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muSpectre/tests/test_materials_toolbox.cc
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/**
* @file test_materials_toolbox.cc
*
* @author Till Junge <till.junge@altermail.ch>
*
* @date 05 Nov 2017
*
* @brief Tests for the materials toolbox
*
* Copyright © 2017 Till Junge
*
* µSpectre is free software; you can redistribute it and/or
* modify it under the terms of the GNU 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 General Public License
* along with GNU Emacs; see the file COPYING. If not, write to the
* Free Software Foundation, Inc., 59 Temple Place - Suite 330,
* Boston, MA 02111-1307, USA.
*/
#include <Eigen/Dense>
#include "tests.hh"
#include "materials/materials_toolbox.hh"
#include "common/T4_map_proxy.hh"
#include "common/tensor_algebra.hh"
#include "tests/test_goodies.hh"
namespace muSpectre {
BOOST_AUTO_TEST_SUITE(materials_toolbox)
BOOST_FIXTURE_TEST_CASE_TEMPLATE(test_strain_conversion, Fix,
testGoodies::dimlist, Fix){
constexpr Dim_t dim{Fix::dim};
using T2 = Eigen::Matrix<Real, dim, dim>;
T2 F{(T2::Random() -.5*T2::Ones())/20 + T2::Identity()};
// checking Green-Lagrange
T2 Eref = .5*(F.transpose()*F-T2::Identity());
T2 E_tb = MatTB::convert_strain<StrainMeasure::Gradient,
StrainMeasure::GreenLagrange>
(Eigen::Map<Eigen::Matrix<Real, dim, dim>>(F.data()));
Real error = (Eref-E_tb).norm();
BOOST_CHECK_LT(error, tol);
// checking Left Cauchy-Green
Eref = F*F.transpose();
E_tb = MatTB::convert_strain<StrainMeasure::Gradient,
StrainMeasure::LCauchyGreen>(F);
error = (Eref-E_tb).norm();
BOOST_CHECK_LT(error, tol);
// checking Right Cauchy-Green
Eref = F.transpose()*F;
E_tb = MatTB::convert_strain<StrainMeasure::Gradient,
StrainMeasure::RCauchyGreen>(F);
error = (Eref-E_tb).norm();
BOOST_CHECK_LT(error, tol);
// checking Hencky (logarithmic) strain
Eref = F.transpose()*F;
Eigen::SelfAdjointEigenSolver<T2> EigSolv(Eref);
Eref.setZero();
for (size_t i{0}; i < dim; ++i) {
auto && vec = EigSolv.eigenvectors().col(i);
auto && val = EigSolv.eigenvalues()(i);
Eref += .5*std::log(val) * vec*vec.transpose();
}
E_tb = MatTB::convert_strain<StrainMeasure::Gradient,
StrainMeasure::Log>(F);
error = (Eref-E_tb).norm();
BOOST_CHECK_LT(error, tol);
auto F_tb = MatTB::convert_strain<StrainMeasure::Gradient, StrainMeasure::Gradient>(F);
error = (F-F_tb).norm();
BOOST_CHECK_LT(error, tol);
}
BOOST_FIXTURE_TEST_CASE_TEMPLATE(dumb_tensor_mult_test, Fix,
testGoodies::dimlist, Fix) {
constexpr Dim_t dim{Fix::dim};
using T4 = T4Mat<Real, dim>;
T4 A,B, R1, R2;
A.setRandom();
B.setRandom();
R1 = A*B;
R2.setZero();
for (Dim_t i = 0; i < dim; ++i) {
for (Dim_t j = 0; j < dim; ++j) {
for (Dim_t a = 0; a < dim; ++a) {
for (Dim_t b = 0; b < dim; ++b) {
for (Dim_t k = 0; k < dim; ++k) {
for (Dim_t l = 0; l < dim; ++l) {
get(R2,i,j,k,l) += get(A, i,j,a,b)*get(B, a,b, k,l);
}
}
}
}
}
}
auto error{(R1-R2).norm()};
BOOST_CHECK_LT(error, tol);
}
BOOST_FIXTURE_TEST_CASE_TEMPLATE(test_PK1_stress, Fix,
testGoodies::dimlist, Fix) {
using namespace Matrices;
constexpr Dim_t dim{Fix::dim};
using T2 = Eigen::Matrix<Real, dim, dim>;
using T4 = T4Mat<Real, dim>;
testGoodies::RandRange<Real> rng;
T2 F=T2::Identity()*2 ;
//F.setRandom();
T2 E_tb = MatTB::convert_strain<StrainMeasure::Gradient, StrainMeasure::GreenLagrange>
(Eigen::Map<Eigen::Matrix<Real, dim, dim>>(F.data()));
Real lambda = 3;//rng.randval(1, 2);
Real mu = 4;//rng.randval(1,2);
T4 J = Itrac<dim>();
T2 I = I2<dim>();
T4 I4 = Isymm<dim>();
