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test_material_evaluator.cc
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/**
* @file test_material_evaluator.cc
*
* @author Till Junge <till.junge@altermail.ch>
*
* @date 13 Jan 2019
*
* @brief tests for the material evaluator mechanism
*
* Copyright © 2019 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 "tests.hh"
#include "common/T4_map_proxy.hh"
#include "materials/material_linear_elastic2.hh"
#include "materials/material_evaluator.hh"
#include "Eigen/Dense"
namespace muSpectre {
BOOST_AUTO_TEST_SUITE(material_evaluator_tests);
/* ---------------------------------------------------------------------- */
BOOST_AUTO_TEST_CASE(without_per_pixel_data) {
using Mat_t = MaterialLinearElastic1<twoD, twoD>;
constexpr Real Young{210e9};
constexpr Real Poisson{.33};
auto mat_eval = Mat_t::make_evaluator(Young, Poisson);
auto & mat = *std::get<0>(mat_eval);
auto & evaluator = std::get<1>(mat_eval);
using T2_t = Eigen::Matrix<Real, twoD, twoD>;
using T4_t = T4Mat<Real, twoD>;
const T2_t F{(T2_t::Random() - (T2_t::Ones() * .5)) * 1e-4 +
T2_t::Identity()};
const T2_t eps{
.5 * ((F - T2_t::Identity()) + (F - T2_t::Identity()).transpose())};
/*
* at this point, the evaluator has been created, but the underlying
* material still has zero pixels. Evaluation is not yet possible, and
* trying to do so has to fail with an explicit error message
*/
BOOST_CHECK_THROW(evaluator.evaluate_stress(eps, Formulation::small_strain),
std::runtime_error);
mat.add_pixel({});
const T2_t sigma{evaluator.evaluate_stress(eps, Formulation::small_strain)};
const T2_t P{evaluator.evaluate_stress(F, Formulation::finite_strain)};
auto J{F.determinant()};
auto P_reconstruct{J * sigma * F.inverse().transpose()};
auto error_comp{[](const auto & a, const auto & b) {
return (a - b).norm() / (a + b).norm();
}};
auto error{error_comp(P, P_reconstruct)};
constexpr Real small_strain_tol{1e-3};
if (not(error <= small_strain_tol)) {
std::cout << "F =" << std::endl << F << std::endl;
std::cout << "ε =" << std::endl << eps << std::endl;
std::cout << "P =" << std::endl << P << std::endl;
std::cout << "σ =" << std::endl << sigma << std::endl;
std::cout << "P_reconstructed =" << std::endl
<< P_reconstruct << std::endl;
}
BOOST_CHECK_LE(error, small_strain_tol);
T2_t sigma2, P2;
T4_t C, K;
std::tie(sigma2, C) =
evaluator.evaluate_stress_tangent(eps, Formulation::small_strain);
std::tie(P2, K) =
evaluator.evaluate_stress_tangent(F, Formulation::finite_strain);
error = error_comp(sigma2, sigma);
BOOST_CHECK_LE(error, tol);
error = error_comp(P2, P);
BOOST_CHECK_LE(error, tol);
error = error_comp(C, K);
if (not(error <= small_strain_tol)) {
std::cout << "F =" << std::endl << F << std::endl;
std::cout << "ε =" << std::endl << eps << std::endl;
std::cout << "P =" << std::endl << P << std::endl;
std::cout << "σ =" << std::endl << sigma << std::endl;
std::cout << "K =" << std::endl << K << std::endl;
std::cout << "C =" << std::endl << C << std::endl;
}
BOOST_CHECK_LE(error, small_strain_tol);
mat.add_pixel({1});
/*
* Now, the material has two pixels, and evaluating it would be ambiguous.
