Homec4science
Diffusion akantu (features/internodes-coupler-refactor) Browse

rAKA/test/test_model/test_solid_mechanics_model/test_materials/test_elastic_materials.cc
3209876a6a8cfeatures/internodes…

Last Change
Raw File

test_elastic_materials.cc
View Options

/* -------------------------------------------------------------------------- */
#include "material_elastic.hh"
#include "material_elastic_orthotropic.hh"
#include "solid_mechanics_model.hh"
#include "test_material_fixtures.hh"
/* -------------------------------------------------------------------------- */
#include <gtest/gtest.h>
#include <type_traits>
/* -------------------------------------------------------------------------- */
using namespace akantu;
using types =
::testing::Types<Traits<MaterialElastic, 1>, Traits<MaterialElastic, 2>,
Traits<MaterialElastic, 3>,
Traits<MaterialElasticOrthotropic, 1>,
Traits<MaterialElasticOrthotropic, 2>,
Traits<MaterialElasticOrthotropic, 3>,
Traits<MaterialElasticLinearAnisotropic, 1>,
Traits<MaterialElasticLinearAnisotropic, 2>,
Traits<MaterialElasticLinearAnisotropic, 3>>;
/* -------------------------------------------------------------------------- */
template <> void FriendMaterial<MaterialElastic<1>>::testComputeStress() {
Real E = 3.;
setParam("E", E);
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;
ASSERT_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;
ASSERT_NEAR(epot, solution, 1e-14);
}
/* -------------------------------------------------------------------------- */
template <>
void FriendMaterial<MaterialElastic<1>>::testComputeTangentModuli() {
Real E = 2;
setParam("E", E);
Matrix<Real> tangent(1, 1);
this->computeTangentModuliOnQuad(tangent);
ASSERT_NEAR(tangent(0, 0), E, 1e-14);
}
/* -------------------------------------------------------------------------- */
template <> void FriendMaterial<MaterialElastic<1>>::testPushWaveSpeed() {
Real E = 3., rho = 2.;
setParam("E", E);
setParam("rho", rho);
auto wave_speed = this->getPushWaveSpeed(Element());
auto solution = std::sqrt(E / rho);
ASSERT_NEAR(wave_speed, solution, 1e-14);
}
/* -------------------------------------------------------------------------- */
template <> void FriendMaterial<MaterialElastic<1>>::testShearWaveSpeed() {
ASSERT_THROW(this->getShearWaveSpeed(Element()), debug::Exception);
}
/* -------------------------------------------------------------------------- */
template <> void FriendMaterial<MaterialElastic<2>>::testComputeStress() {
Real E = 1.;
Real nu = .3;
Real sigma_th = 0.3; // thermal stress
setParam("E", E);
setParam("nu", nu);
Matrix<Real> rotation_matrix = getRandomRotation2d();
auto grad_u = this->getDeviatoricStrain(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);
Matrix<Real> identity(2, 2);
identity.eye();
Matrix<Real> sigma_expected =
0.5 * E / (1 + nu) * (grad_u + grad_u.transpose()) + sigma_th * identity;
auto diff = sigma - sigma_expected;
Real stress_error = diff.norm<L_inf>();
ASSERT_NEAR(stress_error, 0., 1e-14);
}
/* -------------------------------------------------------------------------- */
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);
ASSERT_NEAR(epot, solution, 1e-14);
}
/* -------------------------------------------------------------------------- */
template <>
void FriendMaterial<MaterialElastic<2>>::testComputeTangentModuli() {
Real E = 1.;
Real nu = .3;
setParam("E", E);
setParam("nu", nu);
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>();
ASSERT_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>();
ASSERT_NEAR(tangent_error, 0, 1e-14);
}
/* -------------------------------------------------------------------------- */
template <> void FriendMaterial<MaterialElastic<2>>::testPushWaveSpeed() {
Real E = 1.;
Real nu = .3;
Real rho = 2;
setParam("E", E);
setParam("nu", nu);
setParam("rho", rho);
auto wave_speed = this->getPushWaveSpeed(Element());
Real K = E / (3 * (1 - 2 * nu));
Real mu = E / (2 * (1 + nu));
Real sol = std::sqrt((K + 4. / 3 * mu) / rho);
ASSERT_NEAR(wave_speed, sol, 1e-14);
}
/* -------------------------------------------------------------------------- */
