MathLib::KelvinVector Namespace Reference

Detailed Description

The invariants and the Kelving mapping are explained in detail in the article "On Advantages of the Kelvin Mapping in Finite Element Implementations of Deformation Processes" [30].

Namespaces
namespace	KelvinVector_detail

Classes
struct	Invariants

Typedefs
template<int DisplacementDim>
using	KelvinVectorType
template<int DisplacementDim>
using	KelvinMatrixType

Functions
template<>
Eigen::Matrix< double, 4, 1, Eigen::ColMajor, 4, 1 >	inverse (Eigen::Matrix< double, 4, 1, Eigen::ColMajor, 4, 1 > const &v)
template<>
Eigen::Matrix< double, 6, 1, Eigen::ColMajor, 6, 1 >	inverse (Eigen::Matrix< double, 6, 1, Eigen::ColMajor, 6, 1 > const &v)
template<>
Eigen::Matrix< double, 3, 3 >	kelvinVectorToTensor (Eigen::Matrix< double, 4, 1, Eigen::ColMajor, 4, 1 > const &v)
template<>
Eigen::Matrix< double, 3, 3 >	kelvinVectorToTensor (Eigen::Matrix< double, 6, 1, Eigen::ColMajor, 6, 1 > const &v)
template<>
Eigen::Matrix< double, 3, 3 >	kelvinVectorToTensor (Eigen::Matrix< double, Eigen::Dynamic, 1, Eigen::ColMajor, Eigen::Dynamic, 1 > const &v)
template<>
KelvinVectorType< 2 >	tensorToKelvin< 2 > (Eigen::Matrix< double, 3, 3 > const &m)
template<>
KelvinVectorType< 3 >	tensorToKelvin< 3 > (Eigen::Matrix< double, 3, 3 > const &m)
template<>
Eigen::Matrix< double, 4, 1 >	kelvinVectorToSymmetricTensor (Eigen::Matrix< double, 4, 1, Eigen::ColMajor, 4, 1 > const &v)
template<>
Eigen::Matrix< double, 6, 1 >	kelvinVectorToSymmetricTensor (Eigen::Matrix< double, 6, 1, Eigen::ColMajor, 6, 1 > const &v)
template<>
Eigen::Matrix< double, Eigen::Dynamic, 1, Eigen::ColMajor, Eigen::Dynamic, 1 >	kelvinVectorToSymmetricTensor (Eigen::Matrix< double, Eigen::Dynamic, 1, Eigen::ColMajor, Eigen::Dynamic, 1 > const &v)
template<>
Eigen::Matrix< double, 2, 4 >	liftVectorToKelvin< 2 > (Eigen::Matrix< double, 2, 1 > const &v)
template<>
Eigen::Matrix< double, 3, 6 >	liftVectorToKelvin< 3 > (Eigen::Matrix< double, 3, 1 > const &v)
template<>
Eigen::Matrix< double, 2, 1 >	reduceKelvinToVector< 2 > (Eigen::Matrix< double, 2, 4 > const &m)
template<>
Eigen::Matrix< double, 3, 1 >	reduceKelvinToVector< 3 > (Eigen::Matrix< double, 3, 6 > const &m)
template<>
KelvinMatrixType< 2 >	fourthOrderRotationMatrix< 2 > (Eigen::Matrix< double, 2, 2, Eigen::ColMajor, 2, 2 > const &transformation)
template<>
KelvinMatrixType< 3 >	fourthOrderRotationMatrix< 3 > (Eigen::Matrix< double, 3, 3, Eigen::ColMajor, 3, 3 > const &transformation)
constexpr int	kelvin_vector_dimensions (int const displacement_dim)
	Kelvin vector dimensions for given displacement dimension.
template<int DisplacementDim>
constexpr auto	KVzero ()
	Returns an expressions for a Kelvin vector filled with zero.
template<int DisplacementDim>
constexpr auto	KMzero ()
	Returns an expressions for a Kelvin matrix filled with zero.
template<int DisplacementDim>
constexpr auto	KVnan ()
	Returns an expressions for a Kelvin vector filled with NaN.
template<int DisplacementDim>
constexpr auto	KMnan ()
	Returns an expressions for a Kelvin matrix filled with NaN.
template<int KelvinVectorSize>
Eigen::Matrix< double, KelvinVectorSize, 1, Eigen::ColMajor, KelvinVectorSize, 1 >	inverse (Eigen::Matrix< double, KelvinVectorSize, 1, Eigen::ColMajor, KelvinVectorSize, 1 > const &v)
template<int KelvinVectorSize>
Eigen::Matrix< double, 3, 3 >	kelvinVectorToTensor (Eigen::Matrix< double, KelvinVectorSize, 1, Eigen::ColMajor, KelvinVectorSize, 1 > const &v)
template<int DisplacementDim>
KelvinVectorType< DisplacementDim >	tensorToKelvin (Eigen::Matrix< double, 3, 3 > const &m)
template<int KelvinVectorSize>
Eigen::Matrix< double, KelvinVectorSize, 1, Eigen::ColMajor, KelvinVectorSize, 1 >	kelvinVectorToSymmetricTensor (Eigen::Matrix< double, KelvinVectorSize, 1, Eigen::ColMajor, KelvinVectorSize, 1 > const &v)
template<typename Derived>
Eigen::Matrix< double, Eigen::MatrixBase< Derived >::RowsAtCompileTime, 1 >	symmetricTensorToKelvinVector (Eigen::MatrixBase< Derived > const &v)
template<int DisplacementDim>
KelvinVectorType< DisplacementDim >	symmetricTensorToKelvinVector (std::vector< double > const &values)
template<int DisplacementDim>
Eigen::Matrix< double, DisplacementDim, kelvin_vector_dimensions(DisplacementDim)>	liftVectorToKelvin (Eigen::Matrix< double, DisplacementDim, 1 > const &v)
template<int DisplacementDim>
Eigen::Matrix< double, DisplacementDim, 1 >	reduceKelvinToVector (Eigen::Matrix< double, DisplacementDim, kelvin_vector_dimensions(DisplacementDim)> const &m)
template<int DisplacementDim>
KelvinMatrixType< DisplacementDim >	fourthOrderRotationMatrix (Eigen::Matrix< double, DisplacementDim, DisplacementDim, Eigen::ColMajor, DisplacementDim, DisplacementDim > const &transformation)

Variables
template<int KelvinVectorSize>
const Eigen::Matrix< double, KelvinVectorSize, KelvinVectorSize >	Invariants< KelvinVectorSize >::deviatoric_projection
template<int KelvinVectorSize>
Eigen::Matrix< double, KelvinVectorSize, KelvinVectorSize > const	Invariants< KelvinVectorSize >::spherical_projection
template<int KelvinVectorSize>
const Eigen::Matrix< double, KelvinVectorSize, 1 >	Invariants< KelvinVectorSize >::identity2
template<int KelvinVectorSize>
const Eigen::Matrix< double, KelvinVectorSize, 1 >	Invariants< KelvinVectorSize >::ones2

Typedef Documentation

KelvinMatrixType

template<int DisplacementDim>

using MathLib::KelvinVector::KelvinMatrixType

Initial value:

 
    Eigen::Matrix<double, kelvin_vector_dimensions(DisplacementDim),
                  kelvin_vector_dimensions(DisplacementDim), Eigen::RowMajor>

Kelvin matrix type for given displacement dimension.

