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test_elastic_materials.cc
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/**
* @file test_elastic_materials.cc
*
* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
* @author Lucas Frerot <lucas.frerot@epfl.ch>
* @author Enrico Milanese <enrico.milanese@epfl.ch>
*
* @date creation: Fri Nov 17 2017
* @date last modification: Wed Nov 18 2020
*
* @brief Tests the Elastic materials
*
*
* @section LICENSE
*
* Copyright (©) 2016-2021 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 "test_gtest_utils.hh"
#include "test_material_fixtures.hh"
/* -------------------------------------------------------------------------- */
#include <material_elastic.hh>
#include <material_elastic_orthotropic.hh>
#include <solid_mechanics_model.hh>
/* -------------------------------------------------------------------------- */
#include <gtest/gtest.h>
#include <type_traits>
/* -------------------------------------------------------------------------- */
using namespace akantu;
using mat_types =
::testing::Types<Traits<MaterialElastic, 1>, Traits<MaterialElastic, 2>,
Traits<MaterialElastic, 3>,
Traits<MaterialElasticOrthotropic, 2>,
Traits<MaterialElasticOrthotropic, 3>,
Traits<MaterialElasticLinearAnisotropic, 2>,
Traits<MaterialElasticLinearAnisotropic, 3>>;
/* -------------------------------------------------------------------------- */
template <> void FriendMaterial<MaterialElastic<1>>::setParams() {
Real E = 3.;
Real rho = 2;
setParam("E", E);
setParam("rho", rho);
}
/* -------------------------------------------------------------------------- */
template <> void FriendMaterial<MaterialElastic<1>>::testComputeStress() {
Matrix<Real> eps = {{2}};
Matrix<Real> sigma(1, 1);
Real sigma_th = 2;
this->computeStressOnQuad(eps, sigma, sigma_th);
auto solution = E * eps(0, 0) + sigma_th;
EXPECT_NEAR(sigma(0, 0), solution, 1e-14);
}
/* -------------------------------------------------------------------------- */
template <> void FriendMaterial<MaterialElastic<1>>::testEnergyDensity() {
Real eps = 2, sigma = 2;
Real epot = 0;
this->computePotentialEnergyOnQuad({{eps}}, {{sigma}}, epot);
Real solution = 2;
EXPECT_NEAR(epot, solution, 1e-14);
}
/* -------------------------------------------------------------------------- */
template <>
void FriendMaterial<MaterialElastic<1>>::testComputeTangentModuli() {
Matrix<Real> tangent(1, 1);
this->computeTangentModuliOnQuad(tangent);
EXPECT_NEAR(tangent(0, 0), E, 1e-14);
}
/* -------------------------------------------------------------------------- */
template <> void FriendMaterial<MaterialElastic<1>>::testCelerity() {
auto wave_speed = this->getCelerity(Element());
auto solution = std::sqrt(E / rho);
EXPECT_NEAR(wave_speed, solution, 1e-14);
}
/* -------------------------------------------------------------------------- */
template <> void FriendMaterial<MaterialElastic<2>>::setParams() {
Real E = 1.;
Real nu = .3;
Real rho = 2;
setParam("E", E);
setParam("nu", nu);
setParam("rho", rho);
}
/* -------------------------------------------------------------------------- */
template <> void FriendMaterial<MaterialElastic<2>>::testComputeStress() {
Real bulk_modulus_K = E / (3 * (1 - 2 * nu));
Real shear_modulus_mu = E / (2 * (1 + nu));
auto rotation_matrix = getRandomRotation();
auto grad_u = this->getComposedStrain(1.).block(0, 0, 2, 2);
auto grad_u_rot = this->applyRotation(grad_u, rotation_matrix);
Matrix<Real> sigma_rot(2, 2);
this->computeStressOnQuad(grad_u_rot, sigma_rot, sigma_th);
auto sigma = this->reverseRotation(sigma_rot, rotation_matrix);