template <> void FriendMaterial<MaterialElastic<2>>::testShearWaveSpeed() {
Real E = 1.;
Real nu = .3;
Real rho = 2;
setParam("E", E);
setParam("nu", nu);
setParam("rho", rho);
auto wave_speed = this->getShearWaveSpeed(Element());
Real mu = E / (2 * (1 + nu));
Real sol = std::sqrt(mu / rho);
ASSERT_NEAR(wave_speed, sol, 1e-14);
}
/* -------------------------------------------------------------------------- */
template <> void FriendMaterial<MaterialElastic<3>>::testComputeStress() {
Real E = 1.;
Real nu = .3;
Real sigma_th = 0.3; // thermal stress
setParam("E", E);
setParam("nu", nu);
Matrix<Real> rotation_matrix = getRandomRotation3d();
auto grad_u = this->getDeviatoricStrain(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> sigma_expected =
0.5 * E / (1 + nu) * (grad_u + grad_u.transpose()) + sigma_th * identity;
auto diff = sigma - sigma_expected;
Real stress_error = diff.norm<L_inf>();
ASSERT_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);
ASSERT_NEAR(epot, solution, 1e-14);
}
/* -------------------------------------------------------------------------- */
template <>
void FriendMaterial<MaterialElastic<3>>::testComputeTangentModuli() {
Real E = 1.;
Real nu = .3;
setParam("E", E);
setParam("nu", nu);
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>();
ASSERT_NEAR(tangent_error, 0, 1e-14);
}
/* -------------------------------------------------------------------------- */
template <> void FriendMaterial<MaterialElastic<3>>::testPushWaveSpeed() {
Real E = 1.;
Real nu = .3;
Real rho = 2;
setParam("E", E);
setParam("nu", nu);
setParam("rho", rho);
auto wave_speed = this->getPushWaveSpeed(Element());
Real K = E / (3 * (1 - 2 * nu));
Real mu = E / (2 * (1 + nu));
Real sol = std::sqrt((K + 4. / 3 * mu) / rho);
ASSERT_NEAR(wave_speed, sol, 1e-14);
}
/* -------------------------------------------------------------------------- */
template <> void FriendMaterial<MaterialElastic<3>>::testShearWaveSpeed() {
Real E = 1.;
Real nu = .3;
Real rho = 2;
setParam("E", E);
setParam("nu", nu);
setParam("rho", rho);
auto wave_speed = this->getShearWaveSpeed(Element());
Real mu = E / (2 * (1 + nu));
Real sol = std::sqrt(mu / rho);
ASSERT_NEAR(wave_speed, sol, 1e-14);
}
/* -------------------------------------------------------------------------- */
template <> void FriendMaterial<MaterialElasticOrthotropic<2>>::testComputeStress() {
UInt Dim = 2;
Real E1 = 1.;
Real E2 = 2.;
Real nu12 = 0.1;
Real G12 = 2.;
setParamNoUpdate("E1", E1);
setParamNoUpdate("E2", E2);
setParamNoUpdate("nu12", nu12);
setParamNoUpdate("G12", G12);
// material frame of reference is rotate by rotation_matrix starting from
// canonical basis
Matrix<Real> rotation_matrix = getRandomRotation2d();
// 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)
Vector<Real> v1(Dim);
Vector<Real> v2(Dim);
for (UInt i = 0; i < Dim; ++i) {
v1[i] = rotation_matrix(i, 0);
v2[i] = rotation_matrix(i, 1);
}
setParamNoUpdate("n1", v1.normalize());
setParamNoUpdate("n2", v2.normalize());
// set internal Cijkl matrix expressed in the canonical frame of reference
this->updateInternalParameters();
// gradient in material frame of reference
auto grad_u = ( this->getDeviatoricStrain(2.) + this->getHydrostaticStrain(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);
// 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>();
ASSERT_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);
ASSERT_NEAR(epot, solution, 1e-14);
}
/* -------------------------------------------------------------------------- */
template <> void FriendMaterial<MaterialElasticOrthotropic<2>>::testComputeTangentModuli() {
// 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.;
setParamNoUpdate("n1", n1);
setParamNoUpdate("n2", n2);
setParamNoUpdate("E1", E1);
setParamNoUpdate("E2", E2);
setParamNoUpdate("nu12", nu12);
setParamNoUpdate("G12", G12);
// set internal Cijkl matrix expressed in the canonical frame of reference
this->updateInternalParameters();
// 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>();
ASSERT_NEAR(tangent_error, 0, 1e-14);
}
/* -------------------------------------------------------------------------- */