Note

The Eigen matrix is always a fixed size vector in contrast to a shape matrix policy types like BMatrixPolicyType::KelvinMatrixType.

Definition at line 49 of file KelvinVector.h.

KelvinVectorType

template<int DisplacementDim>

using MathLib::KelvinVector::KelvinVectorType

Initial value:

 
    Eigen::Matrix<double, kelvin_vector_dimensions(DisplacementDim), 1,
                  Eigen::ColMajor>

Kelvin vector type for given displacement dimension.

Note

The Eigen vector is always a fixed size vector in contrast to a shape matrix policy types like BMatrixPolicyType::KelvinVectorType.

Definition at line 41 of file KelvinVector.h.

Function Documentation

fourthOrderRotationMatrix()

template<int DisplacementDim>

KelvinMatrixType< DisplacementDim > MathLib::KelvinVector::fourthOrderRotationMatrix

(

Eigen::Matrix< double, DisplacementDim, DisplacementDim, Eigen::ColMajor, DisplacementDim, DisplacementDim > const &

transformation

)

Rotation tensor for Kelvin mapped vectors and tensors. It is meant to be used for rotation of stress/strain tensors epsilon:Q and tangent stiffness tensors Q*C*Q^t. 2D and 3D implementations available.

Referenced by MaterialLib::Solids::LinearElasticOrthotropic< DisplacementDim >::getElasticTensor(), MaterialLib::Solids::LinearElasticTransverseIsotropic< DisplacementDim >::getElasticTensor(), and MaterialLib::Solids::MFront::MFrontGeneric< DisplacementDim, boost::mp11::mp_list< Strain >, boost::mp11::mp_list< Stress >, boost::mp11::mp_list< Temperature > >::integrateStress().

fourthOrderRotationMatrix< 2 >()

template<>

KelvinMatrixType< 2 > MathLib::KelvinVector::fourthOrderRotationMatrix< 2 >

(

Eigen::Matrix< double, 2, 2, Eigen::ColMajor, 2, 2 > const &

transformation

)

Definition at line 155 of file KelvinVector.cpp.

{
    // 1-based index access for convenience.
    auto Q = [&](int const i, int const j)
    { return transformation(i - 1, j - 1); };
 
    MathLib::KelvinVector::KelvinMatrixType<2> R;
    R << Q(1, 1) * Q(1, 1), Q(1, 2) * Q(1, 2), 0,
        std::sqrt(2) * Q(1, 1) * Q(1, 2), Q(2, 1) * Q(2, 1), Q(2, 2) * Q(2, 2),
        0, std::sqrt(2) * Q(2, 1) * Q(2, 2), 0, 0, 1, 0,
        std::sqrt(2) * Q(1, 1) * Q(2, 1), std::sqrt(2) * Q(1, 2) * Q(2, 2), 0,
        Q(1, 1) * Q(2, 2) + Q(1, 2) * Q(2, 1);
    return R;
}

References kelvinVectorToSymmetricTensor(), OGS_FATAL, and MathLib::v.

fourthOrderRotationMatrix< 3 >()

template<>

KelvinMatrixType< 3 > MathLib::KelvinVector::fourthOrderRotationMatrix< 3 >

(

Eigen::Matrix< double, 3, 3, Eigen::ColMajor, 3, 3 > const &

transformation

)

Definition at line 155 of file KelvinVector.cpp.

{
    // 1-based index access for convenience.
    auto Q = [&](int const i, int const j)
    { return transformation(i - 1, j - 1); };
 
    MathLib::KelvinVector::KelvinMatrixType<3> R;
    R << Q(1, 1) * Q(1, 1), Q(1, 2) * Q(1, 2), Q(1, 3) * Q(1, 3),
        std::sqrt(2) * Q(1, 1) * Q(1, 2), std::sqrt(2) * Q(1, 2) * Q(1, 3),
        std::sqrt(2) * Q(1, 1) * Q(1, 3), Q(2, 1) * Q(2, 1), Q(2, 2) * Q(2, 2),
        Q(2, 3) * Q(2, 3), std::sqrt(2) * Q(2, 1) * Q(2, 2),
        std::sqrt(2) * Q(2, 2) * Q(2, 3), std::sqrt(2) * Q(2, 1) * Q(2, 3),
        Q(3, 1) * Q(3, 1), Q(3, 2) * Q(3, 2), Q(3, 3) * Q(3, 3),
        std::sqrt(2) * Q(3, 1) * Q(3, 2), std::sqrt(2) * Q(3, 2) * Q(3, 3),
        std::sqrt(2) * Q(3, 1) * Q(3, 3), std::sqrt(2) * Q(1, 1) * Q(2, 1),
        std::sqrt(2) * Q(1, 2) * Q(2, 2), std::sqrt(2) * Q(1, 3) * Q(2, 3),
        Q(1, 1) * Q(2, 2) + Q(1, 2) * Q(2, 1),
        Q(1, 2) * Q(2, 3) + Q(1, 3) * Q(2, 2),
        Q(1, 1) * Q(2, 3) + Q(1, 3) * Q(2, 1), std::sqrt(2) * Q(2, 1) * Q(3, 1),
        std::sqrt(2) * Q(2, 2) * Q(3, 2), std::sqrt(2) * Q(2, 3) * Q(3, 3),
        Q(2, 1) * Q(3, 2) + Q(2, 2) * Q(3, 1),
        Q(2, 2) * Q(3, 3) + Q(2, 3) * Q(3, 2),
        Q(2, 1) * Q(3, 3) + Q(2, 3) * Q(3, 1), std::sqrt(2) * Q(1, 1) * Q(3, 1),
        std::sqrt(2) * Q(1, 2) * Q(3, 2), std::sqrt(2) * Q(1, 3) * Q(3, 3),
        Q(1, 1) * Q(3, 2) + Q(1, 2) * Q(3, 1),
        Q(1, 2) * Q(3, 3) + Q(1, 3) * Q(3, 2),
        Q(1, 1) * Q(3, 3) + Q(1, 3) * Q(3, 1);
    return R;
}

inverse() [1/3]

template<>

Eigen::Matrix< double, 4, 1, Eigen::ColMajor, 4, 1 > MathLib::KelvinVector::inverse

(

Eigen::Matrix< double, 4, 1, Eigen::ColMajor, 4, 1 > const &

v

)

Definition at line 27 of file KelvinVector.cpp.

