (mdim == threeD)};
constexpr bool verbose{false};
using Strain_t = Eigen::Matrix<Real, mdim, mdim>;
using traits =
MaterialMuSpectre_traits<MaterialHyperElastoPlastic1<sdim, mdim>>;
using LColl_t = typename traits::LFieldColl_t;
using StrainStField_t =
StateField<TensorField<LColl_t, Real, secondOrder, mdim>>;
using FlowStField_t = StateField<ScalarField<LColl_t, Real>>;
// using StrainStRef_t = typename traits::LStrainMap_t::reference;
// using ScalarStRef_t = typename traits::LScalarMap_t::reference;
// create statefields
LColl_t coll{};
coll.add_pixel({0});
coll.initialise();
auto & F_{make_statefield<StrainStField_t>("previous gradient", coll)};
auto & be_{
make_statefield<StrainStField_t>("previous elastic strain", coll)};
auto & eps_{make_statefield<FlowStField_t>("plastic flow", coll)};
auto F_prev{F_.get_map()};
F_prev[0].current() = Strain_t::Identity();
auto be_prev{be_.get_map()};
be_prev[0].current() = Strain_t::Identity();
auto eps_prev{eps_.get_map()};
eps_prev[0].current() = 0;
// elastic deformation
Strain_t F{Strain_t::Identity()};
F(0, 1) = 1e-5;
F_.cycle();
be_.cycle();
eps_.cycle();
Strain_t stress{
Fix::mat.evaluate_stress(F, F_prev[0], be_prev[0], eps_prev[0])};
if (has_precomputed_values) {
Strain_t tau_ref{};
tau_ref << 1.92999522e-11, 3.86000000e-06, 0.00000000e+00, 3.86000000e-06,
-1.93000510e-11, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
-2.95741950e-17;
Real error{(tau_ref - stress).norm() / tau_ref.norm()};
BOOST_CHECK_LT(error, hi_tol);
Strain_t be_ref{};
be_ref << 1.00000000e+00, 1.00000000e-05, 0.00000000e+00, 1.00000000e-05,
1.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
1.00000000e+00;
error = (be_ref - be_prev[0].current()).norm() / be_ref.norm();
BOOST_CHECK_LT(error, hi_tol);
Real ep_ref{0};
error = ep_ref - eps_prev[0].current();
BOOST_CHECK_LT(error, hi_tol);
}
if (verbose) {
std::cout << "τ =" << std::endl << stress << std::endl;
std::cout << "F =" << std::endl << F << std::endl;
std::cout << "Fₜ =" << std::endl << F_prev[0].current() << std::endl;
std::cout << "bₑ =" << std::endl << be_prev[0].current() << std::endl;
std::cout << "εₚ =" << std::endl << eps_prev[0].current() << std::endl;
}
F_.cycle();
be_.cycle();
eps_.cycle();
// plastic deformation
F(0, 1) = .2;
stress = Fix::mat.evaluate_stress(F, F_prev[0], be_prev[0], eps_prev[0]);
if (has_precomputed_values) {
Strain_t tau_ref{};
tau_ref << 1.98151335e-04, 1.98151335e-03, 0.00000000e+00, 1.98151335e-03,
-1.98151335e-04, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
1.60615155e-16;
Real error{(tau_ref - stress).norm() / tau_ref.norm()};
BOOST_CHECK_LT(error, hi_tol);
Strain_t be_ref{};
be_ref << 1.00052666, 0.00513348, 0., 0.00513348, 0.99949996, 0., 0., 0.,
1.;
error = (be_ref - be_prev[0].current()).norm() / be_ref.norm();
BOOST_CHECK_LT(error, hi_tol);
Real ep_ref{0.11229988};
error = (ep_ref - eps_prev[0].current()) / ep_ref;
BOOST_CHECK_LT(error, hi_tol);
}
if (verbose) {
std::cout << "Post Cycle" << std::endl;
std::cout << "τ =" << std::endl
<< stress << std::endl
<< "F =" << std::endl
<< F << std::endl
<< "Fₜ =" << std::endl
<< F_prev[0].current() << std::endl
<< "bₑ =" << std::endl