template <> void FriendMaterial<MaterialElasticOrthotropic<3>>::testComputeStress() {
UInt Dim = 3;
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.;
setParamNoUpdate("E1", E1);
setParamNoUpdate("E2", E2);
setParamNoUpdate("E3", E3);
setParamNoUpdate("nu12", nu12);
setParamNoUpdate("nu13", nu13);
setParamNoUpdate("nu23", nu23);
setParamNoUpdate("G12", G12);
setParamNoUpdate("G13", G13);
setParamNoUpdate("G23", G23);
// material frame of reference is rotate by rotation_matrix starting from
// canonical basis
Matrix<Real> rotation_matrix = getRandomRotation3d();
// 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)
Vector<Real> v1(Dim);
Vector<Real> v2(Dim);
Vector<Real> v3(Dim);
for (UInt i = 0; i < Dim; ++i) {
v1[i] = rotation_matrix(i, 0);
v2[i] = rotation_matrix(i, 1);
v3[i] = rotation_matrix(i, 2);
}
setParamNoUpdate("n1", v1.normalize());
setParamNoUpdate("n2", v2.normalize());
setParamNoUpdate("n3", v3.normalize());
// set internal Cijkl matrix expressed in the canonical frame of reference
this->updateInternalParameters();
// gradient in material frame of reference
auto grad_u = this->getDeviatoricStrain(2.) + this->getHydrostaticStrain(1.);
// 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>();
ASSERT_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);
ASSERT_NEAR(epot, solution, 1e-14);
}
/* -------------------------------------------------------------------------- */
template <> void FriendMaterial<MaterialElasticOrthotropic<3>>::testComputeTangentModuli() {
// Note: for this test material and canonical basis coincide
UInt Dim = 3;
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.;
setParamNoUpdate("n1", n1);
setParamNoUpdate("n2", n2);
setParamNoUpdate("n3", n3);
setParamNoUpdate("E1", E1);
setParamNoUpdate("E2", E2);
setParamNoUpdate("E3", E3);
setParamNoUpdate("nu12", nu12);
setParamNoUpdate("nu13", nu13);
setParamNoUpdate("nu23", nu23);
setParamNoUpdate("G12", G12);
setParamNoUpdate("G13", G13);
setParamNoUpdate("G23", G23);
// set internal Cijkl matrix expressed in the canonical frame of reference
this->updateInternalParameters();
// 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>();
ASSERT_NEAR(tangent_error, 0, 1e-14);
}
/* -------------------------------------------------------------------------- */
template <> void FriendMaterial<MaterialElasticLinearAnisotropic<2>>::testComputeStress() {
UInt Dim = 2;
Matrix<Real> C = {
{1.0, 0.3, 0.4},
{0.3, 2.0, 0.1},
{0.4, 0.1, 1.5},
};
setParamNoUpdate("C11", C(0,0));
setParamNoUpdate("C12", C(0,1));
setParamNoUpdate("C13", C(0,2));
setParamNoUpdate("C22", C(1,1));
setParamNoUpdate("C23", C(1,2));
setParamNoUpdate("C33", C(2,2));
// material frame of reference is rotate by rotation_matrix starting from
// canonical basis
Matrix<Real> rotation_matrix = getRandomRotation2d();
// 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)
Vector<Real> v1(Dim);
Vector<Real> v2(Dim);
for (UInt i = 0; i < Dim; ++i) {
v1[i] = rotation_matrix(i, 0);
v2[i] = rotation_matrix(i, 1);
}
setParamNoUpdate("n1", v1.normalize());
setParamNoUpdate("n2", v2.normalize());
// set internal Cijkl matrix expressed in the canonical frame of reference
this->updateInternalParameters();
// gradient in material frame of reference
auto grad_u = (this->getDeviatoricStrain(2.) + this->getHydrostaticStrain(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(Dim, Dim);
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>();
ASSERT_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);
ASSERT_NEAR(epot, solution, 1e-14);
}
/* -------------------------------------------------------------------------- */
template <> void FriendMaterial<MaterialElasticLinearAnisotropic<2>>::testComputeTangentModuli() {
// Note: for this test material and canonical basis coincide
Matrix<Real> C = {
{1.0, 0.3, 0.4},
{0.3, 2.0, 0.1},
{0.4, 0.1, 1.5},
};
setParamNoUpdate("C11", C(0,0));
setParamNoUpdate("C12", C(0,1));
setParamNoUpdate("C13", C(0,2));
setParamNoUpdate("C22", C(1,1));
setParamNoUpdate("C23", C(1,2));
setParamNoUpdate("C33", C(2,2));
// set internal Cijkl matrix expressed in the canonical frame of reference