{
    assert(Invariants<4>::determinant(v) != 0);
 
    Eigen::Matrix<double, 4, 1, Eigen::ColMajor, 4, 1> inv;
    inv(0) = v(1) * v(2);
    inv(1) = v(0) * v(2);
    inv(2) = v(0) * v(1) - v(3) * v(3) / 2.;
    inv(3) = -v(3) * v(2);
    return inv / Invariants<4>::determinant(v);
}

References MathLib::KelvinVector::Invariants< KelvinVectorSize >::determinant(), and MathLib::v.

Referenced by MaterialLib::Solids::Ehlers::thetaSigmaDerivatives().

inverse() [2/3]

template<>

Eigen::Matrix< double, 6, 1, Eigen::ColMajor, 6, 1 > MathLib::KelvinVector::inverse

(

Eigen::Matrix< double, 6, 1, Eigen::ColMajor, 6, 1 > const &

v

)

Definition at line 41 of file KelvinVector.cpp.

{
    assert(Invariants<6>::determinant(v) != 0);
 
    Eigen::Matrix<double, 6, 1, Eigen::ColMajor, 6, 1> inv;
    inv(0) = v(1) * v(2) - v(4) * v(4) / 2.;
    inv(1) = v(0) * v(2) - v(5) * v(5) / 2.;
    inv(2) = v(0) * v(1) - v(3) * v(3) / 2.;
    inv(3) = v(4) * v(5) / std::sqrt(2.) - v(3) * v(2);
    inv(4) = v(3) * v(5) / std::sqrt(2.) - v(4) * v(0);
    inv(5) = v(4) * v(3) / std::sqrt(2.) - v(1) * v(5);
    return inv / Invariants<6>::determinant(v);
}

References MathLib::KelvinVector::Invariants< KelvinVectorSize >::determinant(), and MathLib::v.

inverse() [3/3]

template<int KelvinVectorSize>

Eigen::Matrix< double, KelvinVectorSize, 1, Eigen::ColMajor, KelvinVectorSize, 1 > MathLib::KelvinVector::inverse

(

Eigen::Matrix< double, KelvinVectorSize, 1, Eigen::ColMajor, KelvinVectorSize, 1 > const &

v

)

Inverse of a matrix in Kelvin vector representation. There are only implementations for the Kelvin vector size 4 and 6.

References MathLib::v.

kelvin_vector_dimensions()

int MathLib::KelvinVector::kelvin_vector_dimensions ( int const displacement_dim )

constexpr

Kelvin vector dimensions for given displacement dimension.

Definition at line 18 of file KelvinVector.h.

{
    if (displacement_dim == 2)
    {
        return 4;
    }
    else if (displacement_dim == 3)
    {
        return 6;
    }
    OGS_FATAL(
        "Cannot convert displacement dimension {} to kelvin vector dimension.",
        displacement_dim);
}

References OGS_FATAL.