<< be_prev[0].current() << std::endl
<< "εₚ =" << std::endl
<< eps_prev[0].current() << std::endl;
}
}
BOOST_FIXTURE_TEST_CASE_TEMPLATE(test_evaluate_stiffness, Fix, mats, Fix) {
// This test uses precomputed reference values (computed using
// elasto-plasticity.py) for the 3d case only
// need higher tol because of printout precision of reference solutions
constexpr Real hi_tol{2e-7};
constexpr Dim_t mdim{Fix::mdim}, sdim{Fix::sdim};
constexpr bool has_precomputed_values{(mdim == sdim) && (mdim == threeD)};
constexpr bool verbose{has_precomputed_values && false};
using Strain_t = Eigen::Matrix<Real, mdim, mdim>;
using Stiffness_t = T4Mat<Real, mdim>;
using traits =
MaterialMuSpectre_traits<MaterialHyperElastoPlastic1<sdim, mdim>>;
using LColl_t = typename traits::LFieldColl_t;
using StrainStField_t =
StateField<TensorField<LColl_t, Real, secondOrder, mdim>>;
using FlowStField_t = StateField<ScalarField<LColl_t, Real>>;
// using StrainStRef_t = typename traits::LStrainMap_t::reference;
// using ScalarStRef_t = typename traits::LScalarMap_t::reference;
// create statefields
LColl_t coll{};
coll.add_pixel({0});
coll.initialise();
auto & F_{make_statefield<StrainStField_t>("previous gradient", coll)};
auto & be_{
make_statefield<StrainStField_t>("previous elastic strain", coll)};
auto & eps_{make_statefield<FlowStField_t>("plastic flow", coll)};
auto F_prev{F_.get_map()};
F_prev[0].current() = Strain_t::Identity();
auto be_prev{be_.get_map()};
be_prev[0].current() = Strain_t::Identity();
auto eps_prev{eps_.get_map()};
eps_prev[0].current() = 0;
// elastic deformation
Strain_t F{Strain_t::Identity()};
F(0, 1) = 1e-5;
F_.cycle();
be_.cycle();
eps_.cycle();
Strain_t stress{};
Stiffness_t stiffness{};
std::tie(stress, stiffness) =
Fix::mat.evaluate_stress_tangent(F, F_prev[0], be_prev[0], eps_prev[0]);
if (has_precomputed_values) {
Strain_t tau_ref{};
tau_ref << 1.92999522e-11, 3.86000000e-06, 0.00000000e+00, 3.86000000e-06,
-1.93000510e-11, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
-2.95741950e-17;
Real error{(tau_ref - stress).norm() / tau_ref.norm()};
BOOST_CHECK_LT(error, hi_tol);
Strain_t be_ref{};
be_ref << 1.00000000e+00, 1.00000000e-05, 0.00000000e+00, 1.00000000e-05,
1.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
1.00000000e+00;
error = (be_ref - be_prev[0].current()).norm() / be_ref.norm();
BOOST_CHECK_LT(error, hi_tol);
Real ep_ref{0};
error = ep_ref - eps_prev[0].current();
BOOST_CHECK_LT(error, hi_tol);
Stiffness_t temp;
temp << 1.34766667e+00, 3.86000000e-06, 0.00000000e+00, -3.86000000e-06,
5.75666667e-01, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
5.75666667e-01, -3.61540123e-17, 3.86000000e-01, 0.00000000e+00,
3.86000000e-01, 7.12911684e-17, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
3.86000000e-01, 0.00000000e+00, 0.00000000e+00, -1.93000000e-06,
3.86000000e-01, 1.93000000e-06, 0.00000000e+00, -3.61540123e-17,
3.86000000e-01, 0.00000000e+00, 3.86000000e-01, 7.12911684e-17,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
5.75666667e-01, -3.86000000e-06, 0.00000000e+00, 3.86000000e-06,
1.34766667e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
