Marmot::ContinuumMechanics::VoigtNotation::Derivatives Namespace Reference

Functions
Vector6d	dStressMean_dStress ()
template<typename T >
Eigen::Matrix< T, 6, 1 >	dRho_dStress (T rho, const Eigen::Matrix< T, 6, 1 > &stress)
Marmot::Vector6d	dTheta_dStress (double theta, const Marmot::Vector6d &stress)
double	dTheta_dJ2 (const Marmot::Vector6d &stress)
double	dTheta_dJ3 (const Marmot::Vector6d &stress)
double	dThetaStrain_dJ2Strain (const Marmot::Vector6d &strain)
double	dThetaStrain_dJ3Strain (const Marmot::Vector6d &strain)
Marmot::Vector6d	dJ2_dStress (const Marmot::Vector6d &stress)
Marmot::Vector6d	dJ3_dStress (const Marmot::Vector6d &stress)
Marmot::Vector6d	dJ2Strain_dStrain (const Marmot::Vector6d &strain)
Marmot::Vector6d	dJ3Strain_dStrain (const Marmot::Vector6d &strain)
Marmot::Vector6d	dThetaStrain_dStrain (const Marmot::Vector6d &strain)
Marmot::Matrix36	dStressPrincipals_dStress (const Marmot::Vector6d &stress)
Eigen::Vector3d	dStrainVolumetricNegative_dStrainPrincipal (const Marmot::Vector6d &strain)
Matrix6d	dEp_dE (const Matrix6d &CelInv, const Matrix6d &Cep)
RowVector6d	dDeltaEpv_dE (const Matrix6d &CelInv, const Matrix6d &Cep)
Marmot::Matrix36	dSortedStrainPrincipal_dStrain (const Marmot::Vector6d &dEp)
RowVector6d	dDeltaEpvneg_dE (const Marmot::Vector6d &dEp, const Matrix6d &CelInv, const Matrix6d &Cep)

Function Documentation

dStressMean_dStress()

Vector6d Marmot::ContinuumMechanics::VoigtNotation::Derivatives::dStressMean_dStress

(

)

Computes the derivative \( \frac{d\, \sigma_m}{d\, \boldsymbol{\sigma}} \) of the mean stress \( \sigma_m \) with respect to the voigt notated stress vector \( \boldsymbol{\sigma} \)

dRho_dStress()

template<typename T >

Eigen::Matrix< T, 6, 1 > Marmot::ContinuumMechanics::VoigtNotation::Derivatives::dRho_dStress	(	T	rho,
		const Eigen::Matrix< T, 6, 1 > &	stress
	)

Computes the derivative \( \frac{d\, \rho}{d\, \boldsymbol{\sigma}}\) of the haigh westergaard coordinate \( \rho \) with respect to the voigt notated stress vector \( \boldsymbol{\sigma} \)

dTheta_dStress()

Vector6d Marmot::ContinuumMechanics::VoigtNotation::Derivatives::dTheta_dStress	(	double	theta,
		const Marmot::Vector6d &	stress
	)

Computes the derivative \( \frac{d\, \theta}{d\, \boldsymbol{\sigma}}\) of the haigh westergaard coordinate \( \theta \) with respect to the voigt notated stress vector \( \boldsymbol{\sigma} \)

dTheta_dJ2()

double Marmot::ContinuumMechanics::VoigtNotation::Derivatives::dTheta_dJ2

(

const Marmot::Vector6d &

stress

)

Computes the derivative \( \frac{d\, \theta}{d\, J_2}\) of the haigh westergaard coordinate \( \theta \) with respect to the second deviatoric invariant \( J_2 \)

dTheta_dJ3()

double Marmot::ContinuumMechanics::VoigtNotation::Derivatives::dTheta_dJ3

(

const Marmot::Vector6d &

stress

)

Computes the derivative \( \frac{d\, \theta}{d\, J_3}\) of the haigh westergaard coordinate \( \theta \) with respect to the third deviatoric invariant \( J_3 \)

dThetaStrain_dJ2Strain()

double Marmot::ContinuumMechanics::VoigtNotation::Derivatives::dThetaStrain_dJ2Strain

(

const Marmot::Vector6d &

strain

)

Computes the derivative \( \frac{d\, \theta^{(\varepsilon)}}{d\, J^{(\varepsilon)}_2}\) of the haigh westergaard coordinate \( \theta^{(\varepsilon)} \) with respect to the second deviatoric invariant \( J^{(\varepsilon)}_2 \).

dThetaStrain_dJ3Strain()

double Marmot::ContinuumMechanics::VoigtNotation::Derivatives::dThetaStrain_dJ3Strain

(

const Marmot::Vector6d &

strain

)

Computes the derivative \( \frac{d\, \theta^{(\varepsilon)}}{d\, J^{(\varepsilon)}_3}\) of the haigh westergaard coordinate \( \theta^{(\varepsilon)} \) with respect to the third deviatoric invariant \( J^{(\varepsilon)}_3 \).

dJ2_dStress()

Vector6d Marmot::ContinuumMechanics::VoigtNotation::Derivatives::dJ2_dStress

(

const Marmot::Vector6d &

stress

)

Computes the derivative \( \frac{d\, J_2}{d\, \boldsymbol{\sigma}}\) of the second deviatoric invariant \( J_2 \) with respect to the voigt notated stress vector \( \boldsymbol{\sigma} \).

dJ3_dStress()