Referenced by ProcessLib::HMPhaseField::HMPhaseFieldLocalAssembler< ShapeFunction, DisplacementDim >::HMPhaseFieldLocalAssembler(), ProcessLib::HydroMechanics::HydroMechanicsLocalAssembler< ShapeFunctionDisplacement, ShapeFunctionPressure, DisplacementDim >::HydroMechanicsLocalAssembler(), ProcessLib::ThermoHydroMechanics::IntegrationPointData< BMatricesType, ShapeMatricesTypeDisplacement, ShapeMatricesTypePressure, DisplacementDim, ShapeFunctionDisplacement::NPOINTS >::IntegrationPointData(), ProcessLib::PhaseField::PhaseFieldLocalAssembler< ShapeFunction, DisplacementDim >::PhaseFieldLocalAssembler(), ProcessLib::LIE::SmallDeformation::SmallDeformationLocalAssemblerMatrix< ShapeFunction, DisplacementDim >::SmallDeformationLocalAssemblerMatrix(), ProcessLib::LIE::SmallDeformation::SmallDeformationLocalAssemblerMatrixNearFracture< ShapeFunction, DisplacementDim >::SmallDeformationLocalAssemblerMatrixNearFracture(), ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssembler< ShapeFunction, DisplacementDim >::ThermoMechanicsLocalAssembler(), ProcessLib::RichardsMechanics::RichardsMechanicsLocalAssembler< ShapeFunctionDisplacement, ShapeFunctionPressure, DisplacementDim >::assemble(), ProcessLib::HydroMechanics::HydroMechanicsLocalAssembler< ShapeFunctionDisplacement, ShapeFunctionPressure, DisplacementDim >::assembleWithJacobian(), ProcessLib::RichardsMechanics::RichardsMechanicsLocalAssembler< ShapeFunctionDisplacement, ShapeFunctionPressure, DisplacementDim >::assembleWithJacobian(), ProcessLib::RichardsMechanics::RichardsMechanicsLocalAssembler< ShapeFunctionDisplacement, ShapeFunctionPressure, DisplacementDim >::assembleWithJacobianEvalConstitutiveSetting(), ProcessLib::HydroMechanics::HydroMechanicsLocalAssembler< ShapeFunctionDisplacement, ShapeFunctionPressure, DisplacementDim >::assembleWithJacobianForDeformationEquations(), ProcessLib::ThermoRichardsMechanics::ThermoRichardsMechanicsLocalAssembler< ShapeFunctionDisplacement, ShapeFunction, DisplacementDim, ConstitutiveTraits >::assembleWithJacobianSingleIP(), MaterialLib::Solids::Ehlers::calculateDResidualDEps(), MaterialLib::Solids::Phasefield::calculateIsotropicDegradedStress(), MaterialLib::Solids::Phasefield::calculateIsotropicDegradedStressWithRankineEnergy(), MaterialLib::Solids::Phasefield::calculateOrthoVolDevDegradedStress(), MaterialLib::Solids::Ehlers::calculatePlasticJacobian(), MaterialLib::Solids::Ehlers::calculatePlasticResidual(), MaterialLib::Solids::Phasefield::calculateSpectralDegradedStress(), MaterialLib::Solids::Phasefield::calculateVolDevDegradedStress(), ProcessLib::LinearBMatrix::computeBMatrix(), ProcessLib::NonLinearBMatrix::computeBMatrix(), ProcessLib::RichardsMechanics::computeMicroPorosity(), ProcessLib::RichardsMechanics::RichardsMechanicsLocalAssembler< ShapeFunctionDisplacement, ShapeFunctionPressure, DisplacementDim >::computeSecondaryVariableConcrete(), ProcessLib::LIE::HydroMechanics::createHydroMechanicsProcess(), ProcessLib::createInitialStress(), ProcessLib::LargeDeformation::createLargeDeformationProcess(), ProcessLib::SmallDeformation::createSmallDeformationProcess(), MaterialPropertyLib::Function::Implementation< D >::createSymbolTable(), ProcessLib::ThermoMechanics::createThermoMechanicsProcess(), ProcessLib::TH2M::ConstitutiveRelations::PorosityModel< DisplacementDim >::dEval(), ProcessLib::TH2M::ConstitutiveRelations::SolidDensityModel< DisplacementDim >::dEval(), ProcessLib::TH2M::ConstitutiveRelations::PermeabilityModel< DisplacementDim >::eval(), ProcessLib::TH2M::ConstitutiveRelations::PorosityModel< DisplacementDim >::eval(), ProcessLib::TH2M::ConstitutiveRelations::SolidDensityModel< DisplacementDim >::eval(), ProcessLib::TH2M::ConstitutiveRelations::SolidThermalExpansionModel< DisplacementDim >::eval(), ProcessLib::TH2M::ConstitutiveRelations::TotalStressModel< DisplacementDim >::eval(), ProcessLib::TH2M::ConstitutiveRelations::TransportPorosityModel< DisplacementDim >::eval(), ProcessLib::ThermoRichardsMechanics::ConstitutiveStress_StrainTemperature::SolidMechanicsModel< DisplacementDim >::eval(), ProcessLib::ThermoRichardsMechanics::ConstitutiveStress_StrainTemperature::SwellingModel< DisplacementDim >::eval(), ProcessLib::ThermoRichardsMechanics::ConstitutiveStress_StrainTemperature::TransportPorosityModel< DisplacementDim >::eval(), ProcessLib::ThermoRichardsMechanics::ConstitutiveStressSaturation_StrainPressureTemperature::EffectiveStressModel< DisplacementDim >::eval(), ProcessLib::ThermoRichardsMechanics::ConstitutiveStressSaturation_StrainPressureTemperature::TransportPorosityModel< DisplacementDim >::eval(), ProcessLib::ThermoRichardsMechanics::FluidThermalExpansionModel< DisplacementDim >::eval(), ProcessLib::ThermoRichardsMechanics::PermeabilityModel< DisplacementDim >::eval(), ProcessLib::ThermoRichardsMechanics::PorosityModel< DisplacementDim >::eval(), ProcessLib::ThermoRichardsMechanics::SolidDensityModel< DisplacementDim >::eval(), MaterialLib::Solids::MFront::MFrontGeneric< DisplacementDim, boost::mp11::mp_list< Strain >, boost::mp11::mp_list< Stress >, boost::mp11::mp_list< Temperature > >::getBulkModulus(), MaterialLib::Solids::LinearElasticOrthotropic< DisplacementDim >::getElasticTensor(), ProcessLib::HydroMechanics::HydroMechanicsLocalAssembler< ShapeFunctionDisplacement, ShapeFunctionPressure, DisplacementDim >::getEpsilon(), ProcessLib::PhaseField::PhaseFieldLocalAssembler< ShapeFunction, DisplacementDim >::getEpsilon(), ProcessLib::ThermoHydroMechanics::ThermoHydroMechanicsLocalAssembler< ShapeFunctionDisplacement, ShapeFunctionPressure, DisplacementDim >::getEpsilon(), ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssembler< ShapeFunction, DisplacementDim >::getEpsilon(), ProcessLib::ThermoHydroMechanics::ThermoHydroMechanicsLocalAssembler< ShapeFunctionDisplacement, ShapeFunctionPressure, DisplacementDim >::getEpsilon0(), ProcessLib::ThermoHydroMechanics::ThermoHydroMechanicsLocalAssembler< ShapeFunctionDisplacement, ShapeFunctionPressure, DisplacementDim >::getEpsilonM(), ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssembler< ShapeFunction, DisplacementDim >::getEpsilonMechanical(), ProcessLib::getIntegrationPointKelvinVectorData(), ProcessLib::getIntegrationPointKelvinVectorData(), ProcessLib::ThermoHydroMechanics::ThermoHydroMechanicsLocalAssembler< ShapeFunctionDisplacement, ShapeFunctionPressure, DisplacementDim >::getSigma(), ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssembler< ShapeFunction, DisplacementDim >::getSigma(), ProcessLib::NonLinearFbar::identityForF(), ProcessLib::HydroMechanics::HydroMechanicsProcess< DisplacementDim >::initializeConcreteProcess(), ProcessLib::Reflection::detail::GetFlattenedIPDataFromLocAsm< Dim, Accessor_IPDataVecInLocAsm, Accessor_CurrentLevelFromIPDataVecElement >::operator()(), MaterialLib::Solids::Ehlers::predict_sigma(), MaterialLib::Solids::MFront::Variable< Derived >::rows(), ProcessLib::RichardsMechanics::RichardsMechanicsLocalAssembler< ShapeFunctionDisplacement, ShapeFunctionPressure, DisplacementDim >::setInitialConditionsConcrete(), ProcessLib::setIntegrationPointKelvinVectorData(), ProcessLib::Reflection::detail::setIPData(), MaterialLib::Solids::MFront::OGSMFrontTangentOperatorBlocksView< DisplacementDim, ForcesGradsCombinations >::size(), symmetricTensorToKelvinVector(), MaterialLib::Solids::MFront::tangentOperatorDataMFrontToOGS(), MaterialLib::Solids::Lubby2::tangentStiffnessA(), MaterialLib::Solids::Ehlers::thetaSigmaDerivatives(), and ProcessLib::RichardsMechanics::updateSwellingStressAndVolumetricStrain().

kelvinVectorToSymmetricTensor() [1/4]

template<>

Eigen::Matrix< double, 4, 1 > MathLib::KelvinVector::kelvinVectorToSymmetricTensor

(

Eigen::Matrix< double, 4, 1, Eigen::ColMajor, 4, 1 > const &

v

)

Definition at line 135 of file KelvinVector.cpp.