* It should fail with an explicit error message
*/
BOOST_CHECK_THROW(evaluator.evaluate_stress(eps, Formulation::small_strain),
std::runtime_error);
}
/* ---------------------------------------------------------------------- */
BOOST_AUTO_TEST_CASE(with_per_pixel_data) {
using Mat_t = MaterialLinearElastic2<twoD, twoD>;
constexpr Real Young{210e9};
constexpr Real Poisson{.33};
auto mat_eval{Mat_t::make_evaluator(Young, Poisson)};
auto & mat{*std::get<0>(mat_eval)};
auto & evaluator{std::get<1>(mat_eval)};
using T2_t = Eigen::Matrix<Real, twoD, twoD>;
using T4_t = T4Mat<Real, twoD>;
const T2_t F{(T2_t::Random() - (T2_t::Ones() * .5)) * 1e-4 +
T2_t::Identity()};
const T2_t eps{
.5 * ((F - T2_t::Identity()) + (F - T2_t::Identity()).transpose())};
BOOST_CHECK_THROW(evaluator.evaluate_stress(eps, Formulation::small_strain),
std::runtime_error);
T2_t eigen_strain{[](auto x) {
return 1e-4 * (x + x.transpose());
}(T2_t::Random() - T2_t::Ones() * .5)};
mat.add_pixel({}, eigen_strain);
const T2_t sigma{evaluator.evaluate_stress(eps, Formulation::small_strain)};
const T2_t P{evaluator.evaluate_stress(F, Formulation::finite_strain)};
auto J{F.determinant()};
auto P_reconstruct{J * sigma * F.inverse().transpose()};
auto error_comp{[](const auto & a, const auto & b) {
return (a - b).norm() / (a + b).norm();
}};
auto error{error_comp(P, P_reconstruct)};
constexpr Real small_strain_tol{1e-3};
if (not(error <= small_strain_tol)) {
std::cout << "F =" << std::endl << F << std::endl;
std::cout << "ε =" << std::endl << eps << std::endl;
std::cout << "P =" << std::endl << P << std::endl;
std::cout << "σ =" << std::endl << sigma << std::endl;
std::cout << "P_reconstructed =" << std::endl
<< P_reconstruct << std::endl;
}
BOOST_CHECK_LE(error, small_strain_tol);
T2_t sigma2, P2;
T4_t C, K;
std::tie(sigma2, C) =
evaluator.evaluate_stress_tangent(eps, Formulation::small_strain);
std::tie(P2, K) =
evaluator.evaluate_stress_tangent(F, Formulation::finite_strain);
error = error_comp(sigma2, sigma);
BOOST_CHECK_LE(error, tol);
error = error_comp(P2, P);
BOOST_CHECK_LE(error, tol);
error = error_comp(C, K);
if (not(error <= small_strain_tol)) {
std::cout << "F =" << std::endl << F << std::endl;
std::cout << "ε =" << std::endl << eps << std::endl;
std::cout << "P =" << std::endl << P << std::endl;
std::cout << "σ =" << std::endl << sigma << std::endl;
std::cout << "K =" << std::endl << K << std::endl;
std::cout << "C =" << std::endl << C << std::endl;
}
BOOST_CHECK_LE(error, small_strain_tol);
}
/* ---------------------------------------------------------------------- */
BOOST_AUTO_TEST_CASE(tangent_estimation) {
using Mat_t = MaterialLinearElastic1<twoD, twoD>;
constexpr Real Young{210e9};
constexpr Real Poisson{.33};
auto mat_eval = Mat_t::make_evaluator(Young, Poisson);
auto & mat = *std::get<0>(mat_eval);
auto & evaluator = std::get<1>(mat_eval);
using T2_t = Eigen::Matrix<Real, twoD, twoD>;
using T4_t = T4Mat<Real, twoD>;
const T2_t F{(T2_t::Random() - (T2_t::Ones() * .5)) * 1e-4 +
T2_t::Identity()};
const T2_t eps{
.5 * ((F - T2_t::Identity()) + (F - T2_t::Identity()).transpose())};
BOOST_CHECK_THROW(evaluator.evaluate_stress(eps, Formulation::small_strain),
std::runtime_error);
mat.add_pixel({});
T2_t sigma, P;
T4_t C, K;
std::tie(sigma, C) =
evaluator.evaluate_stress_tangent(eps, Formulation::small_strain);
std::tie(P, K) =
evaluator.evaluate_stress_tangent(F, Formulation::finite_strain);
constexpr Real linear_step{1.};
constexpr Real nonlin_step{1.e-6};
T4_t C_estim{evaluator.estimate_tangent(eps, Formulation::small_strain,
linear_step)};
T4_t K_estim{evaluator.estimate_tangent(F, Formulation::finite_strain,
nonlin_step)};
auto error_comp{[](const auto & a, const auto & b) {
return (a - b).norm() / (a + b).norm();
}};
constexpr Real finite_diff_tol{1e-9};
Real error {error_comp(K, K_estim)};
if (not(error <= finite_diff_tol)) {
std::cout << "K =" << std::endl << K << std::endl;
std::cout << "K_estim =" << std::endl << K_estim << std::endl;
}
BOOST_CHECK_LE(error, finite_diff_tol);
error = error_comp(C, C_estim);
if (not(error <= tol)) {
std::cout << "centred difference:" << std::endl;
std::cout << "C =" << std::endl << C << std::endl;
std::cout << "C_estim =" << std::endl << C_estim << std::endl;
}
BOOST_CHECK_LE(error, tol);
C_estim = evaluator.estimate_tangent(eps, Formulation::small_strain,
linear_step, FiniteDiff::forward);
error = error_comp(C, C_estim);
if (not(error <= tol)) {
std::cout << "forward difference:" << std::endl;
std::cout << "C =" << std::endl << C << std::endl;
std::cout << "C_estim =" << std::endl << C_estim << std::endl;
}
BOOST_CHECK_LE(error, tol);
C_estim = evaluator.estimate_tangent(eps, Formulation::small_strain,
linear_step, FiniteDiff::backward);
error = error_comp(C, C_estim);
if (not(error <= tol)) {
std::cout << "backward difference:" << std::endl;
std::cout << "C =" << std::endl << C << std::endl;
std::cout << "C_estim =" << std::endl << C_estim << std::endl;
}
BOOST_CHECK_LE(error, tol);
}
BOOST_AUTO_TEST_SUITE_END();
} // namespace muSpectre

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