auto identity = Matrix<Real>::eye(2, 1.);
auto strain = 0.5 * (grad_u + grad_u.transpose());
auto deviatoric_strain = strain - 1. / 3. * strain.trace() * identity;
auto sigma_expected = 2 * shear_modulus_mu * deviatoric_strain +
(sigma_th + 2. * bulk_modulus_K) * identity;
auto diff = sigma - sigma_expected;
Real stress_error = diff.norm<L_inf>() / sigma_expected.norm<L_inf>();
EXPECT_NEAR(stress_error, 0., 1e-13);
}
/* -------------------------------------------------------------------------- */
template <> void FriendMaterial<MaterialElastic<2>>::testEnergyDensity() {
Matrix<Real> sigma = {{1, 2}, {2, 4}};
Matrix<Real> eps = {{1, 0}, {0, 1}};
Real epot = 0;
Real solution = 2.5;
this->computePotentialEnergyOnQuad(eps, sigma, epot);
EXPECT_NEAR(epot, solution, 1e-14);
}
/* -------------------------------------------------------------------------- */
template <>
void FriendMaterial<MaterialElastic<2>>::testComputeTangentModuli() {
Matrix<Real> tangent(3, 3);
/* Plane Strain */
// clang-format off
Matrix<Real> solution = {
{1 - nu, nu, 0},
{nu, 1 - nu, 0},
{0, 0, (1 - 2 * nu) / 2},
};
// clang-format on
solution *= E / ((1 + nu) * (1 - 2 * nu));
this->computeTangentModuliOnQuad(tangent);
Real tangent_error = (tangent - solution).norm<L_2>();
EXPECT_NEAR(tangent_error, 0, 1e-14);
/* Plane Stress */
this->plane_stress = true;
this->updateInternalParameters();
// clang-format off
solution = {
{1, nu, 0},
{nu, 1, 0},
{0, 0, (1 - nu) / 2},
};
// clang-format on
solution *= E / (1 - nu * nu);
this->computeTangentModuliOnQuad(tangent);
tangent_error = (tangent - solution).norm<L_2>();
EXPECT_NEAR(tangent_error, 0, 1e-14);
}
/* -------------------------------------------------------------------------- */
template <> void FriendMaterial<MaterialElastic<2>>::testCelerity() {
auto push_wave_speed = this->getPushWaveSpeed(Element());
auto celerity = this->getCelerity(Element());
Real K = E / (3 * (1 - 2 * nu));
Real mu = E / (2 * (1 + nu));
Real sol = std::sqrt((K + 4. / 3 * mu) / rho);
EXPECT_NEAR(push_wave_speed, sol, 1e-14);
EXPECT_NEAR(celerity, sol, 1e-14);
auto shear_wave_speed = this->getShearWaveSpeed(Element());
sol = std::sqrt(mu / rho);
EXPECT_NEAR(shear_wave_speed, sol, 1e-14);
}
/* -------------------------------------------------------------------------- */
template <> void FriendMaterial<MaterialElastic<3>>::setParams() {
Real E = 1.;
Real nu = .3;
Real rho = 2;
setParam("E", E);
setParam("nu", nu);
setParam("rho", rho);
}
/* -------------------------------------------------------------------------- */
template <> void FriendMaterial<MaterialElastic<3>>::testComputeStress() {
Real bulk_modulus_K = E / 3. / (1 - 2. * nu);
Real shear_modulus_mu = 0.5 * E / (1 + nu);
Matrix<Real> rotation_matrix = getRandomRotation();
auto grad_u = this->getComposedStrain(1.);
auto grad_u_rot = this->applyRotation(grad_u, rotation_matrix);
Matrix<Real> sigma_rot(3, 3);
this->computeStressOnQuad(grad_u_rot, sigma_rot, sigma_th);
auto sigma = this->reverseRotation(sigma_rot, rotation_matrix);
Matrix<Real> identity(3, 3);
identity.eye();
Matrix<Real> strain = 0.5 * (grad_u + grad_u.transpose());
Matrix<Real> deviatoric_strain = strain - 1. / 3. * strain.trace() * identity;
Matrix<Real> sigma_expected = 2 * shear_modulus_mu * deviatoric_strain +
(sigma_th + 3. * bulk_modulus_K) * identity;
auto diff = sigma - sigma_expected;
Real stress_error = diff.norm<L_inf>();
EXPECT_NEAR(stress_error, 0., 1e-14);
}
/* -------------------------------------------------------------------------- */