{
    Eigen::Matrix<double, 4, 1> m;
    m << v[0], v[1], v[2], v[3] / std::sqrt(2.);
    return m;
}

References MathLib::v.

Referenced by ProcessLib::RichardsMechanics::RichardsMechanicsLocalAssembler< ShapeFunctionDisplacement, ShapeFunctionPressure, DisplacementDim >::assemble(), ProcessLib::HydroMechanics::HydroMechanicsLocalAssembler< ShapeFunctionDisplacement, ShapeFunctionPressure, DisplacementDim >::assembleWithJacobian(), ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssembler< ShapeFunction, DisplacementDim >::assembleWithJacobian(), ProcessLib::RichardsMechanics::RichardsMechanicsLocalAssembler< ShapeFunctionDisplacement, ShapeFunctionPressure, DisplacementDim >::assembleWithJacobianEvalConstitutiveSetting(), ProcessLib::HydroMechanics::HydroMechanicsLocalAssembler< ShapeFunctionDisplacement, ShapeFunctionPressure, DisplacementDim >::assembleWithJacobianForPressureEquations(), ProcessLib::HydroMechanics::HydroMechanicsLocalAssembler< ShapeFunctionDisplacement, ShapeFunctionPressure, DisplacementDim >::computeSecondaryVariableConcrete(), ProcessLib::RichardsMechanics::RichardsMechanicsLocalAssembler< ShapeFunctionDisplacement, ShapeFunctionPressure, DisplacementDim >::computeSecondaryVariableConcrete(), ProcessLib::ThermoHydroMechanics::ThermoHydroMechanicsLocalAssembler< ShapeFunctionDisplacement, ShapeFunctionPressure, DisplacementDim >::computeSecondaryVariableConcrete(), ProcessLib::LIE::SmallDeformation::SmallDeformationLocalAssemblerMatrix< ShapeFunction, DisplacementDim >::computeSecondaryVariableConcreteWithVector(), ProcessLib::LIE::SmallDeformation::SmallDeformationLocalAssemblerMatrixNearFracture< ShapeFunction, DisplacementDim >::computeSecondaryVariableConcreteWithVector(), ProcessLib::TH2M::ConstitutiveRelations::PermeabilityModel< DisplacementDim >::eval(), ProcessLib::ThermoRichardsMechanics::PermeabilityModel< DisplacementDim >::eval(), fourthOrderRotationMatrix< 2 >(), ProcessLib::HydroMechanics::HydroMechanicsLocalAssembler< ShapeFunctionDisplacement, ShapeFunctionPressure, DisplacementDim >::getEpsilon(), ProcessLib::PhaseField::PhaseFieldLocalAssembler< ShapeFunction, DisplacementDim >::getEpsilon(), ProcessLib::getIntegrationPointKelvinVectorData(), MaterialLib::Solids::Ehlers::SolidEhlers< DisplacementDim >::getInternalVariables(), ProcessLib::HydroMechanics::HydroMechanicsLocalAssembler< ShapeFunctionDisplacement, ShapeFunctionPressure, DisplacementDim >::getIntPtDarcyVelocity(), ProcessLib::Reflection::detail::GetFlattenedIPDataFromLocAsm< Dim, Accessor_IPDataVecInLocAsm, Accessor_CurrentLevelFromIPDataVecElement >::operator()(), ProcessLib::LIE::HydroMechanics::HydroMechanicsLocalAssemblerMatrix< ShapeFunctionDisplacement, ShapeFunctionPressure, DisplacementDim >::postTimestepConcreteWithBlockVectors(), ProcessLib::ThermoHydroMechanics::ThermoHydroMechanicsLocalAssembler< ShapeFunctionDisplacement, ShapeFunctionPressure, DisplacementDim >::updateConstitutiveRelations(), and MaterialPropertyLib::updateVariableArrayValues().

kelvinVectorToSymmetricTensor() [2/4]

template<>

Eigen::Matrix< double, 6, 1 > MathLib::KelvinVector::kelvinVectorToSymmetricTensor

(

Eigen::Matrix< double, 6, 1, Eigen::ColMajor, 6, 1 > const &

v

)

Definition at line 144 of file KelvinVector.cpp.

{
    Eigen::Matrix<double, 6, 1> m;
    m << v[0], v[1], v[2], v[3] / std::sqrt(2.), v[4] / std::sqrt(2.),
        v[5] / std::sqrt(2.);
    return m;
}

References MathLib::v.

kelvinVectorToSymmetricTensor() [3/4]

template<>

Eigen::Matrix< double, Eigen::Dynamic, 1, Eigen::ColMajor, Eigen::Dynamic, 1 > MathLib::KelvinVector::kelvinVectorToSymmetricTensor

(

Eigen::Matrix< double, Eigen::Dynamic, 1, Eigen::ColMajor, Eigen::Dynamic, 1 > const &

v

)

Definition at line 155 of file KelvinVector.cpp.

{
    if (v.size() == 4)
    {
        return kelvinVectorToSymmetricTensor<4>(v);
    }
    if (v.size() == 6)
    {
        return kelvinVectorToSymmetricTensor<6>(v);
    }
    OGS_FATAL(
        "Kelvin vector to tensor conversion expected an input vector of size 4 "
        "or 6, but a vector of size {:d} was given.",
        v.size());
}

kelvinVectorToSymmetricTensor() [4/4]

template<int KelvinVectorSize>

Eigen::Matrix< double, KelvinVectorSize, 1, Eigen::ColMajor, KelvinVectorSize, 1 > MathLib::KelvinVector::kelvinVectorToSymmetricTensor

(

Eigen::Matrix< double, KelvinVectorSize, 1, Eigen::ColMajor, KelvinVectorSize, 1 > const &

v

)

Conversion of a Kelvin vector to a short vector representation of a symmetric 3x3 matrix.

In the 2D case the entries for the xx, yy, zz, and xy components are stored. In the 3D case the entries for the xx, yy, zz, xy, yz, and xz components in that particular order are stored.

This is opposite of the symmetricTensorToKelvinVector()

Only implementations for KelvinVectorSize 4 and 6, and dynamic size vectors are provided.

References MathLib::v.

kelvinVectorToTensor() [1/4]

template<>

Eigen::Matrix< double, 3, 3 > MathLib::KelvinVector::kelvinVectorToTensor

(

Eigen::Matrix< double, 4, 1, Eigen::ColMajor, 4, 1 > const &

v

)

Definition at line 57 of file KelvinVector.cpp.