Vector6d Marmot::ContinuumMechanics::VoigtNotation::Derivatives::dJ3_dStress

(

const Marmot::Vector6d &

stress

)

Computes the derivative \( \frac{d\, J_3}{d\, \boldsymbol{\sigma}}\) of the third deviatoric invariant \( J_3 \) with respect to the voigt notated stress vector \( \boldsymbol{\sigma} \).

dJ2Strain_dStrain()

Vector6d Marmot::ContinuumMechanics::VoigtNotation::Derivatives::dJ2Strain_dStrain

(

const Marmot::Vector6d &

strain

)

Computes the derivative \( \frac{d\, J^{(\varepsilon)}_2}{d\, \boldsymbol{\sigma}}\) of the second deviatoric invariant \( J^{(\varepsilon)}_2 \) with respect to the voigt notated strain vector \( \boldsymbol{\varepsilon} \).

dJ3Strain_dStrain()

Vector6d Marmot::ContinuumMechanics::VoigtNotation::Derivatives::dJ3Strain_dStrain

(

const Marmot::Vector6d &

strain

)

Computes the derivative \( \frac{d\, J^{(\varepsilon)}_3}{d\, \boldsymbol{\sigma}}\) of the third deviatoric invariant \( J^{(\varepsilon)}_3 \) with respect to the voigt notated strain vector \( \boldsymbol{\varepsilon} \).

dThetaStrain_dStrain()

Vector6d Marmot::ContinuumMechanics::VoigtNotation::Derivatives::dThetaStrain_dStrain

(

const Marmot::Vector6d &

strain

)

Computes the derivative \( \frac{d\, \theta^{(\varepsilon)}}{d\, \boldsymbol{\varepsilon}}\) of the haigh westergaard coordinate \( \theta^{(\varepsilon)} \) with respect to the voigt notated strain vector \( \boldsymbol{\varepsilon} \)

dStressPrincipals_dStress()

Matrix36 Marmot::ContinuumMechanics::VoigtNotation::Derivatives::dStressPrincipals_dStress

(

const Marmot::Vector6d &

stress

)

Computes the derivative \( \frac{d\, \sigma_I}{d\, \boldsymbol{\sigma}}\) of the principal stresses \( \sigma_I \) with respect to the voigt notated stress vector \( \boldsymbol{\sigma} \)

dStrainVolumetricNegative_dStrainPrincipal()

Vector3d Marmot::ContinuumMechanics::VoigtNotation::Derivatives::dStrainVolumetricNegative_dStrainPrincipal

(

const Marmot::Vector6d &

strain

)

Computes the derivative \( \frac{d\, \varepsilon^{vol}_{\ominus}}{d\, \varepsilon_I}\) of the volumetric strains in compression \( \varepsilon^{vol}_{\ominus} \) with respect to the principal strains \( \varepsilon_I \)

dEp_dE()

Matrix6d Marmot::ContinuumMechanics::VoigtNotation::Derivatives::dEp_dE	(	const Matrix6d &	CelInv,
		const Matrix6d &	Cep
	)

Computes the derivative \( \frac{d\, \boldsymbol{\varepsilon}^{p}}{d\, \boldsymbol{\varepsilon}}\) of the voigt notated plastic strain vector \( \boldsymbol{\varepsilon}^{p} \) with respect to the voigt notated strain vector \( \boldsymbol{\varepsilon} \)

\[ \displaystyle \frac{d\, \boldsymbol{\varepsilon}^{p}}{d\, \boldsymbol{\varepsilon}} = \boldsymbol{I} - \mathbb{C}^{-1}\,\mathbb{C}^{(ep)} \]

using the elastic compliance tensor \( \mathbb{C}^{-1} \) and the elastoplastic stiffness tensor \( \mathbb{C}^{(ep)} \)

dDeltaEpv_dE()

RowVector6d Marmot::ContinuumMechanics::VoigtNotation::Derivatives::dDeltaEpv_dE	(	const Matrix6d &	CelInv,
		const Matrix6d &	Cep
	)

Computes the derivative \( \frac{d\, \Delta\, \varepsilon^{p, vol}}{d\, \boldsymbol{\varepsilon}}\) of the volumetric plastic strain increment \( \Delta\, \varepsilon^{p, vol}\) with respect to the voigt notated strain vector \( \boldsymbol{\varepsilon} \)

dSortedStrainPrincipal_dStrain()

Matrix36 Marmot::ContinuumMechanics::VoigtNotation::Derivatives::dSortedStrainPrincipal_dStrain

(

const Marmot::Vector6d &

dEp

)

Computes the derivative \( \frac{d\, \varepsilon_I}{d\, \boldsymbol{\varepsilon}}\) of the principal strains \( \varepsilon_I \) with respect to the voigt notated strain vector \( \boldsymbol{\varepsilon} \)

dDeltaEpvneg_dE()

RowVector6d Marmot::ContinuumMechanics::VoigtNotation::Derivatives::dDeltaEpvneg_dE	(	const Marmot::Vector6d &	dEp,
		const Matrix6d &	CelInv,
		const Matrix6d &	Cep
	)

Computes the derivative \( \frac{d\, \Delta\, \varepsilon^{p, vol}_{\ominus}}{d\, \boldsymbol{\varepsilon}}\) of the volumetric plastic strain increment in compression \( \Delta\, \varepsilon^{p, vol}_{\ominus}\) with respect to the voigt notated strain vector \( \boldsymbol{\varepsilon} \)