template <> void FriendMaterial<MaterialElastic<3>>::testEnergyDensity() {
Matrix<Real> sigma = {{1, 2, 3}, {2, 4, 5}, {3, 5, 6}};
Matrix<Real> eps = {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}};
Real epot = 0;
Real solution = 5.5;
this->computePotentialEnergyOnQuad(eps, sigma, epot);
EXPECT_NEAR(epot, solution, 1e-14);
}
/* -------------------------------------------------------------------------- */
template <>
void FriendMaterial<MaterialElastic<3>>::testComputeTangentModuli() {
Matrix<Real> tangent(6, 6);
// clang-format off
Matrix<Real> solution = {
{1 - nu, nu, nu, 0, 0, 0},
{nu, 1 - nu, nu, 0, 0, 0},
{nu, nu, 1 - nu, 0, 0, 0},
{0, 0, 0, (1 - 2 * nu) / 2, 0, 0},
{0, 0, 0, 0, (1 - 2 * nu) / 2, 0},
{0, 0, 0, 0, 0, (1 - 2 * nu) / 2},
};
// clang-format on
solution *= E / ((1 + nu) * (1 - 2 * nu));
this->computeTangentModuliOnQuad(tangent);
Real tangent_error = (tangent - solution).norm<L_2>();
EXPECT_NEAR(tangent_error, 0, 1e-14);
}
/* -------------------------------------------------------------------------- */
template <> void FriendMaterial<MaterialElastic<3>>::testCelerity() {
auto push_wave_speed = this->getPushWaveSpeed(Element());
auto celerity = this->getCelerity(Element());
Real K = E / (3 * (1 - 2 * nu));
Real mu = E / (2 * (1 + nu));
Real sol = std::sqrt((K + 4. / 3 * mu) / rho);
EXPECT_NEAR(push_wave_speed, sol, 1e-14);
EXPECT_NEAR(celerity, sol, 1e-14);
auto shear_wave_speed = this->getShearWaveSpeed(Element());
sol = std::sqrt(mu / rho);
EXPECT_NEAR(shear_wave_speed, sol, 1e-14);
}
/* -------------------------------------------------------------------------- */
template <> void FriendMaterial<MaterialElasticOrthotropic<2>>::setParams() {
// Note: for this test material and canonical basis coincide
Vector<Real> n1 = {1, 0};
Vector<Real> n2 = {0, 1};
Real E1 = 1.;
Real E2 = 2.;
Real nu12 = 0.1;
Real G12 = 2.;
Real rho = 2.5;
*this->dir_vecs[0] = n1;
*this->dir_vecs[1] = n2;
this->E1 = E1;
this->E2 = E2;
this->nu12 = nu12;
this->G12 = G12;
this->rho = rho;
}
/* -------------------------------------------------------------------------- */
template <>
void FriendMaterial<MaterialElasticOrthotropic<2>>::testComputeStress() {
UInt Dim = 2;
// material frame of reference is rotate by rotation_matrix starting from
// canonical basis
Matrix<Real> rotation_matrix = getRandomRotation();
// canonical basis as expressed in the material frame of reference, as
// required by MaterialElasticOrthotropic class (it is simply given by the
// columns of the rotation_matrix; the lines give the material basis expressed
// in the canonical frame of reference)
*this->dir_vecs[0] = rotation_matrix(0);
*this->dir_vecs[1] = rotation_matrix(1);
// set internal Cijkl matrix expressed in the canonical frame of reference
this->updateInternalParameters();
// gradient in material frame of reference
auto grad_u = this->getComposedStrain(2.).block(0, 0, 2, 2);
// gradient in canonical basis (we need to rotate *back* to the canonical
// basis)
auto grad_u_rot = this->reverseRotation(grad_u, rotation_matrix);
// stress in the canonical basis
Matrix<Real> sigma_rot(2, 2);
this->computeStressOnQuad(grad_u_rot, sigma_rot);
// stress in the material reference (we need to apply the rotation)
auto sigma = this->applyRotation(sigma_rot, rotation_matrix);
// construction of Cijkl engineering tensor in the *material* frame of
// reference
// ref: http://solidmechanics.org/Text/Chapter3_2/Chapter3_2.php#Sect3_2_13
Real nu21 = nu12 * E2 / E1;
Real gamma = 1 / (1 - nu12 * nu21);
Matrix<Real> C_expected(2 * Dim, 2 * Dim, 0);