5.75666667e-01, 0.00000000e+00, 0.00000000e+00, -1.93000000e-06,
0.00000000e+00, 0.00000000e+00, 3.86000000e-01, 1.93000000e-06,
3.86000000e-01, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
3.86000000e-01, 0.00000000e+00, 0.00000000e+00, -1.93000000e-06,
3.86000000e-01, 1.93000000e-06, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, -1.93000000e-06, 0.00000000e+00, 0.00000000e+00,
3.86000000e-01, 1.93000000e-06, 3.86000000e-01, 0.00000000e+00,
5.75666667e-01, 2.61999996e-17, 0.00000000e+00, 2.61999996e-17,
5.75666667e-01, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
1.34766667e+00;
Stiffness_t K4b_ref{testGoodies::from_numpy(temp)};
error = (K4b_ref - stiffness).norm() / K4b_ref.norm();
BOOST_CHECK_LT(error, hi_tol);
if (not(error < hi_tol)) {
std::cout << "stiffness reference:\n" << K4b_ref << std::endl;
std::cout << "stiffness computed:\n" << stiffness << std::endl;
}
}
if (verbose) {
std::cout << "C₄ =" << std::endl << stiffness << std::endl;
}
F_.cycle();
be_.cycle();
eps_.cycle();
// plastic deformation
F(0, 1) = .2;
std::tie(stress, stiffness) =
Fix::mat.evaluate_stress_tangent(F, F_prev[0], be_prev[0], eps_prev[0]);
if (has_precomputed_values) {
Strain_t tau_ref{};
tau_ref << 1.98151335e-04, 1.98151335e-03, 0.00000000e+00, 1.98151335e-03,
-1.98151335e-04, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
1.60615155e-16;
Real error{(tau_ref - stress).norm() / tau_ref.norm()};
BOOST_CHECK_LT(error, hi_tol);
Strain_t be_ref{};
be_ref << 1.00052666, 0.00513348, 0., 0.00513348, 0.99949996, 0., 0., 0.,
1.;
error = (be_ref - be_prev[0].current()).norm() / be_ref.norm();
BOOST_CHECK_LT(error, hi_tol);
Real ep_ref{0.11229988};
error = (ep_ref - eps_prev[0].current()) / ep_ref;
BOOST_CHECK_LT(error, hi_tol);
Stiffness_t temp{};
temp << 8.46343327e-01, 1.11250597e-03, 0.00000000e+00, -2.85052074e-03,
8.26305692e-01, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
8.26350980e-01, -8.69007382e-04, 1.21749295e-03, 0.00000000e+00,
1.61379562e-03, 8.69007382e-04, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 5.58242059e-18, 0.00000000e+00, 0.00000000e+00,
9.90756677e-03, 0.00000000e+00, 0.00000000e+00, -9.90756677e-04,
1.01057181e-02, 9.90756677e-04, 0.00000000e+00, -8.69007382e-04,
1.21749295e-03, 0.00000000e+00, 1.61379562e-03, 8.69007382e-04,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 5.58242059e-18,
8.26305692e-01, -1.11250597e-03, 0.00000000e+00, 2.85052074e-03,
8.46343327e-01, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
8.26350980e-01, 0.00000000e+00, 0.00000000e+00, -9.90756677e-04,
0.00000000e+00, 0.00000000e+00, 1.01057181e-02, 9.90756677e-04,
9.90756677e-03, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
9.90756677e-03, 0.00000000e+00, 0.00000000e+00, -9.90756677e-04,
1.01057181e-02, 9.90756677e-04, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, -9.90756677e-04, 0.00000000e+00, 0.00000000e+00,
1.01057181e-02, 9.90756677e-04, 9.90756677e-03, 0.00000000e+00,
8.26350980e-01, 0.00000000e+00, 0.00000000e+00, 1.38777878e-17,
8.26350980e-01, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
8.46298039e-01;
Stiffness_t K4b_ref{testGoodies::from_numpy(temp)};
