Marmot::ContinuumMechanics::VoigtNotation Namespace Reference

Namespaces
	Derivatives
	Invariants
	Transformations

Enumerations
enum	VoigtSize { OneD = 1, TwoD = 3, ThreeD = 6, Axial = 4 }

Functions
constexpr VoigtSize	voigtSizeFromDimension (int x)
Eigen::Vector3d	voigtToPlaneVoigt (const Marmot::Vector6d &voigt)
Marmot::Vector6d	planeVoigtToVoigt (const Eigen::Vector3d &voigtPlane)
template<enum VoigtSize voigtSize>
Eigen::Matrix< double, voigtSize, 1 >	reduce3DVoigt (const Marmot::Vector6d &Voigt3D)
template<enum VoigtSize voigtSize>
Marmot::Vector6d	make3DVoigt (const Eigen::Matrix< double, voigtSize, 1 > &Voigt)
template<typename T >
Eigen::Matrix< T, 3, 3 >	voigtToStrain (const Eigen::Matrix< T, 6, 1 > &voigt)
template<typename T >
Eigen::Matrix< T, 3, 3 >	voigtToStress (const Eigen::Matrix< T, 6, 1 > &voigt)
Marmot::Vector6d	strainToVoigt (const Eigen::Matrix3d &strainTensor)
template<typename T = double>
Eigen::Matrix< T, 6, 1 >	stressToVoigt (const Eigen::Matrix< T, 3, 3 > &stressTensor)
template<int nDim>
Eigen::Matrix< double, nDim, nDim >	stressMatrixFromVoigt (const Eigen::Matrix< double, VOIGTFROMDIM(nDim), 1 > &Voigt)
template<int nDim>
Eigen::Matrix< double, VOIGTFROMDIM(nDim), 1 >	voigtFromStrainMatrix (const Eigen::Matrix< double, nDim, nDim > &strain)
Vector6d	strainToVoigt (const Matrix3d &strainTensor)
Vector6d	planeVoigtToVoigt (const Vector3d &voigtPlane)

Variables
const Marmot::Vector6d	P = ( Vector6d() << 1, 1, 1, 2, 2, 2 ).finished()
const Marmot::Vector6d	PInv = ( Vector6d() << 1, 1, 1, .5, .5, .5 ).finished()
const Marmot::Vector6d	I = ( Vector6d() << 1, 1, 1, 0, 0, 0 ).finished()
const Marmot::Vector6d	IHyd = ( Vector6d() << 1. / 3, 1. / 3, 1. / 3, 0, 0, 0 ).finished()
const Matrix6d	IDev

Enumeration Type Documentation

VoigtSize

enum Marmot::ContinuumMechanics::VoigtNotation::VoigtSize

Enumerator
OneD
TwoD
ThreeD
Axial

Function Documentation

voigtSizeFromDimension()

constexpr VoigtSize Marmot::ContinuumMechanics::VoigtNotation::voigtSizeFromDimension ( int  x )

constexpr

voigtToPlaneVoigt()

Vector3d Marmot::ContinuumMechanics::VoigtNotation::voigtToPlaneVoigt

(

const Marmot::Vector6d &

voigt

)

Converts a 3D voigt notated vector to a plane stress vector.

\[ \displaystyle \begin{bmatrix} \sigma_{11}\\ \sigma_{22}\\ \sigma_{33} = 0\\ \sigma_{12}\\ \sigma_{13} = 0\\ \sigma_{23} = 0 \end{bmatrix} \hspace{.5cm} \Rightarrow \hspace{.5cm} \begin{bmatrix} \sigma_{11}\\ \sigma_{22}\\ \sigma_{12} \end{bmatrix} \]

planeVoigtToVoigt() [1/2]

Marmot::Vector6d Marmot::ContinuumMechanics::VoigtNotation::planeVoigtToVoigt

(

const Eigen::Vector3d &

voigtPlane

)

Converts a voigt notated plane stress vector to a 3D vector.