C_expected(0, 0) = gamma * E1;
C_expected(1, 1) = gamma * E2;
C_expected(2, 2) = G12;
C_expected(1, 0) = C_expected(0, 1) = gamma * E1 * nu21;
// epsilon is computed directly in the *material* frame of reference
Matrix<Real> epsilon = 0.5 * (grad_u + grad_u.transpose());
// sigma_expected is computed directly in the *material* frame of reference
Matrix<Real> sigma_expected(Dim, Dim);
for (UInt i = 0; i < Dim; ++i) {
for (UInt j = 0; j < Dim; ++j) {
sigma_expected(i, i) += C_expected(i, j) * epsilon(j, j);
}
}
sigma_expected(0, 1) = sigma_expected(1, 0) =
C_expected(2, 2) * 2 * epsilon(0, 1);
// sigmas are checked in the *material* frame of reference
auto diff = sigma - sigma_expected;
Real stress_error = diff.norm<L_inf>();
EXPECT_NEAR(stress_error, 0., 1e-13);
}
/* -------------------------------------------------------------------------- */
template <>
void FriendMaterial<MaterialElasticOrthotropic<2>>::testEnergyDensity() {
Matrix<Real> sigma = {{1, 2}, {2, 4}};
Matrix<Real> eps = {{1, 0}, {0, 1}};
Real epot = 0;
Real solution = 2.5;
this->computePotentialEnergyOnQuad(eps, sigma, epot);
EXPECT_NEAR(epot, solution, 1e-14);
}
/* -------------------------------------------------------------------------- */
template <>
void FriendMaterial<MaterialElasticOrthotropic<2>>::testComputeTangentModuli() {
// construction of Cijkl engineering tensor in the *material* frame of
// reference
// ref: http://solidmechanics.org/Text/Chapter3_2/Chapter3_2.php#Sect3_2_13
Real nu21 = nu12 * E2 / E1;
Real gamma = 1 / (1 - nu12 * nu21);
Matrix<Real> C_expected(3, 3);
C_expected(0, 0) = gamma * E1;
C_expected(1, 1) = gamma * E2;
C_expected(2, 2) = G12;
C_expected(1, 0) = C_expected(0, 1) = gamma * E1 * nu21;
Matrix<Real> tangent(3, 3);
this->computeTangentModuliOnQuad(tangent);
Real tangent_error = (tangent - C_expected).norm<L_2>();
EXPECT_NEAR(tangent_error, 0, 1e-14);
}
/* -------------------------------------------------------------------------- */
template <> void FriendMaterial<MaterialElasticOrthotropic<2>>::testCelerity() {
// construction of Cijkl engineering tensor in the *material* frame of
// reference
// ref: http://solidmechanics.org/Text/Chapter3_2/Chapter3_2.php#Sect3_2_13
Real nu21 = nu12 * E2 / E1;
Real gamma = 1 / (1 - nu12 * nu21);
Matrix<Real> C_expected(3, 3);
C_expected(0, 0) = gamma * E1;
C_expected(1, 1) = gamma * E2;
C_expected(2, 2) = G12;
C_expected(1, 0) = C_expected(0, 1) = gamma * E1 * nu21;
Vector<Real> eig_expected(3);
C_expected.eig(eig_expected);
auto celerity_expected = std::sqrt(eig_expected(0) / rho);
auto celerity = this->getCelerity(Element());
EXPECT_NEAR(celerity_expected, celerity, 1e-14);
}
/* -------------------------------------------------------------------------- */
template <> void FriendMaterial<MaterialElasticOrthotropic<3>>::setParams() {
Vector<Real> n1 = {1, 0, 0};
Vector<Real> n2 = {0, 1, 0};
Vector<Real> n3 = {0, 0, 1};
Real E1 = 1.;
Real E2 = 2.;
Real E3 = 3.;
Real nu12 = 0.1;
Real nu13 = 0.2;
Real nu23 = 0.3;
Real G12 = 2.;
Real G13 = 3.;
Real G23 = 1.;
Real rho = 2.3;
*this->dir_vecs[0] = n1;
*this->dir_vecs[1] = n2;
*this->dir_vecs[2] = n3;
this->E1 = E1;
this->E2 = E2;
this->E3 = E3;
this->nu12 = nu12;
this->nu13 = nu13;
this->nu23 = nu23;
this->G12 = G12;
this->G13 = G13;
this->G23 = G23;
this->rho = rho;
}
/* -------------------------------------------------------------------------- */
template <>
void FriendMaterial<MaterialElasticOrthotropic<3>>::testComputeStress() {
UInt Dim = 3;
// material frame of reference is rotate by rotation_matrix starting from