T4 C = lambda*J + 2*mu*I4;
T2 S = tensmult(C, E_tb);
T2 Sref = lambda*E_tb.trace()*I + 2*mu*E_tb;
auto error{(Sref-S).norm()};
BOOST_CHECK_LT(error, tol);
T4 K = outer_under(I,S) + outer_under(F,I)*C*outer_under(F.transpose(),I);
// See Curnier, 2000, "Méthodes numériques en mécanique des solides", p 252
T4 Kref;
Real Fkrkr = (F.array()*F.array()).sum();
T2 Fkmkn = F.transpose()*F;
T2 Fisjs = F*F.transpose();
Kref.setZero();
for (Dim_t i = 0; i < dim; ++i) {
for (Dim_t j = 0; j < dim; ++j) {
for (Dim_t m = 0; m < dim; ++m) {
for (Dim_t n = 0; n < dim; ++n) {
get(Kref, i, m, j, n) =
(lambda*((Fkrkr-dim)/2 * I(i,j)*I(m,n) + F(i,m)*F(j,n)) +
mu * (I(i,j)*Fkmkn(m,n) + Fisjs(i,j)*I(m,n) -
I(i,j) *I(m,n) + F(i,n)*F(j,m)));
}
}
}
}
error = (Kref-K).norm();
BOOST_CHECK_LT(error, tol);
T2 P = MatTB::PK1_stress<StressMeasure::PK2, StrainMeasure::GreenLagrange>(F, S);
T2 Pref = F*S;
error = (P-Pref).norm();
BOOST_CHECK_LT(error, tol);
auto && stress_tgt = MatTB::PK1_stress<StressMeasure::PK2, StrainMeasure::GreenLagrange>(F, S, C);
T2 P_t = std::move(std::get<0>(stress_tgt));
T4 K_t = std::move(std::get<1>(stress_tgt));
error = (P_t-Pref).norm();
BOOST_CHECK_LT(error, tol);
error = (K_t-Kref).norm();
BOOST_CHECK_LT(error, tol);
auto && stress_tgt_trivial =
MatTB::PK1_stress<StressMeasure::PK1, StrainMeasure::Gradient>(F, P, K);
T2 P_u = std::move(std::get<0>(stress_tgt_trivial));
T4 K_u = std::move(std::get<1>(stress_tgt_trivial));
error = (P_u-Pref).norm();
BOOST_CHECK_LT(error, tol);
error = (K_u-Kref).norm();
BOOST_CHECK_LT(error, tol);
T2 P_g;
T4 K_g;
std::tie(P_g, K_g) = testGoodies::objective_hooke_explicit(lambda, mu, F);
error = (P_g-Pref).norm();
BOOST_CHECK_LT(error, tol);
error = (K_g-Kref).norm();
BOOST_CHECK_LT(error, tol);
}
BOOST_AUTO_TEST_CASE(elastic_modulus_conversions)
{
// define original input
constexpr Real E{123.456};
constexpr Real nu{.3};
using namespace MatTB;
// derived values
constexpr Real K{convert_elastic_modulus<ElasticModulus::Bulk,
ElasticModulus::Young,
ElasticModulus::Poisson>(E, nu)};
constexpr Real lambda{convert_elastic_modulus<ElasticModulus::lambda,
ElasticModulus::Young,
ElasticModulus::Poisson>(E, nu)};
constexpr Real mu{convert_elastic_modulus<ElasticModulus::Shear,
ElasticModulus::Young,
ElasticModulus::Poisson>(E, nu)};
// recover original inputs
Real comp = convert_elastic_modulus<ElasticModulus::Young,
ElasticModulus::Bulk,
ElasticModulus::Shear>(K, mu);
Real err = E - comp;
BOOST_CHECK_LT(err, tol);
comp = convert_elastic_modulus<ElasticModulus::Poisson,
ElasticModulus::Bulk,
ElasticModulus::Shear>(K, mu);
err = nu - comp;
BOOST_CHECK_LT(err, tol);
comp = convert_elastic_modulus<ElasticModulus::Young,
ElasticModulus::lambda,
ElasticModulus::Shear>(lambda, mu);
err = E - comp;
BOOST_CHECK_LT(err, tol);
// check inversion resistance
Real compA = convert_elastic_modulus<ElasticModulus::Poisson,
ElasticModulus::Bulk,
ElasticModulus::Shear>(K, mu);
Real compB = convert_elastic_modulus<ElasticModulus::Poisson,
ElasticModulus::Shear,
ElasticModulus::Bulk>(mu, K);
BOOST_CHECK_EQUAL(compA, compB);
// check trivial self-returning
comp = convert_elastic_modulus<ElasticModulus::Bulk,
ElasticModulus::Bulk,
ElasticModulus::Shear>(K, mu);
BOOST_CHECK_EQUAL(K, comp);
comp = convert_elastic_modulus<ElasticModulus::Shear,
ElasticModulus::Bulk,
ElasticModulus::Shear>(K, mu);
BOOST_CHECK_EQUAL(mu, comp);
}
BOOST_AUTO_TEST_SUITE_END();
} // muSpectre
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