\[ \displaystyle \begin{bmatrix} \sigma_{11}\\ \sigma_{22}\\ \sigma_{12} \end{bmatrix} \hspace{.5cm} \Rightarrow \hspace{.5cm} \begin{bmatrix} \sigma_{11}\\ \sigma_{22}\\ 0\\ \sigma_{12}\\ 0\\ 0 \end{bmatrix} \]

reduce3DVoigt()

template<enum VoigtSize voigtSize>

Eigen::Matrix< double, voigtSize, 1 > Marmot::ContinuumMechanics::VoigtNotation::reduce3DVoigt

(

const Marmot::Vector6d &

Voigt3D

)

Reduces a 3D voigt notated vector to a lower dimension defined by the template parameter 'voigtSize'.

Considered cases:

• voigtSize \( = 1 \):

  \[ \displaystyle \begin{bmatrix} \sigma_{11}\\ \sigma_{22} = 0\\ \sigma_{33} = 0\\ \sigma_{12} = 0\\ \sigma_{13} = 0\\ \sigma_{23} = 0 \end{bmatrix} \hspace{.5cm} \Rightarrow \hspace{.5cm} \sigma_{11} \]

• voigtSize \( = 3 \): Calls function voigtToPlaneVoigt().
• voigtSize \( = 6 \): Returns the input vector

make3DVoigt()

template<enum VoigtSize voigtSize>

Marmot::Vector6d Marmot::ContinuumMechanics::VoigtNotation::make3DVoigt

(

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

Voigt

)

Computes a 3D voigt notated vector from a vector of lower dimension defined by the template parameter 'voigtSize'.

Considered cases:

• voigtSize \( = 1 \):

  \[ \displaystyle \sigma_{11} \hspace{.5cm} \Rightarrow \hspace{.5cm} \begin{bmatrix} \sigma_{11}\\ 0\\ 0\\ 0\\ 0\\ 0 \end{bmatrix} \]

• voigtSize \( = 3 \): Calls function planeVoigtToVoigt().
• voigtSize \( = 6 \): Returns the input vector

voigtToStrain()

template<typename T >

Eigen::Matrix< T, 3, 3 > Marmot::ContinuumMechanics::VoigtNotation::voigtToStrain

(

const Eigen::Matrix< T, 6, 1 > &

voigt

)

Converts a voigt notated strain vector to its corresponding strain tensor

\[ \displaystyle \begin{bmatrix} \varepsilon_{11}\\ \varepsilon_{22}\\ \varepsilon_{33}\\ \gamma_{12}\\ \gamma_{13}\\ \gamma_{23} \end{bmatrix} \hspace{.5cm} \Rightarrow \hspace{.5cm} \begin{bmatrix} \varepsilon_{11} & \gamma_{12}/2 & \gamma_{13}/2 \\ \gamma_{12}/2 & \varepsilon_{22} & \gamma_{23}/2 \\ \gamma_{13}/2 & \gamma_{23}/2 & \varepsilon_{33} \\ \end{bmatrix} \]

voigtToStress()

template<typename T >

Eigen::Matrix< T, 3, 3 > Marmot::ContinuumMechanics::VoigtNotation::voigtToStress

(

const Eigen::Matrix< T, 6, 1 > &

voigt

)

Converts a voigt notated stress vector to its corresponding stress tensor

\[ \displaystyle \begin{bmatrix} \sigma_{11}\\ \sigma_{22}\\ \sigma_{33}\\ \sigma_{12}\\ \sigma_{13}\\ \sigma_{23} \end{bmatrix} \hspace{.5cm} \Rightarrow \hspace{.5cm} \begin{bmatrix} \sigma_{11} & \sigma_{12} & \sigma_{13} \\ \sigma_{12} & \sigma_{22} & \sigma_{23} \\ \sigma_{13} & \sigma_{23} & \sigma_{33} \\ \end{bmatrix} \]

strainToVoigt() [1/2]