{
    Eigen::Matrix<double, 3, 3> m;
    m << v[0], v[3] / std::sqrt(2.), 0, v[3] / std::sqrt(2.), v[1], 0, 0, 0,
        v[2];
    return m;
}

References MathLib::v.

Referenced by ProcessLib::HMPhaseField::HMPhaseFieldLocalAssembler< ShapeFunction, DisplacementDim >::approximateFractureWidth(), ProcessLib::LargeDeformation::LargeDeformationLocalAssembler< ShapeFunction, DisplacementDim >::assembleWithJacobian(), MaterialLib::Solids::Phasefield::calculateIsotropicDegradedStressWithRankineEnergy(), MaterialLib::Solids::Phasefield::calculateOrthoMasonryDegradedStress(), MaterialLib::Solids::Phasefield::calculateSpectralDegradedStress(), ProcessLib::HydroMechanics::HydroMechanicsLocalAssembler< ShapeFunctionDisplacement, ShapeFunctionPressure, DisplacementDim >::computeSecondaryVariableConcrete(), ProcessLib::SmallDeformation::SmallDeformationLocalAssemblerInterface< DisplacementDim >::computeSecondaryVariableConcrete(), MaterialPropertyLib::EmbeddedFracturePermeability< DisplacementDim >::dValue(), MaterialPropertyLib::OrthotropicEmbeddedFracturePermeability< DisplacementDim >::dValue(), kelvinVectorToTensor(), MaterialPropertyLib::EmbeddedFracturePermeability< DisplacementDim >::value(), and MaterialPropertyLib::OrthotropicEmbeddedFracturePermeability< DisplacementDim >::value().

kelvinVectorToTensor() [2/4]

template<>

Eigen::Matrix< double, 3, 3 > MathLib::KelvinVector::kelvinVectorToTensor

(

Eigen::Matrix< double, 6, 1, Eigen::ColMajor, 6, 1 > const &

v

)

Definition at line 67 of file KelvinVector.cpp.

{
    Eigen::Matrix<double, 3, 3> m;
    m << v[0], v[3] / std::sqrt(2.), v[5] / std::sqrt(2.), v[3] / std::sqrt(2.),
        v[1], v[4] / std::sqrt(2.), v[5] / std::sqrt(2.), v[4] / std::sqrt(2.),
        v[2];
    return m;
}

References MathLib::v.

kelvinVectorToTensor() [3/4]

template<>

Eigen::Matrix< double, 3, 3 > MathLib::KelvinVector::kelvinVectorToTensor

(

Eigen::Matrix< double, Eigen::Dynamic, 1, Eigen::ColMajor, Eigen::Dynamic, 1 > const &

v

)

Definition at line 78 of file KelvinVector.cpp.

{
    if (v.size() == 4)
    {
        Eigen::Matrix<double, 4, 1, Eigen::ColMajor, 4, 1> v4;
        v4 << v[0], v[1], v[2], v[3];
        return kelvinVectorToTensor(v4);
    }
    if (v.size() == 6)
    {
        Eigen::Matrix<double, 6, 1, Eigen::ColMajor, 6, 1> v6;
        v6 << v[0], v[1], v[2], v[3], v[4], v[5];
        return kelvinVectorToTensor(v6);
    }
    OGS_FATAL(
        "Conversion of dynamic Kelvin vector of size {:d} to a tensor is not "
        "possible. Kelvin vector must be of size 4 or 6.",
        v.size());
}

References kelvinVectorToTensor(), OGS_FATAL, and MathLib::v.

kelvinVectorToTensor() [4/4]

template<int KelvinVectorSize>

Eigen::Matrix< double, 3, 3 > MathLib::KelvinVector::kelvinVectorToTensor

(

Eigen::Matrix< double, KelvinVectorSize, 1, Eigen::ColMajor, KelvinVectorSize, 1 > const &

v

)

Conversion of a Kelvin vector to a 3x3 matrix Only implementations for KelvinVectorSize 4 and 6 are provided.

References MathLib::v.

KMnan()

template<int DisplacementDim>

auto MathLib::KelvinVector::KMnan ( )

constexpr

Returns an expressions for a Kelvin matrix filled with NaN.

Definition at line 77 of file KelvinVector.h.

{
    return KelvinMatrixType<DisplacementDim>::Constant(
        std::numeric_limits<double>::quiet_NaN());
}

KMzero()

template<int DisplacementDim>

auto MathLib::KelvinVector::KMzero ( )

constexpr

Returns an expressions for a Kelvin matrix filled with zero.

Definition at line 62 of file KelvinVector.h.

{
    return KelvinMatrixType<DisplacementDim>::Zero();
}

KVnan()

template<int DisplacementDim>

auto MathLib::KelvinVector::KVnan ( )

constexpr

Returns an expressions for a Kelvin vector filled with NaN.

Definition at line 69 of file KelvinVector.h.

{
    return KelvinVectorType<DisplacementDim>::Constant(
        std::numeric_limits<double>::quiet_NaN());
}

KVzero()

template<int DisplacementDim>

auto MathLib::KelvinVector::KVzero ( )

constexpr

Returns an expressions for a Kelvin vector filled with zero.

Definition at line 55 of file KelvinVector.h.

{
    return KelvinVectorType<DisplacementDim>::Zero();
}

liftVectorToKelvin()

template<int DisplacementDim>

Eigen::Matrix< double, DisplacementDim, kelvin_vector_dimensions(DisplacementDim)> MathLib::KelvinVector::liftVectorToKelvin

(

Eigen::Matrix< double, DisplacementDim, 1 > const &

v

)

Lifting of a vector to a Kelvin matrix. \( a -> A\) s.t. \(k_{ij} a_{j} = A_[\alpha\beta} k_{\beta} \). Conversion for 2D -> 4D and 3D -> 6D are implemented.

References MathLib::v.

Referenced by ProcessLib::HydroMechanics::HydroMechanicsLocalAssembler< ShapeFunctionDisplacement, ShapeFunctionPressure, DisplacementDim >::assembleWithJacobian().

liftVectorToKelvin< 2 >()

template<>

Eigen::Matrix< double, 2, 4 > MathLib::KelvinVector::liftVectorToKelvin< 2 >

(

Eigen::Matrix< double, 2, 1 > const &

v

)

Definition at line 155 of file KelvinVector.cpp.