this->updateInternalParameters();
Matrix<Real> tangent(3,3);
this->computeTangentModuliOnQuad(tangent);
Real tangent_error = (tangent - C).norm<L_2>();
ASSERT_NEAR(tangent_error, 0, 1e-14);
}
/* -------------------------------------------------------------------------- */
template <> void FriendMaterial<MaterialElasticLinearAnisotropic<3>>::testComputeStress() {
UInt Dim = 3;
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},
};
setParamNoUpdate("C11", C(0,0));
setParamNoUpdate("C12", C(0,1));
setParamNoUpdate("C13", C(0,2));
setParamNoUpdate("C14", C(0,3));
setParamNoUpdate("C15", C(0,4));
setParamNoUpdate("C16", C(0,5));
setParamNoUpdate("C22", C(1,1));
setParamNoUpdate("C23", C(1,2));
setParamNoUpdate("C24", C(1,3));
setParamNoUpdate("C25", C(1,4));
setParamNoUpdate("C26", C(1,5));
setParamNoUpdate("C33", C(2,2));
setParamNoUpdate("C34", C(2,3));
setParamNoUpdate("C35", C(2,4));
setParamNoUpdate("C36", C(2,5));
setParamNoUpdate("C44", C(3,3));
setParamNoUpdate("C45", C(3,4));
setParamNoUpdate("C46", C(3,5));
setParamNoUpdate("C55", C(4,4));
setParamNoUpdate("C56", C(4,5));
setParamNoUpdate("C66", C(5,5));
// material frame of reference is rotate by rotation_matrix starting from
// canonical basis
Matrix<Real> rotation_matrix = getRandomRotation3d();
// 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)
Vector<Real> v1(Dim);
Vector<Real> v2(Dim);
Vector<Real> v3(Dim);
for (UInt i = 0; i < Dim; ++i) {
v1[i] = rotation_matrix(i, 0);
v2[i] = rotation_matrix(i, 1);
v3[i] = rotation_matrix(i, 2);
}
setParamNoUpdate("n1", v1.normalize());
setParamNoUpdate("n2", v2.normalize());
setParamNoUpdate("n3", v3.normalize());
// set internal Cijkl matrix expressed in the canonical frame of reference
this->updateInternalParameters();
// gradient in material frame of reference
auto grad_u = this->getDeviatoricStrain(2.) + this->getHydrostaticStrain(1.);
// 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(Dim, Dim);
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>();
ASSERT_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);
ASSERT_NEAR(epot, solution, 1e-14);
}
/* -------------------------------------------------------------------------- */
template <> void FriendMaterial<MaterialElasticLinearAnisotropic<3>>::testComputeTangentModuli() {
// 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},
};
setParamNoUpdate("C11", C(0,0));
setParamNoUpdate("C12", C(0,1));
setParamNoUpdate("C13", C(0,2));
setParamNoUpdate("C14", C(0,3));
setParamNoUpdate("C15", C(0,4));
setParamNoUpdate("C16", C(0,5));
setParamNoUpdate("C22", C(1,1));
setParamNoUpdate("C23", C(1,2));
setParamNoUpdate("C24", C(1,3));
setParamNoUpdate("C25", C(1,4));
setParamNoUpdate("C26", C(1,5));
setParamNoUpdate("C33", C(2,2));
setParamNoUpdate("C34", C(2,3));
setParamNoUpdate("C35", C(2,4));
setParamNoUpdate("C36", C(2,5));
setParamNoUpdate("C44", C(3,3));
setParamNoUpdate("C45", C(3,4));
setParamNoUpdate("C46", C(3,5));
setParamNoUpdate("C55", C(4,4));
setParamNoUpdate("C56", C(4,5));
setParamNoUpdate("C66", C(5,5));
// set internal Cijkl matrix expressed in the canonical frame of reference
this->updateInternalParameters();
Matrix<Real> tangent(6,6);
this->computeTangentModuliOnQuad(tangent);
Real tangent_error = (tangent - C).norm<L_2>();
ASSERT_NEAR(tangent_error, 0, 1e-14);
}
/* -------------------------------------------------------------------------- */
namespace {
template <typename T>
class TestElasticMaterialFixture : public ::TestMaterialFixture<T> {};
TYPED_TEST_CASE(TestElasticMaterialFixture, types);
TYPED_TEST(TestElasticMaterialFixture, ElasticComputeStress) {
this->material->testComputeStress();
}
TYPED_TEST(TestElasticMaterialFixture, ElasticEnergyDensity) {
this->material->testEnergyDensity();
}
TYPED_TEST(TestElasticMaterialFixture, ElasticComputeTangentModuli) {
this->material->testComputeTangentModuli();
}
TYPED_TEST(TestElasticMaterialFixture, ElasticComputePushWaveSpeed) {
this->material->testPushWaveSpeed();
}
TYPED_TEST(TestElasticMaterialFixture, ElasticComputeShearWaveSpeed) {
this->material->testShearWaveSpeed();
}
} // namespace
c4science · Help