// canonical basis
Matrix<Real> rotation_matrix = getRandomRotation();
// canonical basis as expressed in the material frame of reference, as
// required by MaterialElasticOrthotropic class (it is simply given by the
// columns of the rotation_matrix; the lines give the material basis expressed
// in the canonical frame of reference)
*this->dir_vecs[0] = rotation_matrix(0);
*this->dir_vecs[1] = rotation_matrix(1);
*this->dir_vecs[2] = rotation_matrix(2);
// set internal Cijkl matrix expressed in the canonical frame of reference
this->updateInternalParameters();
// gradient in material frame of reference
auto grad_u = this->getComposedStrain(2.);
// gradient in canonical basis (we need to rotate *back* to the canonical
// basis)
auto grad_u_rot = this->reverseRotation(grad_u, rotation_matrix);
// stress in the canonical basis
Matrix<Real> sigma_rot(3, 3);
this->computeStressOnQuad(grad_u_rot, sigma_rot);
// stress in the material reference (we need to apply the rotation)
auto sigma = this->applyRotation(sigma_rot, rotation_matrix);
// construction of Cijkl engineering tensor in the *material* frame of
// reference
// ref: http://solidmechanics.org/Text/Chapter3_2/Chapter3_2.php#Sect3_2_13
Real nu21 = nu12 * E2 / E1;
Real nu31 = nu13 * E3 / E1;
Real nu32 = nu23 * E3 / E2;
Real gamma = 1 / (1 - nu12 * nu21 - nu23 * nu32 - nu31 * nu13 -
2 * nu21 * nu32 * nu13);
Matrix<Real> C_expected(6, 6);
C_expected(0, 0) = gamma * E1 * (1 - nu23 * nu32);
C_expected(1, 1) = gamma * E2 * (1 - nu13 * nu31);
C_expected(2, 2) = gamma * E3 * (1 - nu12 * nu21);
C_expected(1, 0) = C_expected(0, 1) = gamma * E1 * (nu21 + nu31 * nu23);
C_expected(2, 0) = C_expected(0, 2) = gamma * E1 * (nu31 + nu21 * nu32);
C_expected(2, 1) = C_expected(1, 2) = gamma * E2 * (nu32 + nu12 * nu31);
C_expected(3, 3) = G23;
C_expected(4, 4) = G13;
C_expected(5, 5) = G12;
// epsilon is computed directly in the *material* frame of reference
Matrix<Real> epsilon = 0.5 * (grad_u + grad_u.transpose());
// sigma_expected is computed directly in the *material* frame of reference
Matrix<Real> sigma_expected(Dim, Dim);
for (UInt i = 0; i < Dim; ++i) {
for (UInt j = 0; j < Dim; ++j) {
sigma_expected(i, i) += C_expected(i, j) * epsilon(j, j);
}
}
sigma_expected(0, 1) = C_expected(5, 5) * 2 * epsilon(0, 1);
sigma_expected(0, 2) = C_expected(4, 4) * 2 * epsilon(0, 2);
sigma_expected(1, 2) = C_expected(3, 3) * 2 * epsilon(1, 2);
sigma_expected(1, 0) = sigma_expected(0, 1);
sigma_expected(2, 0) = sigma_expected(0, 2);
sigma_expected(2, 1) = sigma_expected(1, 2);
// sigmas are checked in the *material* frame of reference
auto diff = sigma - sigma_expected;
Real stress_error = diff.norm<L_inf>();
EXPECT_NEAR(stress_error, 0., 1e-13);
}
/* -------------------------------------------------------------------------- */
template <>
void FriendMaterial<MaterialElasticOrthotropic<3>>::testEnergyDensity() {
Matrix<Real> sigma = {{1, 2, 3}, {2, 4, 5}, {3, 5, 6}};
Matrix<Real> eps = {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}};
Real epot = 0;
Real solution = 5.5;
this->computePotentialEnergyOnQuad(eps, sigma, epot);
EXPECT_NEAR(epot, solution, 1e-14);
}
/* -------------------------------------------------------------------------- */
template <>
void FriendMaterial<MaterialElasticOrthotropic<3>>::testComputeTangentModuli() {
// Note: for this test material and canonical basis coincide
UInt Dim = 3;
// construction of Cijkl engineering tensor in the *material* frame of
// reference
// ref: http://solidmechanics.org/Text/Chapter3_2/Chapter3_2.php#Sect3_2_13