Marmot::Vector6d Marmot::ContinuumMechanics::VoigtNotation::strainToVoigt

(

const Eigen::Matrix3d &

strainTensor

)

Converts a strain tensor to its corresponding voigt notated strain vector

\[ \displaystyle \begin{bmatrix} \varepsilon_{11} & \varepsilon_{12} & \varepsilon_{13}\\ \varepsilon_{21} & \varepsilon_{22} & \varepsilon_{23} \\ \varepsilon_{31} & \varepsilon_{32} & \varepsilon_{33} \\ \end{bmatrix} \hspace{.5cm} \Rightarrow \hspace{.5cm} \begin{bmatrix} \varepsilon_{11}\\ \varepsilon_{22}\\ \varepsilon_{33}\\ 2\,\varepsilon_{12}\\ 2\,\varepsilon_{13}\\ 2\,\varepsilon_{23} \end{bmatrix} \]

stressToVoigt()

template<typename T = double>

Eigen::Matrix< T, 6, 1 > Marmot::ContinuumMechanics::VoigtNotation::stressToVoigt

(

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

stressTensor

)

Converts a stress tensor to its corresponding voigt notated stress vector

\[ \displaystyle \begin{bmatrix} \sigma_{11} & \sigma_{12} & \sigma_{13}\\ \sigma_{21} & \sigma_{22} & \sigma_{23} \\ \sigma_{31} & \sigma_{32} & \sigma_{33} \\ \end{bmatrix} \hspace{.5cm} \Rightarrow \hspace{.5cm} \begin{bmatrix} \sigma_{11}\\ \sigma_{22}\\ \sigma_{33}\\ \sigma_{12}\\ \sigma_{13}\\ \sigma_{23} \end{bmatrix} \]

stressMatrixFromVoigt()

template<int nDim>

Eigen::Matrix< double, nDim, nDim > Marmot::ContinuumMechanics::VoigtNotation::stressMatrixFromVoigt

(

const Eigen::Matrix< double, VOIGTFROMDIM(nDim), 1 > &

Voigt

)

voigtFromStrainMatrix()

template<int nDim>

Eigen::Matrix< double, VOIGTFROMDIM( nDim ), 1 > Marmot::ContinuumMechanics::VoigtNotation::voigtFromStrainMatrix

(

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

strain

)

strainToVoigt() [2/2]

Vector6d Marmot::ContinuumMechanics::VoigtNotation::strainToVoigt

(

const Matrix3d &

strainTensor

)

planeVoigtToVoigt() [2/2]

Vector6d Marmot::ContinuumMechanics::VoigtNotation::planeVoigtToVoigt

(

const Vector3d &

voigtPlane

)

Variable Documentation

P

const Vector6d Marmot::ContinuumMechanics::VoigtNotation::P = ( Vector6d() << 1, 1, 1, 2, 2, 2 ).finished()

PInv

const Vector6d Marmot::ContinuumMechanics::VoigtNotation::PInv = ( Vector6d() << 1, 1, 1, .5, .5, .5 ).finished()

I

const Vector6d Marmot::ContinuumMechanics::VoigtNotation::I = ( Vector6d() << 1, 1, 1, 0, 0, 0 ).finished()

IHyd

const Vector6d Marmot::ContinuumMechanics::VoigtNotation::IHyd = ( Vector6d() << 1. / 3, 1. / 3, 1. / 3, 0, 0, 0 ).finished()

IDev

const Matrix6d Marmot::ContinuumMechanics::VoigtNotation::IDev

Initial value:

= ( Matrix6d() <<
                              
        2./3,    -1./3,   -1./3,    0,  0,  0,
        -1./3,   2./3,    -1./3,    0,  0,  0,
        -1./3,   -1./3,   2./3,     0,  0,  0,
        0,          0,      0,      1,  0,  0,
        0,          0,      0,      0,  1,  0,
        0,          0,      0,      0,  0,  1).finished()