{
    Eigen::Matrix<double, 2, 4> m;
    m << v[0], 0, 0, v[1] / std::sqrt(2.), 0, v[1], 0, v[0] / std::sqrt(2.);
    return m;
}

liftVectorToKelvin< 3 >()

template<>

Eigen::Matrix< double, 3, 6 > MathLib::KelvinVector::liftVectorToKelvin< 3 >

(

Eigen::Matrix< double, 3, 1 > const &

v

)

Definition at line 155 of file KelvinVector.cpp.

{
    Eigen::Matrix<double, 3, 6> m;
    m << v[0], 0, 0, v[1] / std::sqrt(2.), 0, v[2] / std::sqrt(2.), 0, v[1], 0,
        v[0] / std::sqrt(2.), v[2] / std::sqrt(2.), 0, 0, 0, v[2], 0,
        v[1] / std::sqrt(2.), v[0] / std::sqrt(2.);
    return m;
}

reduceKelvinToVector()

template<int DisplacementDim>

Eigen::Matrix< double, DisplacementDim, 1 > MathLib::KelvinVector::reduceKelvinToVector

(

Eigen::Matrix< double, DisplacementDim, kelvin_vector_dimensions(DisplacementDim)> const &

m

)

Reducing a Kelvin matrix to a vector. Conversion for 4D -> 2D and 6D -> 3D are implemented.

reduceKelvinToVector< 2 >()

template<>

Eigen::Matrix< double, 2, 1 > MathLib::KelvinVector::reduceKelvinToVector< 2 >

(

Eigen::Matrix< double, 2, 4 > const &

m

)

Definition at line 155 of file KelvinVector.cpp.

{
    assert(m(0, 1) == 0);
    assert(m(0, 2) == 0);
    assert(m(1, 0) == 0);
    assert(m(1, 2) == 0);
    Eigen::Matrix<double, 2, 1> v;
    v << m(0, 0), m(1, 1);
    return v;
}

reduceKelvinToVector< 3 >()

template<>

Eigen::Matrix< double, 3, 1 > MathLib::KelvinVector::reduceKelvinToVector< 3 >

(

Eigen::Matrix< double, 3, 6 > const &

m

)

Definition at line 155 of file KelvinVector.cpp.

{
    assert(m(0, 1) == 0);
    assert(m(0, 2) == 0);
    assert(m(0, 4) == 0);
    assert(m(1, 0) == 0);
    assert(m(1, 2) == 0);
    assert(m(1, 5) == 0);
    assert(m(2, 0) == 0);
    assert(m(2, 1) == 0);
    assert(m(2, 3) == 0);
    assert(std::abs(m(0, 3) - m(2, 4)) <
           std::numeric_limits<double>::epsilon());
    assert(std::abs(m(0, 5) - m(1, 4)) <
           std::numeric_limits<double>::epsilon());
    assert(std::abs(m(1, 3) - m(2, 5)) <
           std::numeric_limits<double>::epsilon());
    Eigen::Matrix<double, 3, 1> v;
    v << m(0, 0), m(1, 1), m(2, 2);
    return v;
}

symmetricTensorToKelvinVector() [1/2]

template<typename Derived>

Eigen::Matrix< double, Eigen::MatrixBase< Derived >::RowsAtCompileTime, 1 > MathLib::KelvinVector::symmetricTensorToKelvinVector

(

Eigen::MatrixBase< Derived > const &

v

)

Conversion of a short vector representation of a symmetric 3x3 matrix to a Kelvin vector.

This is opposite of the kelvinVectorToSymmetricTensor()

Only implementations for KelvinVectorSize 4 and 6, and dynamic size vectors are provided.

Definition at line 199 of file KelvinVector.h.

{
    static_assert(
        (Eigen::MatrixBase<Derived>::ColsAtCompileTime == 1) ||
            (Eigen::MatrixBase<Derived>::ColsAtCompileTime == Eigen::Dynamic),
        "KelvinVector must be a column vector");
    if (v.cols() != 1)
    {
        OGS_FATAL(
            "KelvinVector must be a column vector, but input has {:d} columns.",
            v.cols());
    }
 
    Eigen::Matrix<double, Eigen::MatrixBase<Derived>::RowsAtCompileTime, 1>
        result;
    if (v.rows() == 4)
    {
        result.resize(4, 1);
        result << v[0], v[1], v[2], v[3] * std::sqrt(2.);
    }
    else if (v.rows() == 6)
    {
        result.resize(6, 1);
        result << v[0], v[1], v[2], v[3] * std::sqrt(2.), v[4] * std::sqrt(2.),
            v[5] * std::sqrt(2.);
    }
    else
    {
        OGS_FATAL(
            "Symmetric tensor to Kelvin vector conversion expected an input "
            "vector of size 4 or 6, but a vector of size {:d} was given.",
            v.size());
    }
    return result;
}

References OGS_FATAL, and MathLib::v.

Referenced by ProcessLib::HydroMechanics::HydroMechanicsLocalAssembler< ShapeFunctionDisplacement, ShapeFunctionPressure, DisplacementDim >::initializeConcrete(), ProcessLib::LargeDeformation::LargeDeformationLocalAssembler< ShapeFunction, DisplacementDim >::initializeConcrete(), ProcessLib::PhaseField::PhaseFieldLocalAssembler< ShapeFunction, DisplacementDim >::initializeConcrete(), ProcessLib::RichardsMechanics::RichardsMechanicsLocalAssembler< ShapeFunctionDisplacement, ShapeFunctionPressure, DisplacementDim >::initializeConcrete(), ProcessLib::SmallDeformation::SmallDeformationLocalAssembler< ShapeFunction, DisplacementDim >::initializeConcrete(), ProcessLib::TH2M::TH2MLocalAssembler< ShapeFunctionDisplacement, ShapeFunctionPressure, DisplacementDim >::initializeConcrete(), ProcessLib::ThermoHydroMechanics::ThermoHydroMechanicsLocalAssembler< ShapeFunctionDisplacement, ShapeFunctionPressure, DisplacementDim >::initializeConcrete(), ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssembler< ShapeFunction, DisplacementDim >::initializeConcrete(), ProcessLib::ThermoRichardsMechanics::ThermoRichardsMechanicsLocalAssembler< ShapeFunctionDisplacement, ShapeFunction, DisplacementDim, ConstitutiveTraits >::initializeConcrete(), ProcessLib::setIntegrationPointKelvinVectorData(), ProcessLib::Reflection::detail::setIPData(), and symmetricTensorToKelvinVector().

symmetricTensorToKelvinVector() [2/2]

template<int DisplacementDim>

KelvinVectorType< DisplacementDim > MathLib::KelvinVector::symmetricTensorToKelvinVector

(

std::vector< double > const &

values

)

Conversion of a short vector representation of a symmetric 3x3 matrix to a Kelvin vector.