Real nu21 = nu12 * E2 / E1;
Real nu31 = nu13 * E3 / E1;
Real nu32 = nu23 * E3 / E2;
Real gamma = 1 / (1 - nu12 * nu21 - nu23 * nu32 - nu31 * nu13 -
2 * nu21 * nu32 * nu13);
Matrix<Real> C_expected(2 * Dim, 2 * Dim, 0);
C_expected(0, 0) = gamma * E1 * (1 - nu23 * nu32);
C_expected(1, 1) = gamma * E2 * (1 - nu13 * nu31);
C_expected(2, 2) = gamma * E3 * (1 - nu12 * nu21);
C_expected(1, 0) = C_expected(0, 1) = gamma * E1 * (nu21 + nu31 * nu23);
C_expected(2, 0) = C_expected(0, 2) = gamma * E1 * (nu31 + nu21 * nu32);
C_expected(2, 1) = C_expected(1, 2) = gamma * E2 * (nu32 + nu12 * nu31);
C_expected(3, 3) = G23;
C_expected(4, 4) = G13;
C_expected(5, 5) = G12;
Matrix<Real> tangent(6, 6);
this->computeTangentModuliOnQuad(tangent);
Real tangent_error = (tangent - C_expected).norm<L_2>();
EXPECT_NEAR(tangent_error, 0, 1e-14);
}
/* -------------------------------------------------------------------------- */
template <> void FriendMaterial<MaterialElasticOrthotropic<3>>::testCelerity() {
// Note: for this test material and canonical basis coincide
UInt Dim = 3;
// construction of Cijkl engineering tensor in the *material* frame of
// reference
// ref: http://solidmechanics.org/Text/Chapter3_2/Chapter3_2.php#Sect3_2_13
Real nu21 = nu12 * E2 / E1;
Real nu31 = nu13 * E3 / E1;
Real nu32 = nu23 * E3 / E2;
Real gamma = 1 / (1 - nu12 * nu21 - nu23 * nu32 - nu31 * nu13 -
2 * nu21 * nu32 * nu13);
Matrix<Real> C_expected(2 * Dim, 2 * Dim, 0);
C_expected(0, 0) = gamma * E1 * (1 - nu23 * nu32);
C_expected(1, 1) = gamma * E2 * (1 - nu13 * nu31);
C_expected(2, 2) = gamma * E3 * (1 - nu12 * nu21);
C_expected(1, 0) = C_expected(0, 1) = gamma * E1 * (nu21 + nu31 * nu23);
C_expected(2, 0) = C_expected(0, 2) = gamma * E1 * (nu31 + nu21 * nu32);
C_expected(2, 1) = C_expected(1, 2) = gamma * E2 * (nu32 + nu12 * nu31);
C_expected(3, 3) = G23;
C_expected(4, 4) = G13;
C_expected(5, 5) = G12;
Vector<Real> eig_expected(6);
C_expected.eig(eig_expected);
auto celerity_expected = std::sqrt(eig_expected(0) / rho);
auto celerity = this->getCelerity(Element());
EXPECT_NEAR(celerity_expected, celerity, 1e-14);
}
/* -------------------------------------------------------------------------- */
template <>
void FriendMaterial<MaterialElasticLinearAnisotropic<2>>::setParams() {
Matrix<Real> C = {
{1.0, 0.3, 0.4},
{0.3, 2.0, 0.1},
{0.4, 0.1, 1.5},
};
for (auto i = 0u; i < C.rows(); ++i)
for (auto j = 0u; j < C.cols(); ++j)
this->Cprime(i, j) = C(i, j);
this->rho = 2.7;
// material frame of reference is rotate by rotation_matrix starting from
// canonical basis
Matrix<Real> rotation_matrix = getRandomRotation();
// canonical basis as expressed in the material frame of reference, as
// required by MaterialElasticLinearAnisotropic class (it is simply given by
// the columns of the rotation_matrix; the lines give the material basis
// expressed in the canonical frame of reference)
*this->dir_vecs[0] = rotation_matrix(0);
*this->dir_vecs[1] = rotation_matrix(1);
}
/* -------------------------------------------------------------------------- */
template <>
void FriendMaterial<MaterialElasticLinearAnisotropic<2>>::testComputeStress() {
Matrix<Real> C = {
{1.0, 0.3, 0.4},
{0.3, 2.0, 0.1},
{0.4, 0.1, 1.5},
};
Matrix<Real> rotation_matrix(2, 2);
rotation_matrix(0) = *this->dir_vecs[0];
rotation_matrix(1) = *this->dir_vecs[1];
// gradient in material frame of reference
auto grad_u = this->getComposedStrain(1.).block(0, 0, 2, 2);
// gradient in canonical basis (we need to rotate *back* to the canonical
// basis)