error = (K4b_ref - stiffness).norm() / K4b_ref.norm();
error = (K4b_ref - stiffness).norm() / K4b_ref.norm();
BOOST_CHECK_LT(error, hi_tol);
if (not(error < hi_tol)) {
std::cout << "stiffness reference:\n" << K4b_ref << std::endl;
std::cout << "stiffness computed:\n" << stiffness << std::endl;
}
// check also whether pull_back is correct
Stiffness_t intermediate{stiffness};
Stiffness_t zero_mediate{Stiffness_t::Zero()};
for (int i{0}; i < mdim; ++i) {
for (int j{0}; j < mdim; ++j) {
for (int m{0}; m < mdim; ++m) {
const auto & k{i};
const auto & l{j};
// k,m inverted for right transpose
get(zero_mediate, i, j, k, m) -= stress(l, m);
get(intermediate, i, j, k, m) -= stress(l, m);
}
}
}
temp << 8.46145176e-01, -8.69007382e-04, 0.00000000e+00, -2.85052074e-03,
8.26305692e-01, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
8.26350980e-01, -2.85052074e-03, 1.41564428e-03, 0.00000000e+00,
1.61379562e-03, 8.69007382e-04, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 5.58242059e-18, 0.00000000e+00, 0.00000000e+00,
9.90756677e-03, 0.00000000e+00, 0.00000000e+00, -9.90756677e-04,
1.01057181e-02, 9.90756677e-04, 0.00000000e+00, -8.69007382e-04,
1.21749295e-03, 0.00000000e+00, 1.41564428e-03, -1.11250597e-03,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 5.58242059e-18,
8.26305692e-01, -1.11250597e-03, 0.00000000e+00, 8.69007382e-04,
8.46541479e-01, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
8.26350980e-01, 0.00000000e+00, 0.00000000e+00, -9.90756677e-04,
0.00000000e+00, 0.00000000e+00, 1.01057181e-02, 9.90756677e-04,
9.90756677e-03, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
9.90756677e-03, 0.00000000e+00, 0.00000000e+00, -9.90756677e-04,
9.90756677e-03, -9.90756677e-04, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, -9.90756677e-04, 0.00000000e+00, 0.00000000e+00,
1.01057181e-02, -9.90756677e-04, 1.01057181e-02, 0.00000000e+00,
8.26350980e-01, 0.00000000e+00, 0.00000000e+00, 1.38777878e-17,
8.26350980e-01, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
8.46298039e-01;
Stiffness_t K4c_ref{testGoodies::from_numpy(temp)};
error = (K4b_ref + zero_mediate - K4c_ref).norm() / zero_mediate.norm();
BOOST_CHECK_LT(error, hi_tol); // rel error on small difference between
// inexacly read doubles
if (not(error < hi_tol)) {
std::cout << "decrement reference:\n" << K4c_ref - K4b_ref << std::endl;
std::cout << "zero_mediate computed:\n" << zero_mediate << std::endl;
}
error = (K4c_ref - intermediate).norm() / K4c_ref.norm();
BOOST_CHECK_LT(error, hi_tol);
if (not(error < hi_tol)) {
std::cout << "stiffness reference:\n" << K4c_ref << std::endl;
std::cout << "stiffness computed:\n" << intermediate << std::endl;
std::cout << "zero-mediate computed:\n" << zero_mediate << std::endl;
std::cout << "difference:\n" << K4c_ref - intermediate << std::endl;
}
}
if (verbose) {
std::cout << "Post Cycle" << std::endl;
std::cout << "C₄ =" << std::endl << stiffness << std::endl;
}
}
/* ---------------------------------------------------------------------- */
BOOST_FIXTURE_TEST_CASE_TEMPLATE(stress_strain_test, Fix, mats, Fix) {}
BOOST_AUTO_TEST_SUITE_END();
} // namespace muSpectre

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