This overload takes a std::vector for the tensor values.

Definition at line 240 of file KelvinVector.h.

{
    constexpr int kelvin_vector_size =
        kelvin_vector_dimensions(DisplacementDim);
 
    if (values.size() != kelvin_vector_size)
    {
        OGS_FATAL(
            "Symmetric tensor to Kelvin vector conversion expected an input "
            "vector of size {:d}, but a vector of size {:d} was given.",
            kelvin_vector_size, values.size());
    }
 
    return symmetricTensorToKelvinVector(
        Eigen::Map<typename MathLib::KelvinVector::KelvinVectorType<
            DisplacementDim> const>(
            values.data(), kelvin_vector_dimensions(DisplacementDim), 1));
}

References kelvin_vector_dimensions(), OGS_FATAL, and symmetricTensorToKelvinVector().

tensorToKelvin()

template<int DisplacementDim>

KelvinVectorType< DisplacementDim > MathLib::KelvinVector::tensorToKelvin

(

Eigen::Matrix< double, 3, 3 > const &

m

)

Conversion of a 3x3 matrix to a Kelvin vector. Only implementations for KelvinVectorSize 4 and 6 are provided.

Referenced by ProcessLib::RichardsMechanics::RichardsMechanicsLocalAssembler< ShapeFunctionDisplacement, ShapeFunctionPressure, DisplacementDim >::assemble(), ProcessLib::RichardsMechanics::RichardsMechanicsLocalAssembler< ShapeFunctionDisplacement, ShapeFunctionPressure, DisplacementDim >::assembleWithJacobian(), MaterialLib::Solids::Phasefield::calculateOrthoMasonryDegradedStress(), MaterialLib::Solids::Phasefield::calculateSpectralDegradedStress(), ProcessLib::RichardsMechanics::computeMicroPorosity(), ProcessLib::HydroMechanics::HydroMechanicsLocalAssembler< ShapeFunctionDisplacement, ShapeFunctionPressure, DisplacementDim >::computeSecondaryVariableConcrete(), ProcessLib::SmallDeformation::SmallDeformationLocalAssemblerInterface< DisplacementDim >::computeSecondaryVariableConcrete(), MaterialPropertyLib::EmbeddedFracturePermeability< DisplacementDim >::dValue(), MaterialPropertyLib::OrthotropicEmbeddedFracturePermeability< DisplacementDim >::dValue(), ProcessLib::TH2M::ConstitutiveRelations::SwellingModel< DisplacementDim >::eval(), ProcessLib::ThermoRichardsMechanics::ConstitutiveStress_StrainTemperature::SwellingModel< DisplacementDim >::eval(), MaterialPropertyLib::FormKelvinVector< GlobalDim >::operator()(), and ProcessLib::RichardsMechanics::updateSwellingStressAndVolumetricStrain().

tensorToKelvin< 2 >()

template<>

KelvinVectorType< 2 > MathLib::KelvinVector::tensorToKelvin< 2 >

(

Eigen::Matrix< double, 3, 3 > const &

m

)

Definition at line 78 of file KelvinVector.cpp.

{
    assert(std::abs(m(0, 1) - m(1, 0)) <
           std::numeric_limits<double>::epsilon());
    assert(m(0, 2) == 0);
    assert(m(1, 2) == 0);
    assert(m(2, 0) == 0);
    assert(m(2, 1) == 0);
 
    KelvinVectorType<2> v;
    v << m(0, 0), m(1, 1), m(2, 2), m(0, 1) * std::sqrt(2.);
    return v;
}

tensorToKelvin< 3 >()

template<>

KelvinVectorType< 3 > MathLib::KelvinVector::tensorToKelvin< 3 >

(

Eigen::Matrix< double, 3, 3 > const &

m

)

Definition at line 78 of file KelvinVector.cpp.

{
    assert(std::abs(m(0, 1) - m(1, 0)) <
           std::numeric_limits<double>::epsilon());
    assert(std::abs(m(1, 2) - m(2, 1)) <
           std::numeric_limits<double>::epsilon());
    assert(std::abs(m(0, 2) - m(2, 0)) <
           std::numeric_limits<double>::epsilon());
 
    KelvinVectorType<3> v;
    v << m(0, 0), m(1, 1), m(2, 2), m(0, 1) * std::sqrt(2.),
        m(1, 2) * std::sqrt(2.), m(0, 2) * std::sqrt(2.);
    return v;
}

Variable Documentation

Invariants< KelvinVectorSize >::deviatoric_projection

template<int KelvinVectorSize>

const Eigen::Matrix<double, KelvinVectorSize, KelvinVectorSize> MathLib::KelvinVector::Invariants< KelvinVectorSize >::deviatoric_projection

Initial value:

=
        KelvinVector_detail::initDeviatoricProjection<KelvinVectorSize>()

Definition at line 115 of file KelvinVector-impl.h.

Invariants< KelvinVectorSize >::identity2

template<int KelvinVectorSize>

const Eigen::Matrix<double, KelvinVectorSize, 1> MathLib::KelvinVector::Invariants< KelvinVectorSize >::identity2

Initial value:

=
        KelvinVector_detail::initIdentity2<KelvinVectorSize>()

Definition at line 125 of file KelvinVector-impl.h.

Referenced by MaterialLib::Solids::MFront::MFrontGeneric< DisplacementDim, boost::mp11::mp_list< Strain >, boost::mp11::mp_list< Stress >, boost::mp11::mp_list< Temperature > >::getBulkModulus().

Invariants< KelvinVectorSize >::ones2

template<int KelvinVectorSize>

const Eigen::Matrix<double, KelvinVectorSize, 1> MathLib::KelvinVector::Invariants< KelvinVectorSize >::ones2

Initial value:

=
        KelvinVector_detail::initOnes2<KelvinVectorSize>()

Definition at line 130 of file KelvinVector-impl.h.

Invariants< KelvinVectorSize >::spherical_projection

template<int KelvinVectorSize>

Eigen::Matrix<double, KelvinVectorSize, KelvinVectorSize> const MathLib::KelvinVector::Invariants< KelvinVectorSize >::spherical_projection

Initial value:

=
        KelvinVector_detail::initSphericalProjection<KelvinVectorSize>()

Definition at line 120 of file KelvinVector-impl.h.