auto grad_u_rot = this->reverseRotation(grad_u, rotation_matrix);
// stress in the canonical basis
Matrix<Real> sigma_rot(2, 2);
this->computeStressOnQuad(grad_u_rot, sigma_rot);
// stress in the material reference (we need to apply the rotation)
auto sigma = this->applyRotation(sigma_rot, rotation_matrix);
// epsilon is computed directly in the *material* frame of reference
Matrix<Real> epsilon = 0.5 * (grad_u + grad_u.transpose());
Vector<Real> epsilon_voigt(3);
epsilon_voigt(0) = epsilon(0, 0);
epsilon_voigt(1) = epsilon(1, 1);
epsilon_voigt(2) = 2 * epsilon(0, 1);
// sigma_expected is computed directly in the *material* frame of reference
Vector<Real> sigma_voigt = C * epsilon_voigt;
Matrix<Real> sigma_expected(2, 2);
sigma_expected(0, 0) = sigma_voigt(0);
sigma_expected(1, 1) = sigma_voigt(1);
sigma_expected(0, 1) = sigma_expected(1, 0) = sigma_voigt(2);
// sigmas are checked in the *material* frame of reference
auto diff = sigma - sigma_expected;
Real stress_error = diff.norm<L_inf>();
EXPECT_NEAR(stress_error, 0., 1e-13);
}
/* -------------------------------------------------------------------------- */
template <>
void FriendMaterial<MaterialElasticLinearAnisotropic<2>>::testEnergyDensity() {
Matrix<Real> sigma = {{1, 2}, {2, 4}};
Matrix<Real> eps = {{1, 0}, {0, 1}};
Real epot = 0;
Real solution = 2.5;
this->computePotentialEnergyOnQuad(eps, sigma, epot);
EXPECT_NEAR(epot, solution, 1e-14);
}
/* -------------------------------------------------------------------------- */
template <>
void FriendMaterial<
MaterialElasticLinearAnisotropic<2>>::testComputeTangentModuli() {
Matrix<Real> tangent(3, 3);
this->computeTangentModuliOnQuad(tangent);
Real tangent_error = (tangent - C).norm<L_2>();
EXPECT_NEAR(tangent_error, 0, 1e-14);
}
/* -------------------------------------------------------------------------- */
template <>
void FriendMaterial<MaterialElasticLinearAnisotropic<2>>::testCelerity() {
Vector<Real> eig_expected(3);
C.eig(eig_expected);
auto celerity_expected = std::sqrt(eig_expected(0) / this->rho);
auto celerity = this->getCelerity(Element());
EXPECT_NEAR(celerity_expected, celerity, 1e-14);
}
/* -------------------------------------------------------------------------- */
template <>
void FriendMaterial<MaterialElasticLinearAnisotropic<3>>::setParams() {
// Note: for this test material and canonical basis coincide
Matrix<Real> C = {
{1.0, 0.3, 0.4, 0.3, 0.2, 0.1}, {0.3, 2.0, 0.1, 0.2, 0.3, 0.2},
{0.4, 0.1, 1.5, 0.1, 0.4, 0.3}, {0.3, 0.2, 0.1, 2.4, 0.1, 0.4},
{0.2, 0.3, 0.4, 0.1, 0.9, 0.1}, {0.1, 0.2, 0.3, 0.4, 0.1, 1.2},
};
for (auto i = 0u; i < C.rows(); ++i)
for (auto j = 0u; j < C.cols(); ++j)
this->Cprime(i, j) = C(i, j);
this->rho = 2.9;
// material frame of reference is rotate by rotation_matrix starting from
// canonical basis
Matrix<Real> rotation_matrix = getRandomRotation();
// canonical basis as expressed in the material frame of reference, as
// required by MaterialElasticLinearAnisotropic class (it is simply given by
// the columns of the rotation_matrix; the lines give the material basis
// expressed in the canonical frame of reference)
*this->dir_vecs[0] = rotation_matrix(0);
*this->dir_vecs[1] = rotation_matrix(1);
*this->dir_vecs[2] = rotation_matrix(2);
}
/* -------------------------------------------------------------------------- */
template <>
void FriendMaterial<MaterialElasticLinearAnisotropic<3>>::testComputeStress() {
Matrix<Real> C = {
{1.0, 0.3, 0.4, 0.3, 0.2, 0.1}, {0.3, 2.0, 0.1, 0.2, 0.3, 0.2},
{0.4, 0.1, 1.5, 0.1, 0.4, 0.3}, {0.3, 0.2, 0.1, 2.4, 0.1, 0.4},
{0.2, 0.3, 0.4, 0.1, 0.9, 0.1}, {0.1, 0.2, 0.3, 0.4, 0.1, 1.2},
};
Matrix<Real> rotation_matrix(3, 3);
rotation_matrix(0) = *this->dir_vecs[0];
rotation_matrix(1) = *this->dir_vecs[1];
rotation_matrix(2) = *this->dir_vecs[2];
// gradient in material frame of reference
auto grad_u = this->getComposedStrain(2.);
// gradient in canonical basis (we need to rotate *back* to the canonical
// basis)
auto grad_u_rot = this->reverseRotation(grad_u, rotation_matrix);
// stress in the canonical basis
Matrix<Real> sigma_rot(3, 3);
this->computeStressOnQuad(grad_u_rot, sigma_rot);
// stress in the material reference (we need to apply the rotation)
auto sigma = this->applyRotation(sigma_rot, rotation_matrix);
// epsilon is computed directly in the *material* frame of reference
Matrix<Real> epsilon = 0.5 * (grad_u + grad_u.transpose());
Vector<Real> epsilon_voigt(6);
epsilon_voigt(0) = epsilon(0, 0);
epsilon_voigt(1) = epsilon(1, 1);
epsilon_voigt(2) = epsilon(2, 2);
epsilon_voigt(3) = 2 * epsilon(1, 2);
epsilon_voigt(4) = 2 * epsilon(0, 2);
epsilon_voigt(5) = 2 * epsilon(0, 1);
// sigma_expected is computed directly in the *material* frame of reference
Vector<Real> sigma_voigt = C * epsilon_voigt;
Matrix<Real> sigma_expected(3, 3);
sigma_expected(0, 0) = sigma_voigt(0);
sigma_expected(1, 1) = sigma_voigt(1);
sigma_expected(2, 2) = sigma_voigt(2);
sigma_expected(1, 2) = sigma_expected(2, 1) = sigma_voigt(3);
sigma_expected(0, 2) = sigma_expected(2, 0) = sigma_voigt(4);
sigma_expected(0, 1) = sigma_expected(1, 0) = sigma_voigt(5);
// sigmas are checked in the *material* frame of reference
auto diff = sigma - sigma_expected;
Real stress_error = diff.norm<L_inf>();
EXPECT_NEAR(stress_error, 0., 1e-13);
}
/* -------------------------------------------------------------------------- */
template <>
void FriendMaterial<MaterialElasticLinearAnisotropic<3>>::testEnergyDensity() {
Matrix<Real> sigma = {{1, 2, 3}, {2, 4, 5}, {3, 5, 6}};
Matrix<Real> eps = {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}};
Real epot = 0;
Real solution = 5.5;
this->computePotentialEnergyOnQuad(eps, sigma, epot);
EXPECT_NEAR(epot, solution, 1e-14);
}
/* -------------------------------------------------------------------------- */
template <>
void FriendMaterial<
MaterialElasticLinearAnisotropic<3>>::testComputeTangentModuli() {
Matrix<Real> tangent(6, 6);
this->computeTangentModuliOnQuad(tangent);
Real tangent_error = (tangent - C).norm<L_2>();
EXPECT_NEAR(tangent_error, 0, 1e-14);
}
/* -------------------------------------------------------------------------- */
template <>
void FriendMaterial<MaterialElasticLinearAnisotropic<3>>::testCelerity() {
Vector<Real> eig_expected(6);
C.eig(eig_expected);
auto celerity_expected = std::sqrt(eig_expected(0) / this->rho);
auto celerity = this->getCelerity(Element());
EXPECT_NEAR(celerity_expected, celerity, 1e-14);
}
/* -------------------------------------------------------------------------- */
namespace {
template <typename T>
class TestElasticMaterialFixture : public ::TestMaterialFixture<T> {};
TYPED_TEST_SUITE(TestElasticMaterialFixture, mat_types, );
TYPED_TEST(TestElasticMaterialFixture, ComputeStress) {
this->material->testComputeStress();
}
TYPED_TEST(TestElasticMaterialFixture, EnergyDensity) {
this->material->testEnergyDensity();
}
TYPED_TEST(TestElasticMaterialFixture, ComputeTangentModuli) {
this->material->testComputeTangentModuli();
}
TYPED_TEST(TestElasticMaterialFixture, ComputeCelerity) {
this->material->testCelerity();
}
} // namespace

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